C₅×#5750 #11756135

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅×#5750

Splittings

Fitting	C₃×C₅×#131 ⋊ C₂
Hall	C₃×C₅ ⋊ #568
Sylow	C₃ ⋊ C₅×#568

Subgroups

	subgroup	G/H
center	C₄×C₅	C₂³×D₃
commutator	C₂×C₃	C₂³×C₄×C₅
Frattini	C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#131	C₂
socle	C₂×C₃×C₅	C₂³×C₄
prime radical	C₅×D₃×#41	C₂
cosocle	C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#131	D₃
hypocenter	C₃	C₅×#568
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₅×#131

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×#79889, C₅×#79898, #14418143, …
maximal normal subgroup of	C₅×#79889, C₅×#79898, #14418143, …
maximal quotient of	C₅×#78548, C₅×#83782, C₅×#78550, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10330);

C5×#5750 #11756135