C₅×#5063 #11750562

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#5063

Splittings

Hall	C₃×C₅ ⋊ #479
Sylow	C₃ ⋊ C₅×#479

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂³×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#125	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×D₄
hypercenter	C₅×#125	D₃
hypocenter	C₃	C₅×#479
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#125

180 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 32
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#479, C₂×C₅×#5063, D₅×#5063, …
maximal normal subgroup of	C₅×D₃×#479, C₂×C₅×#5063, D₅×#5063, …
maximal quotient of	C₅×#69559, C₅×#69631, C₅×#69632, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4757);