C₂×#3496 #62764

order	256
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁴

Aliases

	subgroup	G/H
center, socle	C₂³	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂² ▷ C₁

6189 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 6 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55752);