C₂×#3492 #62768

order	256
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹³

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

3955 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 6 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55756);