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C₂×#6029 #87803

order	400
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂×C₅

Aliases

Splittings

C₅² ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	C₅⋊D₅
commutator, hypocenter	C₅²	C₂×C₈
Frattini	C₄	C₂×C₅⋊D₅
Fitting	C₂×C₄×C₅²	C₂
socle, prime radical	C₂²×C₅²	C₄
cosocle	C₄×C₅²	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₄

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 400

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₅×#168, #11716595, #11716597, …
maximal normal subgroup of	Dic₅×#168, #11716595, #11716597, …
maximal quotient of	C₄×#6029, C₄⋊#6029, C₂×#87756, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 97);