C₂×#2973 #60221

order	256
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	Aut(G) order 262144
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

1305 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)(5,9)(6,8)(7,10)(11,12,13,16,14,15,17,18);(3,5)(4,7)(6,10)(8,9);(5,10)(7,9)(12,15)(16,18);(4,8)(7,9)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53209);