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C₄×#1039 #87805

order	400
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄×C₅

Aliases

Splittings

C₅² ⋊ C₄²

Subgroups

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

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 400

A minimal faithful permutation representation — 3 generators on 18 points:

(2,3)(4,5)(7,8)(9,10)(15,16,17,18);(6,7,9,10,8)(11,12,13,14);(1,2,4,5,3)

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716594, #11716596, #11716609, …
maximal normal subgroup of	#11716594, #11716596, #11716609, …
maximal quotient of	C₄×#6029, #11716670, C₈×#1039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 99);