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C₅×#4494 #11746193

order	960
isoclinism	isoclinic class of #4487
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Hall	C₃×C₅ ⋊ #365
Sylow	C₃ ⋊ C₅×#365

Subgroups

	subgroup	G/H
center	C₂×C₅	#808
commutator	C₃×C₈	C₂×C₄×C₅
Frattini	C₂×C₈	C₂×C₅×D₃
Fitting	C₃×C₅×#108	C₂
socle	C₂×C₃×C₅	#106
prime radical	C₂²×C₃×C₅	SD₁₆
cosocle	C₂×C₃×C₈	C₂²×C₅
hypercenter	C₅×#108	D₃
hypocenter	C₃	C₅×#365
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₅×#108

84 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:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#365, C₂×C₅×#4494, D₅×#4494, …
maximal normal subgroup of	C₅×D₃×#365, C₂×C₅×#4494, D₅×#4494, …
maximal quotient of	C₅×#67464, C₅×#67730, C₂×C₅×#4494

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 388);