Finite Group Databasebeta

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C₂×#6057 #87918

order	400
isoclinism	isoclinic class of #6057
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²×C₅

Aliases

Splittings

Fitting, socle	C₂×C₅² ⋊ Q₈
Sylow	C₅² ⋊ C₂×Q₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂	#6057
commutator, cosocle	C₅⋊D₅	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₅²	Q₈
prime radical	C₂×C₅⋊D₅	C₂²
hypocenter	C₅²	C₂×Q₈
LCS	G ▷ C₅⋊D₅ ▷ C₅²
UCS	C₁ ◁ C₂

62 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 20

A minimal faithful permutation representation — 3 generators on 12 points:

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

Conjugacy classes & character table

16 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11717308, #11717310, #11717312, …
maximal normal subgroup of	#11717308, #11717310, #11717312, …
maximal quotient of	#11717401, C₄×#6057, C₄⋊#6057, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 212);