C₅×#4797 #11750296

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₅×#4797

Splittings

Hall	C₃×C₅ ⋊ #491
Sylow	C₃ ⋊ C₅×#491

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, prime radical	C₂²×C₃×C₅	C₂×D₄
hypercenter	C₅×#103	D₃
hypocenter	C₃	C₅×#491
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#103

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

normal subgroups only

This group has 180 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) = 960

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

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#491, C₂×C₅×#4797, D₅×#4797, …
maximal normal subgroup of	C₅×D₃×#491, C₂×C₅×#4797, D₅×#4797, …
maximal quotient of	C₅×#68849, C₅×#70256, C₅×#68854, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4491);