C₂×C₄×#23900 #72342216

order	2048
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁷

Aliases

At least 7440 conjugacy classes of subgroups; only the 9560 normal subgroups are shown.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

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

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

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

maximal subgroup of	C₂×C₄×#87588⋊C₂
maximal quotient of	C₂×C₄×#245225

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

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