C₂×#153854 #72334579

order	1024
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂¹³×C₄

Aliases

73477 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 5 generators on 22 points:

(4,6)(7,8,9,10)(12,14);(4,6)(8,10)(11,12,13,14)(16,18)(19,20,21,22);(15,16,17,18);(1,2);(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)

304 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₂×D₄×C₂²⋊#95, C₂×#72298505, C₂×#72298440, …
maximal normal subgroup of	C₂×D₄×C₂²⋊#95, C₂×#72298505, C₂×#72298440, …

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((4,6)(7,8,9,10)(12,14), (4,6)(8,10)(11,12,13,14)(16,18)(19,20,21,22), (15,16,17,18), (1,2), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14));