C₃×#65201 #11749809

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃×#65201

Splittings

Fitting	C₃×C₅×D₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ #508
Sylow	C₅ ⋊ C₃×#508

Subgroups

	subgroup	G/H
center	C₂×C₃	D₅×D₈
commutator, cosocle	C₅×C₈	C₂³×C₃
Frattini	C₈	C₂²×C₃×D₅
Fitting	C₃×C₅×D₁₆	C₂
socle	C₂×C₃×C₅	C₂×D₈
hypercenter	C₃×D₁₆	D₅
hypocenter	C₅	C₃×#508
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×D₁₆

168 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 62 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) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3)(4,5,7,8,6)(10,16)(11,20)(12,24)(13,25)(15,28)(17,34)(19,33)(21,22)(23,39)(26,40)(27,38)(29,36)(30,37)(31,35);(9,11)(10,15)(12,20)(13,27)(14,23)(16,19)(17,33)(18,36)(21,24)(22,25)(26,39)(28,31)(29,35)(30,32)(34,37)(38,40);(5,6)(7,8)(9,10)(11,19)(12,17)(13,18)(14,16)(15,23)(20,28)(21,37)(22,36)(24,35)(25,32)(26,31)(27,30)(29,38)(33,39)(34,40)

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#10598680, #14279609, C₃×#10598679, …
maximal normal subgroup of	C₃×#10598680, #14279609, C₃×#10598679, …
maximal quotient of	C₃×#10599981, C₃×#10600118, C₃×Dic₅×D₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4004);