C₅×#5140 #11750639

order	960
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₈ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#5140

Splittings

Hall	C₃×C₅ ⋊ #504
Sylow	C₃ ⋊ C₅×#504

Subgroups

	subgroup	G/H
center	C₅×C₈	C₂²×D₃
commutator	C₂×C₃	C₂²×C₅×C₈
Frattini	C₈	C₂²×C₅×D₃
Fitting	C₃×C₅×#131	C₂
socle	C₂×C₃×C₅	C₂²×C₈
prime radical	C₃×C₅×#41	C₄
cosocle	C₃×C₈	C₂³×C₅
hypercenter	C₅×#131	D₃
hypocenter	C₃	C₅×#504
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₈ ◁ C₅×#131

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5)(6,7,8)(11,19)(15,25)(20,31)(21,32)(26,35)(27,36)(33,39)(37,40);(9,11)(10,15)(12,20)(13,21)(14,19)(16,26)(17,27)(18,25)(22,33)(23,31)(24,32)(28,37)(29,35)(30,36)(34,39)(38,40);(7,8)(9,10,12,16,13,17,22,28,14,18,23,29,24,30,34,38)(11,15,20,26,21,27,33,37,19,25,31,35,32,36,39,40)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×#69122, C₅×#70923, #14315209, …
maximal normal subgroup of	C₅×#69122, C₅×#70923, #14315209, …
maximal quotient of	C₅×#69881, C₅×#72004, C₅×#69882, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4834);

C5×#5140 #11750639