C₂×#534900 #72332905

order	1024
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁵

Aliases

49589 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 6 generators on 18 points:

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

maximal subgroup of	C₂×#72323420, C₂×#72323422, C₂×#72323421
maximal normal subgroup of	C₂×#72323420, C₂×#72323422, C₂×#72323421

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

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