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C₅×Dic₂₂ #89171

order	440
isoclinism	isoclinic class of Dic₂₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

C₅×Dic₂₂

Splittings

Hall	C₅×C₁₁ ⋊ Q₈
Sylow	C₁₁ ⋊ C₅×Q₈

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂×D₁₁
commutator, cosocle	C₂×C₁₁	C₂²×C₅
Frattini	C₂	C₂×C₅×D₁₁
Fitting	C₄×C₅×C₁₁	C₂
socle, prime radical	C₂×C₅×C₁₁	C₂²
hypercenter	C₄×C₅	D₁₁
hypocenter	C₁₁	C₅×Q₈
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

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

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11724875, #11724877, #11724880, …
maximal normal subgroup of	#11724875, #11724877, #11724880, …
maximal quotient of	C₅×Dic₁₁⋊C₄, C₅×C₄⋊Dic₁₁, C₂×C₅×Dic₂₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 24);