C₅×#4888 #11750387

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

Aliases

direct product

C₅×#4888

Splittings

Fitting	C₃×C₅×#107 ⋊ C₂
Hall	C₃×C₅ ⋊ #485
Sylow	C₃ ⋊ C₅×#485

Subgroups

	subgroup	G/H
center	C₂²×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂³×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#107	C₂
socle	C₂²×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₃	D₄
hypercenter	C₅×#107	D₃
hypocenter	C₃	C₅×#485
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#107

192 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 480

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

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

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#485, C₂×C₅×#4888, D₅×#4888, …
maximal normal subgroup of	C₅×D₃×#485, C₂×C₅×#4888, D₅×#4888, …
maximal quotient of	C₅×#68873, C₅×#70633, C₅×#68879, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4582);