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C₄×#1043 #87857

order	400
isoclinism	isoclinic class of #1043
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	#1043
commutator, hypocenter	C₅²	C₄²
Frattini	C₂	C₂×#1043
Fitting	C₄×C₅²	C₄
socle	C₂×C₅²	C₂×C₄
prime radical, cosocle	C₂×C₅⋊D₅	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₄

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 100

A minimal faithful permutation representation — 3 generators on 14 points:

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

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716761, #11716763, #11716770, …
maximal normal subgroup of	#11716761, #11716763, #11716770, …
maximal quotient of	C₈×#1043, #11716860, C₄×#6033, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 151);