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C₄×#1042 #87850

order	400
isoclinism	isoclinic class of #1042
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

Splittings

Fitting	C₄×C₅² ⋊ C₄
derived, Sylow	C₅² ⋊ C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₄	#1042
commutator, hypocenter	C₅²	C₄²
Frattini	C₂	C₂×#1042
Fitting	C₄×C₅²	C₄
socle	C₂×C₅²	C₂×C₄
prime radical, cosocle	C₂×C₅×D₅	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₄

63 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 14 points:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716731, #11716733, #11716738, …
maximal normal subgroup of	#11716731, #11716733, #11716738, …
maximal quotient of	C₈×#1042, #11716835, C₄×#6032, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 144);