Finite Group Databasebeta

← Prev (#11746072) Next (#11746074) →

C3×#64716 #11746073

order960
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#64716

Splittings

HallC3×C5 ⋊ #362
SylowC5 ⋊ C3×#362

Subgroups

subgroupG/H
centerC2×C3#3941
commutatorC5×C8C2×C3×C4
FrattiniC2×C8C2×C3×D5
FittingC3×C5×#108C2
socleC2×C3×C5#102
prime radicalC22×C3×C5SD16
cosocleC2×C5×C8C22×C3
hypercenterC3×#108D5
hypocenterC5C3×#362
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#108

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×#362, C2×C3×#64716, #14314220, …
maximal normal subgroup ofC3×D5×#362, C2×C3×#64716, #14314220, …
maximal quotient ofC3×#10597957, C3×#10597979, C3×#10597965, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 268);