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C₂×#6039 #87884

order	400
isoclinism	isoclinic class of #6037
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

C₅² ⋊ C₂×Q₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	D₅²
commutator, cosocle	C₂×C₅²	C₂³
Frattini	C₂	C₂×D₅²
Fitting, socle, prime radical	C₂²×C₅²	C₂²
hypocenter	C₅²	C₂×Q₈
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂²

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716758, #11716782, #11716798, …
maximal normal subgroup of	#11716758, #11716782, #11716798, …
maximal quotient of	#11716988, #11716991, C₄×#6039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 178);