C₅×#4795 #11750294

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

Aliases

direct product

C₅×#4795

Splittings

Hall	C₃×C₅ ⋊ #462
Sylow	C₃ ⋊ C₅×#462

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×#103	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×D₄
hypercenter	C₅×#103	D₃
hypocenter	C₃	C₅×#462
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#103

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

normal subgroups only

This group has 216 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) = 28
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#462, C₂×C₅×#4795, D₅×#4795, …
maximal normal subgroup of	C₅×D₃×#462, C₂×C₅×#4795, D₅×#4795, …
maximal quotient of	C₅×#68466, C₅×#68508, C₅×#68467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4489);