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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
2.1 | $C_2$ | $2$ | $2$ | $2$ | $C_2$ | Cyclic |
3.1 | $C_3$ | $3$ | $3$ | $3$ | $C_3$ | Cyclic |
4.1 | $C_4$ | $2^{2}$ | $2^{2}$ | $4$ | $C_4$ | Cyclic |
4.2 | $C_2^2$ | $2^{2}$ | $2$ | $4$ | $C_2^2$ | Abelian - 2 |
5.1 | $C_5$ | $5$ | $5$ | $5$ | $C_5$ | Cyclic |
6.2 | $C_6$ | $2 \cdot 3$ | $2 \cdot 3$ | $6$ | $C_6$ | Cyclic |
7.1 | $C_7$ | $7$ | $7$ | $7$ | $C_7$ | Cyclic |
8.1 | $C_8$ | $2^{3}$ | $2^{3}$ | $8$ | $C_8$ | Cyclic |
8.2 | $C_2\times C_4$ | $2^{3}$ | $2^{2}$ | $8$ | $C_2\times C_4$ | Abelian - 2 |
8.5 | $C_2^3$ | $2^{3}$ | $2$ | $8$ | $C_2^3$ | Abelian - 3 |
9.1 | $C_9$ | $3^{2}$ | $3^{2}$ | $9$ | $C_9$ | Cyclic |
9.2 | $C_3^2$ | $3^{2}$ | $3$ | $9$ | $C_3^2$ | Abelian - 2 |
10.2 | $C_{10}$ | $2 \cdot 5$ | $2 \cdot 5$ | $10$ | $C_{10}$ | Cyclic |
11.1 | $C_{11}$ | $11$ | $11$ | $11$ | $C_{11}$ | Cyclic |
12.2 | $C_{12}$ | $2^{2} \cdot 3$ | $2^{2} \cdot 3$ | $12$ | $C_{12}$ | Cyclic |
12.5 | $C_2\times C_6$ | $2^{2} \cdot 3$ | $2 \cdot 3$ | $12$ | $C_2\times C_6$ | Abelian - 2 |
13.1 | $C_{13}$ | $13$ | $13$ | $13$ | $C_{13}$ | Cyclic |
14.2 | $C_{14}$ | $2 \cdot 7$ | $2 \cdot 7$ | $14$ | $C_{14}$ | Cyclic |
15.1 | $C_{15}$ | $3 \cdot 5$ | $3 \cdot 5$ | $15$ | $C_{15}$ | Cyclic |
16.1 | $C_{16}$ | $2^{4}$ | $2^{4}$ | $16$ | $C_{16}$ | Cyclic |
16.2 | $C_4^2$ | $2^{4}$ | $2^{2}$ | $16$ | $C_4^2$ | Abelian - 2 |
16.5 | $C_2\times C_8$ | $2^{4}$ | $2^{3}$ | $16$ | $C_2\times C_8$ | Abelian - 2 |
16.10 | $C_2^2\times C_4$ | $2^{4}$ | $2^{2}$ | $16$ | $C_2^2\times C_4$ | Abelian - 3 |
16.14 | $C_2^4$ | $2^{4}$ | $2$ | $16$ | $C_2^4$ | Abelian - 4 |
17.1 | $C_{17}$ | $17$ | $17$ | $17$ | $C_{17}$ | Cyclic |
18.2 | $C_{18}$ | $2 \cdot 3^{2}$ | $2 \cdot 3^{2}$ | $18$ | $C_{18}$ | Cyclic |
18.5 | $C_3\times C_6$ | $2 \cdot 3^{2}$ | $2 \cdot 3$ | $18$ | $C_3\times C_6$ | Abelian - 2 |
19.1 | $C_{19}$ | $19$ | $19$ | $19$ | $C_{19}$ | Cyclic |
20.2 | $C_{20}$ | $2^{2} \cdot 5$ | $2^{2} \cdot 5$ | $20$ | $C_{20}$ | Cyclic |
20.5 | $C_2\times C_{10}$ | $2^{2} \cdot 5$ | $2 \cdot 5$ | $20$ | $C_2\times C_{10}$ | Abelian - 2 |
21.2 | $C_{21}$ | $3 \cdot 7$ | $3 \cdot 7$ | $21$ | $C_{21}$ | Cyclic |
22.2 | $C_{22}$ | $2 \cdot 11$ | $2 \cdot 11$ | $22$ | $C_{22}$ | Cyclic |
23.1 | $C_{23}$ | $23$ | $23$ | $23$ | $C_{23}$ | Cyclic |
24.2 | $C_{24}$ | $2^{3} \cdot 3$ | $2^{3} \cdot 3$ | $24$ | $C_{24}$ | Cyclic |
24.9 | $C_2\times C_{12}$ | $2^{3} \cdot 3$ | $2^{2} \cdot 3$ | $24$ | $C_2\times C_{12}$ | Abelian - 2 |
24.15 | $C_2^2\times C_6$ | $2^{3} \cdot 3$ | $2 \cdot 3$ | $24$ | $C_2^2\times C_6$ | Abelian - 3 |
25.1 | $C_{25}$ | $5^{2}$ | $5^{2}$ | $25$ | $C_{25}$ | Cyclic |
25.2 | $C_5^2$ | $5^{2}$ | $5$ | $25$ | $C_5^2$ | Abelian - 2 |
26.2 | $C_{26}$ | $2 \cdot 13$ | $2 \cdot 13$ | $26$ | $C_{26}$ | Cyclic |
27.1 | $C_{27}$ | $3^{3}$ | $3^{3}$ | $27$ | $C_{27}$ | Cyclic |
27.2 | $C_3\times C_9$ | $3^{3}$ | $3^{2}$ | $27$ | $C_3\times C_9$ | Abelian - 2 |
27.5 | $C_3^3$ | $3^{3}$ | $3$ | $27$ | $C_3^3$ | Abelian - 3 |
28.2 | $C_{28}$ | $2^{2} \cdot 7$ | $2^{2} \cdot 7$ | $28$ | $C_{28}$ | Cyclic |
28.4 | $C_2\times C_{14}$ | $2^{2} \cdot 7$ | $2 \cdot 7$ | $28$ | $C_2\times C_{14}$ | Abelian - 2 |
29.1 | $C_{29}$ | $29$ | $29$ | $29$ | $C_{29}$ | Cyclic |
30.4 | $C_{30}$ | $2 \cdot 3 \cdot 5$ | $2 \cdot 3 \cdot 5$ | $30$ | $C_{30}$ | Cyclic |
31.1 | $C_{31}$ | $31$ | $31$ | $31$ | $C_{31}$ | Cyclic |
32.1 | $C_{32}$ | $2^{5}$ | $2^{5}$ | $32$ | $C_{32}$ | Cyclic |
32.3 | $C_4\times C_8$ | $2^{5}$ | $2^{3}$ | $32$ | $C_4\times C_8$ | Abelian - 2 |
32.16 | $C_2\times C_{16}$ | $2^{5}$ | $2^{4}$ | $32$ | $C_2\times C_{16}$ | Abelian - 2 |