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Results (1-50 of 32081 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
60.5 $A_5$ $2^{2} \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ $5$ $C_1$ $A_5$ $A_5$ $C_1$ Simple
120.5 $\SL(2,5)$ $2^{3} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $9$ $C_2$ $A_5$ $\SL(2,5)$ $C_1$ Non-Solvable - 2
120.34 $S_5$ $2^{3} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $7$ $C_1$ $S_5$ $A_5$ $C_{2}$ Non-Solvable - 2
120.35 $C_2\times A_5$ $2^{3} \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ $10$ $C_2$ $A_5$ $A_5$ $C_{2}$ Non-Solvable - 2
168.42 $\GL(3,2)$ $2^{3} \cdot 3 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $6$ $C_1$ $\GL(3,2)$ $\GL(3,2)$ $C_1$ Simple
180.19 $\GL(2,4)$ $2^{2} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ $15$ $C_3$ $A_5$ $A_5$ $C_{3}$ Non-Solvable - 2
240.89 $C_2.S_5$ $2^{4} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $12$ $C_2$ $S_5$ $\SL(2,5)$ $C_{2}$ Non-Solvable - 3
240.90 $\SL(2,5):C_2$ $2^{4} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $12$ $C_2$ $S_5$ $\SL(2,5)$ $C_{2}$ Non-Solvable - 3
240.91 $A_5:C_4$ $2^{4} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $14$ $C_2$ $S_5$ $A_5$ $C_{4}$ Non-Solvable - 3
240.92 $C_4\times A_5$ $2^{4} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $20$ $C_4$ $A_5$ $A_5$ $C_{4}$ Non-Solvable - 3
240.93 $\SL(2,5):C_2$ $2^{4} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $18$ $C_4$ $A_5$ $\SL(2,5)$ $C_{2}$ Non-Solvable - 3
240.94 $C_2\times \SL(2,5)$ $2^{4} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $18$ $C_2^2$ $A_5$ $\SL(2,5)$ $C_{2}$ Non-Solvable - 3
240.189 $C_2\times S_5$ $2^{4} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $14$ $C_2$ $S_5$ $A_5$ $C_{2}^{2}$ Non-Solvable - 3
240.190 $C_2^2\times A_5$ $2^{4} \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ $20$ $C_2^2$ $A_5$ $A_5$ $C_{2}^{2}$ Non-Solvable - 3
300.22 $C_5\times A_5$ $2^{2} \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ $25$ $C_5$ $A_5$ $A_5$ $C_{5}$ Non-Solvable - 2
336.114 $\SL(2,7)$ $2^{4} \cdot 3 \cdot 7$ $2^{3} \cdot 3 \cdot 7$ $11$ $C_2$ $\GL(3,2)$ $\SL(2,7)$ $C_1$ Non-Solvable - 2
336.208 $\PGL(2,7)$ $2^{4} \cdot 3 \cdot 7$ $2^{3} \cdot 3 \cdot 7$ $9$ $C_1$ $\PGL(2,7)$ $\GL(3,2)$ $C_{2}$ Non-Solvable - 2
336.209 $C_2\times \GL(3,2)$ $2^{4} \cdot 3 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ $12$ $C_2$ $\GL(3,2)$ $\GL(3,2)$ $C_{2}$ Non-Solvable - 2
360.51 $C_3\times \SL(2,5)$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $27$ $C_6$ $A_5$ $\SL(2,5)$ $C_{3}$ Non-Solvable - 3
360.118 $A_6$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $7$ $C_1$ $A_6$ $A_6$ $C_1$ Simple
360.119 $C_3\times S_5$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $21$ $C_3$ $S_5$ $A_5$ $C_{6}$ Non-Solvable - 3
360.120 $C_3:S_5$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $12$ $C_1$ $C_3:S_5$ $\GL(2,4)$ $C_{2}$ Non-Solvable - 3
360.121 $S_3\times A_5$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ $15$ $C_1$ $S_3\times A_5$ $\GL(2,4)$ $C_{2}$ Non-Solvable - 3
360.122 $C_6\times A_5$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ $30$ $C_6$ $A_5$ $A_5$ $C_{6}$ Non-Solvable - 3
420.13 $C_7\times A_5$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ $2 \cdot 3 \cdot 5 \cdot 7$ $35$ $C_7$ $A_5$ $A_5$ $C_{7}$ Non-Solvable - 2
480.217 $A_5:C_8$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $28$ $C_4$ $S_5$ $A_5$ $C_{8}$ Non-Solvable - 4
480.218 $\GL(2,5)$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $24$ $C_4$ $S_5$ $\SL(2,5)$ $C_{4}$ Non-Solvable - 4
480.219 $\SL(2,5):C_4$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $24$ $C_2^2$ $S_5$ $\SL(2,5)$ $C_{4}$ Non-Solvable - 4
480.220 $C_8\times A_5$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $40$ $C_8$ $A_5$ $A_5$ $C_{8}$ Non-Solvable - 4
480.221 $C_8.A_5$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $36$ $C_8$ $A_5$ $\SL(2,5)$ $C_{4}$ Non-Solvable - 4
480.222 $C_4\times \SL(2,5)$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $36$ $C_2\times C_4$ $A_5$ $\SL(2,5)$ $C_{4}$ Non-Solvable - 4
480.943 $C_4\times S_5$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $28$ $C_4$ $S_5$ $A_5$ $C_{2} \times C_{4}$ Non-Solvable - 4
480.944 $C_4:S_5$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $19$ $C_2$ $C_2\times S_5$ $C_2\times A_5$ $C_{2}^{2}$ Non-Solvable - 4
480.945 $A_5:Q_8$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $19$ $C_2$ $C_2\times S_5$ $C_2\times A_5$ $C_{2}^{2}$ Non-Solvable - 4
480.946 $C_4.S_5$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $24$ $C_4$ $S_5$ $\SL(2,5)$ $C_{2}^{2}$ Non-Solvable - 4
480.947 $C_4.S_5$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $18$ $C_2$ $C_2\times S_5$ $\SL(2,5)$ $C_{2}^{2}$ Non-Solvable - 4
480.948 $C_4.S_5$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $18$ $C_2$ $C_2\times S_5$ $\SL(2,5)$ $C_{2}^{2}$ Non-Solvable - 4
480.949 $C_2^2.S_5$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $24$ $C_2^2$ $S_5$ $\SL(2,5)$ $C_{2}^{2}$ Non-Solvable - 4
480.950 $\SL(2,5):C_2^2$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $24$ $C_2^2$ $S_5$ $\SL(2,5)$ $C_{2}^{2}$ Non-Solvable - 4
480.951 $C_2^2:S_5$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $19$ $C_2$ $C_2\times S_5$ $C_2\times A_5$ $C_{2}^{2}$ Non-Solvable - 4
480.952 $C_2^2.S_5$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $28$ $C_2^2$ $S_5$ $A_5$ $C_{2} \times C_{4}$ Non-Solvable - 4
480.953 $C_2^2.S_5$ $2^{5} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $18$ $C_2$ $C_2\times S_5$ $\SL(2,5)$ $C_{2}^{2}$ Non-Solvable - 4
480.954 $C_2\times C_4\times A_5$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $40$ $C_2\times C_4$ $A_5$ $A_5$ $C_{2} \times C_{4}$ Non-Solvable - 4
480.955 $\SL(2,5):C_2^2$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $36$ $C_2\times C_4$ $A_5$ $\SL(2,5)$ $C_{2}^{2}$ Non-Solvable - 4
480.956 $D_4\times A_5$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $25$ $C_2$ $C_2^2\times A_5$ $C_2\times A_5$ $C_{2}^{2}$ Non-Solvable - 4
480.957 $D_4.A_5$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $24$ $C_2$ $C_2^2\times A_5$ $\SL(2,5)$ $C_{2}^{2}$ Non-Solvable - 4
480.958 $Q_8\times A_5$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $25$ $C_2$ $C_2^2\times A_5$ $C_2\times A_5$ $C_{2}^{2}$ Non-Solvable - 4
480.959 $\SL(2,5):C_2^2$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $24$ $C_2$ $C_2^2\times A_5$ $\SL(2,5)$ $C_{2}^{2}$ Non-Solvable - 4
480.960 $C_2^2\times \SL(2,5)$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $36$ $C_2^3$ $A_5$ $\SL(2,5)$ $C_{2}^{2}$ Non-Solvable - 4
480.1186 $C_2^2\times S_5$ $2^{5} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $28$ $C_2^2$ $S_5$ $A_5$ $C_{2}^{3}$ Non-Solvable - 4
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