C₂×#2991 #60258

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	Aut(G) order 393216
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

1093 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);(4,7)(5,9)(11,12,15,17,14,16,13,18);(3,4)(5,8)(6,7)(9,10)(12,16)(17,18);(4,7)(8,10)(12,16)(17,18);(3,5,6,9)(4,8,7,10)(11,13,14,15)(12,17,16,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53246);