C₅×#4813 #11750312

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

Aliases

direct product

C₅×#4813

Splittings

Fitting	C₃×C₅×#103 ⋊ C₂
Hall	C₃×C₅ ⋊ #467
Sylow	C₃ ⋊ C₅×#467

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	C₂²×C₅×D₃	D₄
hypercenter	C₅×#103	D₃
hypocenter	C₃	C₅×#467
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#103

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

normal subgroups only

This group has 228 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) = 480

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

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#467, C₂×C₅×#4813, D₅×#4813, …
maximal normal subgroup of	C₅×D₃×#467, C₂×C₅×#4813, D₅×#4813, …
maximal quotient of	C₅×#68441, C₅×#68465, C₅×#68497, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4507);