C₃×#2196 #72911

order	384
nilpotency class	4
isoclinism	isoclinic class of #2196
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂×C₃	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂³×C₃
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃ ◁ C₂×C₃×D₄ ◁ G

354 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

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

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 3 generators on 11 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5487);