C₂×C₃×B(4,𝔽₂) #84887

order	384
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁷

Aliases

	subgroup	G/H
center, socle	C₂²×C₃	#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂⁴×C₃ ◁ G

1018 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.

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

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 4 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 17463);