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C₅×#826 #91069

order	480
isoclinism	isoclinic class of #826
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

Splittings

Fitting	C₃×C₅×D₈ ⋊ C₂
Hall	C₃×C₅ ⋊ D₁₆
Sylow	C₃ ⋊ C₅×D₁₆

Subgroups

	subgroup	G/H
center	C₂×C₅	#213
commutator, cosocle	C₃×C₈	C₂²×C₅
Frattini	C₈	C₂×C₅×D₃
Fitting	C₃×C₅×D₈	C₂
socle	C₂×C₃×C₅	D₈
hypercenter	C₅×D₈	D₃
hypocenter	C₃	C₅×D₁₆
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×D₈

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

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

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₅×#826, #11748265, #11748268, …
maximal normal subgroup of	D₅×#826, #11748265, #11748268, …
maximal quotient of	C₅×#4489, C₅×#4491, C₅×#4519, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 145);