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C₂×C₅×D₂₄ #91706

order	480
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₅×D₂₄

Splittings

Fitting	C₂×C₃×C₅×C₈ ⋊ C₂
Hall	C₃×C₅ ⋊ C₂×D₈
Sylow	C₃ ⋊ C₂×C₅×D₈

Subgroups

	subgroup	G/H
center	C₂²×C₅	D₁₂
commutator, cosocle	C₃×C₄	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₈	C₂
socle	C₂²×C₃×C₅	D₄
hypercenter	C₂×C₅×C₈	D₃
hypocenter	C₃	C₂×C₅×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 240

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

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11745893, #11745894, #11745917, …
maximal normal subgroup of	#11745893, #11745894, #11745917, …
maximal quotient of	C₅×#4682, C₄×C₅×D₂₄, C₅×#4694, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 782);