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C3×#64737 #11746094

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

Aliases

direct productC3×#64737

Splittings

HallC3×C5 ⋊ #362
SylowC5 ⋊ C3×#362

Subgroups

subgroupG/H
centerC2×C3#3953
commutatorC5×C8C2×C3×C4
FrattiniC2×C8C2×C3×D5
FittingC3×C5×M32C2
socleC2×C3×C5#102
prime radicalC22×C3×C5SD16
cosocleC2×C5×C8C22×C3
hypercenterC3×M32D5
hypocenterC5C3×#362
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×M32

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

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×#362, C2×C3×#64737, #14314232, …
maximal normal subgroup ofC3×D5×#362, C2×C3×#64737, #14314232, …
maximal quotient ofC3×#10598008, C3×#10598020, C3×#10598052, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 289);