C₅×#4907 #11750406

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

Aliases

direct product

C₅×#4907

Splittings

Fitting	C₃×C₅×M₃₂ ⋊ C₂
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×M₃₂	C₂
socle	C₂×C₃×C₅	C₂²×C₈
prime radical	C₅×#235	C₄
cosocle	C₃×C₈	C₂³×C₅
hypercenter	C₅×M₃₂	D₃
hypocenter	C₃	C₅×#504
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₈ ◁ C₅×M₃₂

168 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×#69122, C₅×#69300, #14315203, …
maximal normal subgroup of	C₅×#69122, C₅×#69300, #14315203, …
maximal quotient of	C₅×#69072, C₅×#71419, C₅×#69107, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4601);