C₂×#2324 #34064

order	256
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	Aut(G) order 1048576
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

1967 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27052);