C₅×#4733 #11750232

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

Aliases

direct product

C₅×#4733

Splittings

Fitting	C₃×C₅×C₂²⋊C₈ ⋊ C₂
Hall	C₃×C₅ ⋊ #452
Sylow	C₃ ⋊ C₅×#452

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×C₂²⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#235	C₂
hypercenter	C₅×C₂²⋊C₈	D₃
hypocenter	C₃	C₅×#452
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×C₂²⋊C₈

304 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 480

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

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

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#452, C₂×C₅×#4733, D₅×#4733, …
maximal normal subgroup of	C₅×D₃×#452, C₂×C₅×#4733, D₅×#4733, …
maximal quotient of	C₅×#68132, C₅×#68109, C₅×#68136, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4427);