C₂×#5934 #87513

order	384
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂⁴

Aliases

Fitting	C₂×H(5,𝔽₂) ⋊ D₃
derived	#997 ⋊ C₂²

	subgroup	G/H
center, socle, hypercenter	C₂²	#1020
commutator, cosocle, hypocenter	#997	C₂²
Frattini	C₂	C₂×#1020
Fitting	C₂×H(5,𝔽₂)	D₃
LCS	G ▷ #997
UCS	C₁ ◁ C₂²

439 conjugacy classes of subgroups; only the 18 normal subgroups are shown.

normal subgroups only

This group has 439 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.

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

minimal degree	μ(G) = 10
transitive degree	μ_t(G) = 16

A minimal faithful permutation representation — 2 generators on 10 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 20089);