C₅×#4919 #11750418

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#4919

Splittings

Fitting	C₃×C₅×Q₃₂ ⋊ C₂
Hall	C₃×C₅ ⋊ #508
Sylow	C₃ ⋊ C₅×#508

Subgroups

	subgroup	G/H
center	C₂×C₅	D₃×D₈
commutator, cosocle	C₃×C₈	C₂³×C₅
Frattini	C₈	C₂²×C₅×D₃
Fitting	C₃×C₅×Q₃₂	C₂
socle	C₂×C₃×C₅	C₂×D₈
hypercenter	C₅×Q₃₂	D₃
hypocenter	C₃	C₅×#508
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×Q₃₂

168 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 62 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)(9,11,14,19)(10,16,15,30)(12,24,27,40)(13,29,25,22)(17,35,31,39)(18,36,28,33)(20,38,37,23)(21,34,32,26);(9,10,14,15)(11,20,19,37)(12,23,27,38)(13,28,25,18)(16,32,30,21)(17,34,31,26)(22,39,29,35)(24,36,40,33);(7,8)(10,15)(11,19)(17,31)(18,28)(21,32)(22,29)(23,38)(24,40)

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#69379, C₅×#69383, #14319232, …
maximal normal subgroup of	C₅×#69379, C₅×#69383, #14319232, …
maximal quotient of	C₅×#69220, C₅×#69325, C₅×#69317, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4613);