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C₅×#688 #87795

order	400
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Fitting	C₅²×Q₈ ⋊ C₂
Sylow	C₅² ⋊ SD₁₆

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂²×C₅
Frattini	C₄	C₂×C₅×D₅
Fitting	C₅²×Q₈	C₂
socle	C₂×C₅²	D₄
prime radical	C₅×D₂₀	C₂
hypercenter	C₅×Q₈	D₅
hypocenter	C₅	C₅×SD₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×Q₈

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 18 points:

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

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₅×#688, #11717057, #11717058, …
maximal normal subgroup of	D₅×#688, #11717057, #11717058, …
maximal quotient of	C₅×#3940, C₅×#3941, C₅×#3967, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 89);