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C₅×D₈₈ #11724893

order	880
isoclinism	isoclinic class of #4314
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

C₅×D₈₈

Splittings

Fitting	C₅×C₈×C₁₁ ⋊ C₂
Hall	C₅×C₁₁ ⋊ D₈
Sylow	C₁₁ ⋊ C₅×D₈

Subgroups

	subgroup	G/H
center	C₂×C₅	D₄₄
commutator, cosocle	C₄×C₁₁	C₂²×C₅
Frattini	C₄	C₂×C₅×D₁₁
Fitting	C₅×C₈×C₁₁	C₂
socle	C₂×C₅×C₁₁	D₄
hypercenter	C₅×C₈	D₁₁
hypocenter	C₁₁	C₅×D₈
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 440

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24);(7,13)(8,12)(9,11)(15,24)(16,23)(17,22)(18,21)(19,20)

Conjugacy classes & character table

235 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#13182266, #13182267, #13182269, …
maximal normal subgroup of	#13182266, #13182267, #13182269, …
maximal quotient of	C₅×#66864, C₅×D₁₇₆, C₅×Dic₈₈, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 61);