C₂²×#547 #62699

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁴

Aliases

	subgroup	G/H
center, socle	C₂⁴	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ G
LECS	G ▷ C₂² ▷ C₁

6115 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 6 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55687);