C₅×#4815 #11750314

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

Aliases

direct product

C₅×#4815

Splittings

Fitting	C₃×C₅×#103 ⋊ C₂
Hall	C₃×C₅ ⋊ #485
Sylow	C₃ ⋊ C₅×#485

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×#485
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#103

192 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 480

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5)(6,7,8)(10,14)(13,16)(17,19,21,27)(18,23,22,25)(20,29,28,26)(24,31,30,32);(9,11,12,15)(10,13,14,16)(18,22)(19,26)(20,28)(23,31)(25,32)(27,29);(7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,25)(20,24)(21,22)(23,27)(26,31)(28,30)(29,32)

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#485, C₂×C₅×#4815, D₅×#4815, …
maximal normal subgroup of	C₅×D₃×#485, C₂×C₅×#4815, D₅×#4815, …
maximal quotient of	C₅×#68873, C₅×#68876, C₅×#70269, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4509);