C₂×#3151 #60636

order	256
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

	subgroup	G/H
center, socle	C₂³	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

1975 conjugacy classes of subgroups; only the 583 normal subgroups are shown.

normal subgroups only

This group has 1975 conjugacy classes of subgroups — too many to draw. Only its 583 normal subgroups are shown.

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

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

A minimal faithful permutation representation — 5 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53624);