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C₂×#6037 #87882

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

Aliases

Splittings

C₅² ⋊ C₂×D₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	D₅²
commutator, cosocle	C₂×C₅²	C₂³
Frattini	C₂	C₂×D₅²
Fitting, socle	C₂²×C₅²	C₂²
hypocenter	C₅²	C₂×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂²

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716755, #11716781, #11716797, …
maximal normal subgroup of	#11716755, #11716781, #11716797, …
maximal quotient of	C₂×#87770, #11716940, #11716941, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 176);