Abstract group search results

Results (25 matches)

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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
768.539	$C_3\times D_{128}$	$2^{8} \cdot 3$	$2^{7} \cdot 3$	$7$	$2$	$9$	$2$	201	$526$	$46$	$22$	$C_6$	$D_{64}$	$C_{64}$	$C_{2} \times C_{6}$	$2^{14}$	$2^{7}$	$384$	$131$	$2$	$4$	$128$	$2$	$4$	$66$	Nilpotent - 7
768.541	$C_3\times Q_{256}$	$2^{8} \cdot 3$	$2^{7} \cdot 3$	$7$	$2$	$9$	$2$	201	$270$	$42$	$22$	$C_6$	$D_{64}$	$C_{64}$	$C_{2} \times C_{6}$	$2^{14}$	$2^{7}$	$768$	$259$	$2$	$4$	$128$	$2$	$4$	$128$	Nilpotent - 7
1280.540	$C_5\times \SD_{256}$	$2^{8} \cdot 5$	$2^{7} \cdot 5$	$7$	$2$	$9$	$2$	335	$398$	$44$	$22$	$C_{10}$	$D_{64}$	$C_{64}$	$C_{2} \times C_{10}$	$2^{14}$	$2^{7}$	$640$	$133$	$2$	$4$	$256$	$2$	$4$	$68$	Nilpotent - 7
1536.2018	$C_3\times C_8^2.D_4$	$2^{9} \cdot 3$	$2^{4} \cdot 3$	$7$	$3$	$10$	$2$	96	$1324$	$228$	$32$	$C_6$	$D_4^2:C_4$	$C_4:Q_{16}$	$C_{2} \times C_{12}$	$2^{12}$	$2^{4}$	$96$	$35$	$4$	$8$	$32$	$4$	$8$	$18$	Nilpotent - 7
1536.2021	$(C_8\times C_{16}).C_{12}$	$2^{9} \cdot 3$	$2^{4} \cdot 3$	$7$	$2$	$10$	$2$	123	$1724$	$224$	$32$	$C_6$	$C_8^2:C_4$	$C_8^2$	$C_{2} \times C_{12}$	$2^{15}$	$2^{7}$	$96$	$35$	$4$	$8$	$32$	?	?	?	Nilpotent - 7
1792.539	$C_7\times D_{128}$	$2^{8} \cdot 7$	$2^{7} \cdot 7$	$7$	$2$	$9$	$2$	469	$526$	$46$	$22$	$C_{14}$	$D_{64}$	$C_{64}$	$C_{2} \times C_{14}$	$2^{14} \cdot 3$	$2^{7} \cdot 3$	$896$	$135$	$2$	$4$	$384$	$2$	$4$	$70$	Nilpotent - 7
1792.541	$C_7\times Q_{256}$	$2^{8} \cdot 7$	$2^{7} \cdot 7$	$7$	$2$	$9$	$2$	469	$270$	$42$	$22$	$C_{14}$	$D_{64}$	$C_{64}$	$C_{2} \times C_{14}$	$2^{14} \cdot 3$	$2^{7} \cdot 3$	$1792$	$263$	$2$	$4$	$384$	$2$	$4$	$134$	Nilpotent - 7
3072.dk	$C_3\times Q_{16}^2:C_2^2$	$2^{10} \cdot 3$	$2^{4} \cdot 3$	$7$	$3$	$11$	$3$	147	$6266$	$772$	$62$	$C_6$	$D_8\wr C_2$	$C_8:Q_{16}$	$C_{2}^{2} \times C_{6}$	$2^{14}$	$2^{5}$	$96$	$35$	$4$	$8$	$32$	$4$	$8$	$18$	Nilpotent - 7
4864.540	$C_{19}\times \SD_{256}$	$2^{8} \cdot 19$	$2^{7} \cdot 19$	$7$	$2$	$9$	$2$	1273	$398$	$44$	$22$	$C_{38}$	$D_{64}$	$C_{64}$	$C_{2} \times C_{38}$	$2^{13} \cdot 3^{2}$	$2^{6} \cdot 3^{2}$	$2432$	$147$	$2$	?	?	?	?	?	Nilpotent - 7
24576.bc	$D_{64}.C_{192}$	$2^{13} \cdot 3$	$2^{7} \cdot 3$	$7$	$2$	$14$	$2$	6432	$2996$	$628$	$152$	$C_{192}$	$D_{64}$	$C_{64}$	$C_{2} \times C_{192}$	$2^{18}$	$2^{11}$	$384$	$131$	$2$	?	?	?	?	?	Nilpotent - 7
48896.539	$C_{191}\times D_{128}$	$2^{8} \cdot 191$	$2^{7} \cdot 191$	$7$	$2$	$9$	$2$	12797	$526$	$46$	$22$	$C_{382}$	$D_{64}$	$C_{64}$	$C_{2} \times C_{382}$	$2^{14} \cdot 5 \cdot 19$	$2^{7} \cdot 5 \cdot 19$	$24448$	$319$	?	?	?	?	?	?	Nilpotent - 7
48896.541	$C_{191}\times Q_{256}$	$2^{8} \cdot 191$	$2^{7} \cdot 191$	$7$	$2$	$9$	$2$	12797	$270$	$42$	$22$	$C_{382}$	$D_{64}$	$C_{64}$	$C_{2} \times C_{382}$	$2^{14} \cdot 5 \cdot 19$	$2^{7} \cdot 5 \cdot 19$	$48896$	$447$	?	?	?	?	?	?	Nilpotent - 7
57344.a	$D_{64}.C_{448}$	$2^{13} \cdot 7$	$2^{7} \cdot 7$	$7$	$2$	$14$	$2$	15008	$2996$	$628$	$152$	$C_{448}$	$D_{64}$	$C_{64}$	$C_{2} \times C_{448}$	$2^{18} \cdot 3$	$2^{11} \cdot 3$	$896$	$135$	?	?	?	?	?	?	Nilpotent - 7
118098.w	$C_9^3.C_3^3:C_6$	$2 \cdot 3^{10}$	$2 \cdot 3^{4}$	$7$	$3$	$11$	$2$	370	$18688$	$564$	$40$	$C_6$		$C_9^3.C_3^2$	$C_{3} \times C_{6}$	$2 \cdot 3^{11}$	$2 \cdot 3^{2}$	$162$	$83$	$27$	$54$	$54$	?	?	?	Nilpotent - 7
354294.b	$C_9^3.C_3^4:C_6$	$2 \cdot 3^{11}$	$2 \cdot 3^{4}$	$7$	$3$	$12$	$3$	1110			$192$	$C_3\times C_6$		$C_9^3.C_3^2$	$C_{3}^{2} \times C_{6}$	$2^{2} \cdot 3^{14}$	$2^{2} \cdot 3^{5}$		$86$	$-$	?	$-$	?	?	?	Nilpotent - 7
354294.c	$(C_3\times C_9^3).C_3^3:C_6$	$2 \cdot 3^{11}$	$2 \cdot 3^{4}$	$7$	$3$	$12$	$2$	1110	$98346$	$3358$	$156$	$C_3\times C_6$		$C_9^3.C_3^2$	$C_{3} \times C_{18}$	$2 \cdot 3^{14}$	$2 \cdot 3^{5}$	$1458$	$92$	$-$	?	$-$	?	?	?	Nilpotent - 7
354294.br	$C_9^3.C_3^3:C_{18}$	$2 \cdot 3^{11}$	$2 \cdot 3^{4}$	$7$	$3$	$12$	$2$	1110			$156$	$C_3\times C_6$		$C_9^3.C_3^2$	$C_{3} \times C_{18}$	$2 \cdot 3^{14}$	$2 \cdot 3^{5}$		$92$	$-$	?	$-$	?	?	?	Nilpotent - 7
354294.bs	$C_9^3.C_{18}.\He_3$	$2 \cdot 3^{11}$	$2 \cdot 3^{4}$	$7$	$3$	$12$	$2$	1110			$156$	$C_3\times C_6$		$C_9^3.C_3^2$	$C_{3} \times C_{18}$	$2 \cdot 3^{14}$	$2 \cdot 3^{5}$		$92$	$-$	?	$-$	?	?	?	Nilpotent - 7
354294.bt	$C_9^3.\He_3:C_{18}$	$2 \cdot 3^{11}$	$2 \cdot 3^{4}$	$7$	$3$	$12$	$2$	1110			$156$	$C_3\times C_6$		$C_9^3.C_3^2$	$C_{3} \times C_{18}$	$2 \cdot 3^{14}$	$2 \cdot 3^{5}$		$92$	$-$	?	$-$	?	?	?	Nilpotent - 7
1062882.d	$C_9^4.C_3^3:C_6$	$2 \cdot 3^{12}$	$2 \cdot 3^{4}$	$7$	$3$	$13$	$3$	3330			$344$	$C_3\times C_{18}$		$C_9^3.C_3^2$	$C_{3}^{2} \times C_{18}$	$2^{2} \cdot 3^{15}$	$2^{2} \cdot 3^{6}$		$92$	$-$	?	?	?	?	?	Nilpotent - 7
1062882.e	$C_9^4.C_3^3:C_6$	$2 \cdot 3^{12}$	$2 \cdot 3^{4}$	$7$	$3$	$13$	$2$	3330			$272$	$C_3\times C_{18}$		$C_9^3.C_3^2$	$C_{3} \times C_{54}$	$2 \cdot 3^{15}$	$2 \cdot 3^{6}$		$110$	?	?	?	?	?	?	Nilpotent - 7
1062882.l	$C_9^3.C_3^3:C_{54}$	$2 \cdot 3^{12}$	$2 \cdot 3^{4}$	$7$	$3$	$13$	$2$	3330			$272$	$C_3\times C_{18}$		$C_9^3.C_3^2$	$C_{3} \times C_{54}$	$2 \cdot 3^{15}$	$2 \cdot 3^{6}$		$110$	$-$	?	?	?	?	?	Nilpotent - 7
1062882.m	$C_9^3.\He_3:C_{54}$	$2 \cdot 3^{12}$	$2 \cdot 3^{4}$	$7$	$3$	$13$	$2$	3330			$272$	$C_3\times C_{18}$		$C_9^3.C_3^2$	$C_{3} \times C_{54}$	$2 \cdot 3^{15}$	$2 \cdot 3^{6}$		$110$	$-$	?	?	?	?	?	Nilpotent - 7
1062882.n	$C_9^4.C_3^3:C_6$	$2 \cdot 3^{12}$	$2 \cdot 3^{4}$	$7$	$3$	$13$	$2$	3330			$272$	$C_3\times C_{18}$		$C_9^3.C_3^2$	$C_{3} \times C_{54}$	$2 \cdot 3^{15}$	$2 \cdot 3^{6}$		$110$	$-$	?	?	?	?	?	Nilpotent - 7
3188646.b	$C_9^4.C_3^4:C_6$	$2 \cdot 3^{13}$	$2 \cdot 3^{4}$	$7$	$3$	$14$	$3$	9990			$496$	$C_3\times C_{54}$		$C_9^3.C_3^2$	$C_{3}^{2} \times C_{54}$	$2^{2} \cdot 3^{16}$	$2^{2} \cdot 3^{7}$		$110$	?	?	?	?	?	?	Nilpotent - 7

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