C₅×#4798 #11750297

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

Aliases

direct product

C₅×#4798

Splittings

Fitting	C₃×C₅×#103 ⋊ C₂
Hall	C₃×C₅ ⋊ #464
Sylow	C₃ ⋊ C₅×#464

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	C₂²×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×D₁₂	C₂²
hypercenter	C₅×#103	D₃
hypocenter	C₃	C₅×#464
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#103

224 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 78 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)(9,10)(11,12)(13,15,17,22)(14,18,20,26)(16,24,23,21)(19,28,27,25);(9,10,11,12)(15,21)(16,23)(18,25)(19,27)(22,24)(26,28);(7,8)(9,10,11,12)(13,14,17,20)(15,18,22,26)(16,19,23,27)(21,25,24,28)

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#464, C₂×C₅×#4798, D₅×#4798, …
maximal normal subgroup of	C₅×D₃×#464, C₂×C₅×#4798, D₅×#4798, …
maximal quotient of	C₅×#68510, C₅×#68469, C₅×#68470, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4492);