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C₄×#1044 #87864

order	400
isoclinism	isoclinic class of #1044
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄×C₅

Aliases

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₄	#1044
commutator, hypocenter	C₅²	C₄²
Frattini	C₂	C₂×#1044
Fitting	C₄×C₅²	C₄
socle	C₂×C₅²	C₂×C₄
prime radical, cosocle	C₂×C₅⋊D₅	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₄

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 40

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

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

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716762, #11716764, #11716769, …
maximal normal subgroup of	#11716762, #11716764, #11716769, …
maximal quotient of	C₈×#1044, #11716885, C₄×#6034, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 158);