C₅×#4829 #11750328

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

Aliases

direct product

C₅×#4829

Splittings

Hall	C₃×C₅ ⋊ #479
Sylow	C₃ ⋊ C₅×#479

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂³×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×C₄⋊C₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×D₄
hypercenter	C₅×C₄⋊C₈	D₃
hypocenter	C₃	C₅×#479
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×C₄⋊C₈

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

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#479, C₂×C₅×#4829, D₅×#4829, …
maximal normal subgroup of	C₅×D₃×#479, C₂×C₅×#4829, D₅×#4829, …
maximal quotient of	C₅×#70486, C₅×#68683, C₅×#68684, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4523);