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C₂×#6034 #87866

order	400
isoclinism	isoclinic class of #1044
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂×C₅

Aliases

Splittings

C₅² ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	#1044
commutator, hypocenter	C₅²	C₂×C₈
Frattini	C₂	C₂×#1044
Fitting, socle, prime radical	C₂²×C₅²	C₄
cosocle	#1039	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 20 points:

(4,5,6,7)(9,10,11,12)(13,14,15,17,16,18,19,20);(1,2)(3,4,5,7,6)(8,9,12,10,11)

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716777, #11716778, #11716779, …
maximal normal subgroup of	#11716777, #11716778, #11716779, …
maximal quotient of	C₂×#87765, #11716891, C₄×#6034, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 160);