C₂×#392113 #72236645

order	1024
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁵

Aliases

408221 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 5 generators on 18 points:

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

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)(11,12,13,16,14,15,17,18), (4,6)(12,15)(13,17), (8,10), (12,15)(13,17));