Abstract group search results

Note: Search results may be incomplete due to uncomputed quantities: Monomial (207665 objects)

Results (22 matches)

 

Label	Name	Order	Exponent	Nilp. class	Der. length	Comp. length	Rank	$\card{\mathrm{conj}(G)}$	Subgroups	Subgroup classes	Normal subgroups	Center	Central quotient	Commutator	Abelianization	$\card{\mathrm{Aut}(G)}$	$\card{\mathrm{Out}(G)}$	Tr. deg	Perm. deg	$\C$-irrep deg	$\R$-irrep deg	$\Q$-irrep deg	$\C$-rep deg	$\R$-rep deg	$\Q$-rep deg	Type - length
12.3	$A_4$	$2^{2} \cdot 3$	$2 \cdot 3$	$-1$	$2$	$3$	$2$	$4$	$10$	$5$	$3$	$C_1$	$A_4$	$C_2^2$	$C_{3}$	$2^{3} \cdot 3$	$2$	$4$	$4$	$3$	$3$	$3$	$3$	$3$	$3$	Solvable - 2
36.3	$C_2^2:C_9$	$2^{2} \cdot 3^{2}$	$2 \cdot 3^{2}$	$-1$	$2$	$4$	$2$	$12$	$15$	$8$	$5$	$C_3$	$A_4$	$C_2^2$	$C_{9}$	$2^{3} \cdot 3^{2}$	$2 \cdot 3$	$18$	$13$	$3$	$6$	$6$	$3$	$5$	$6$	Solvable - 2
36.9	$C_3^2:C_4$	$2^{2} \cdot 3^{2}$	$2^{2} \cdot 3$	$-1$	$2$	$4$	$2$	$6$	$38$	$10$	$4$	$C_1$	$C_3^2:C_4$	$C_3^2$	$C_{4}$	$2^{4} \cdot 3^{2}$	$2^{2}$	$6$	$6$	$4$	$4$	$4$	$4$	$4$	$4$	Solvable - 2
36.11	$C_3\times A_4$	$2^{2} \cdot 3^{2}$	$2 \cdot 3$	$-1$	$2$	$4$	$2$	$12$	$30$	$14$	$8$	$C_3$	$A_4$	$C_2^2$	$C_{3}^{2}$	$2^{4} \cdot 3^{2}$	$2^{2} \cdot 3$	$12$	$7$	$3$	$6$	$6$	$3$	$5$	$5$	Solvable - 2
75.2	$C_5^2:C_3$	$3 \cdot 5^{2}$	$3 \cdot 5$	$-1$	$2$	$3$	$2$	$11$	$34$	$6$	$3$	$C_1$	$C_5^2:C_3$	$C_5^2$	$C_{3}$	$2^{4} \cdot 3 \cdot 5^{2}$	$2^{4}$	$15$	$15$	$3$	$6$	$12$	$3$	$6$	$12$	Solvable - 2
196.8	$C_7^2:C_4$	$2^{2} \cdot 7^{2}$	$2^{2} \cdot 7$	$-1$	$2$	$4$	$2$	$16$	$166$	$14$	$4$	$C_1$	$C_7^2:C_4$	$C_7^2$	$C_{4}$	$2^{5} \cdot 3 \cdot 7^{2}$	$2^{3} \cdot 3$	$14$	$14$	$4$	$4$	$12$	$4$	$4$	$12$	Solvable - 2
225.3	$C_5^2:C_9$	$3^{2} \cdot 5^{2}$	$3^{2} \cdot 5$	$-1$	$2$	$4$	$2$	$33$	$42$	$10$	$5$	$C_3$	$C_5^2:C_3$	$C_5^2$	$C_{9}$	$2^{4} \cdot 3^{2} \cdot 5^{2}$	$2^{4} \cdot 3$	$45$	$24$	$3$	$6$	$24$	$3$	$6$	$18$	Solvable - 2
225.5	$C_5^2:C_3^2$	$3^{2} \cdot 5^{2}$	$3 \cdot 5$	$-1$	$2$	$4$	$2$	$33$	$120$	$16$	$8$	$C_3$	$C_5^2:C_3$	$C_5^2$	$C_{3}^{2}$	$2^{5} \cdot 3^{2} \cdot 5^{2}$	$2^{5} \cdot 3$	$45$	$18$	$3$	$6$	$24$	$3$	$6$	$14$	Solvable - 2
363.2	$C_{11}^2:C_3$	$3 \cdot 11^{2}$	$3 \cdot 11$	$-1$	$2$	$3$	$2$	$43$	$136$	$8$	$3$	$C_1$	$C_{11}^2:C_3$	$C_{11}^2$	$C_{3}$	$2^{4} \cdot 3 \cdot 5 \cdot 11^{2}$	$2^{4} \cdot 5$	$33$	$33$	$3$	$6$	$30$	$3$	$6$	$30$	Solvable - 2
484.8	$C_{11}^2:C_4$	$2^{2} \cdot 11^{2}$	$2^{2} \cdot 11$	$-1$	$2$	$4$	$2$	$34$	$390$	$18$	$4$	$C_1$	$C_{11}^2:C_4$	$C_{11}^2$	$C_{4}$	$2^{4} \cdot 3 \cdot 5 \cdot 11^{2}$	$2^{2} \cdot 3 \cdot 5$	$22$	$22$	$4$	$4$	$20$	$4$	$4$	$20$	Solvable - 2
867.2	$C_{17}^2:C_3$	$3 \cdot 17^{2}$	$3 \cdot 17$	$-1$	$2$	$3$	$2$	$99$	$310$	$10$	$3$	$C_1$	$C_{17}^2:C_3$	$C_{17}^2$	$C_{3}$	$2^{6} \cdot 3^{2} \cdot 17^{2}$	$2^{6} \cdot 3$	$51$	$51$	$3$	$6$	$48$	$3$	$6$	$48$	Solvable - 2
1089.3	$C_{11}^2:C_9$	$3^{2} \cdot 11^{2}$	$3^{2} \cdot 11$	$-1$	$2$	$4$	$2$	$129$	$150$	$14$	$5$	$C_3$	$C_{11}^2:C_3$	$C_{11}^2$	$C_{9}$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 11^{2}$	$2^{4} \cdot 3 \cdot 5$	$99$	$42$	$3$	$6$	$60$	$3$	$6$	$36$	Solvable - 2
1089.5	$C_{11}^2:C_3^2$	$3^{2} \cdot 11^{2}$	$3 \cdot 11$	$-1$	$2$	$4$	$2$	$129$	$516$	$20$	$8$	$C_3$	$C_{11}^2:C_3$	$C_{11}^2$	$C_{3}^{2}$	$2^{5} \cdot 3^{2} \cdot 5 \cdot 11^{2}$	$2^{5} \cdot 3 \cdot 5$	$99$	$36$	$3$	$6$	$60$	$3$	$6$	$32$	Solvable - 2
1183.2	$C_{13}^2:C_7$	$7 \cdot 13^{2}$	$7 \cdot 13$	$-1$	$2$	$3$	$2$	$31$	$186$	$6$	$3$	$C_1$	$C_{13}^2:C_7$	$C_{13}^2$	$C_{7}$	$2^{4} \cdot 3 \cdot 7 \cdot 13^{2}$	$2^{4} \cdot 3$	$91$	$91$	$7$	$14$	$84$	$7$	$14$	$84$	Solvable - 2
1444.8	$C_{19}^2:C_4$	$2^{2} \cdot 19^{2}$	$2^{2} \cdot 19$	$-1$	$2$	$4$	$2$	$94$	$1126$	$26$	$4$	$C_1$	$C_{19}^2:C_4$	$C_{19}^2$	$C_{4}$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 19^{2}$	$2^{2} \cdot 3^{2} \cdot 5$	$38$	$38$	$4$	$4$	$36$	$4$	$4$	$36$	Solvable - 2
1587.2	$C_{23}^2:C_3$	$3 \cdot 23^{2}$	$3 \cdot 23$	$-1$	$2$	$3$	$2$	$179$	$556$	$12$	$3$	$C_1$	$C_{23}^2:C_3$	$C_{23}^2$	$C_{3}$	$2^{5} \cdot 3 \cdot 11 \cdot 23^{2}$	$2^{5} \cdot 11$	$69$	$69$	$3$	$6$	$66$	$3$	$6$	$66$	Solvable - 2
1805.2	$C_{19}^2:C_5$	$5 \cdot 19^{2}$	$5 \cdot 19$	$-1$	$2$	$3$	$2$	$77$	$384$	$8$	$3$	$C_1$	$C_{19}^2:C_5$	$C_{19}^2$	$C_{5}$	$2^{4} \cdot 3^{2} \cdot 5 \cdot 19^{2}$	$2^{4} \cdot 3^{2}$	$95$	$95$	$5$	$10$	$90$	$5$	$10$	$90$	Solvable - 2
2601.5	$C_{17}^2:C_9$	$3^{2} \cdot 17^{2}$	$3^{2} \cdot 17$	$-1$	$2$	$4$	$2$	$297$	$330$	$18$	$5$	$C_3$	$C_{17}^2:C_3$	$C_{17}^2$	$C_{9}$	$2^{6} \cdot 3^{3} \cdot 17^{2}$	$2^{6} \cdot 3^{2}$	$153$	$60$	$3$	$6$	$96$	$3$	$6$	$54$	Solvable - 2
2601.6	$C_{17}^2:C_9$	$3^{2} \cdot 17^{2}$	$3^{2} \cdot 17$	$-1$	$2$	$4$	$2$	$41$	$600$	$8$	$4$	$C_1$	$C_{17}^2:C_9$	$C_{17}^2$	$C_{9}$	$2^{6} \cdot 3^{2} \cdot 17^{2}$	$2^{6}$	$153$	$153$	$9$	$18$	$144$	$9$	$18$	$144$	Solvable - 2
2601.7	$C_{17}^2:C_3^2$	$3^{2} \cdot 17^{2}$	$3 \cdot 17$	$-1$	$2$	$4$	$2$	$297$	$1200$	$24$	$8$	$C_3$	$C_{17}^2:C_3$	$C_{17}^2$	$C_{3}^{2}$	$2^{7} \cdot 3^{3} \cdot 17^{2}$	$2^{7} \cdot 3^{2}$	$153$	$54$	$3$	$6$	$96$	$3$	$6$	$50$	Solvable - 2
8281.6	$C_{13}^2:C_7^2$	$7^{2} \cdot 13^{2}$	$7 \cdot 13$	$-1$	$2$	$4$	$2$	$217$	$1392$	$24$	$12$	$C_7$	$C_{13}^2:C_7$	$C_{13}^2$	$C_{7}^{2}$	$2^{5} \cdot 3^{2} \cdot 7^{2} \cdot 13^{2}$	$2^{5} \cdot 3^{2} \cdot 7$	$637$	$98$	$7$	$14$	$504$	$7$	$14$	$90$	Solvable - 2
9025.6	$C_{19}^2:C_5^2$	$5^{2} \cdot 19^{2}$	$5 \cdot 19$	$-1$	$2$	$4$	$2$	$385$	$2216$	$24$	$10$	$C_5$	$C_{19}^2:C_5$	$C_{19}^2$	$C_{5}^{2}$	$2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19^{2}$	$2^{6} \cdot 3^{2} \cdot 5$	$475$	$100$	$5$	$10$	$360$	$5$	$10$	$94$	Solvable - 2