C₂²×#534 #62669

order	256
nilpotency class	2
isoclinism	isoclinic class of #534
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

7615 conjugacy classes of subgroups; only the 3183 normal subgroups are shown.

normal subgroups only

This group has 7615 conjugacy classes of subgroups — too many to draw. Only its 3183 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 64

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55657);