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C₈×C₅⋊D₅ #87798

order	400
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂×C₅

Aliases

C₈×C₅⋊D₅

Splittings

Fitting	C₅²×C₈ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₈	C₅⋊D₅
commutator, hypocenter	C₅²	C₂×C₈
Frattini	C₄	C₂×C₅⋊D₅
Fitting	C₅²×C₈	C₂
socle	C₂×C₅²	C₂×C₄
prime radical	C₂×C₅⋊D₅	C₄
cosocle	C₄×C₅²	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₈

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 200

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

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716583, #11716585, C₁₆×C₅⋊D₅, …
maximal normal subgroup of	#11716583, #11716585, C₁₆×C₅⋊D₅, …
maximal quotient of	C₁₆×C₅⋊D₅, #11716665, C₈×#1039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 92);