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C3×#65791 #11752324

order960
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×#65791

Splittings

HallC3×C5 ⋊ #504
SylowC5 ⋊ C3×#504

Subgroups

subgroupG/H
centerC3×C4C22×AGL(1,𝔽5)
commutatorC2×C5C22×C3×C8
FrattiniC4C22×C3×AGL(1,𝔽5)
Fitting, prime radicalC3×C5×#41C4
socleC2×C3×C5C22×C8
cosocle#168C23×C3
hypercenterC3×#41AGL(1,𝔽5)
hypocenterC5C3×#504
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C3×#41

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10603999, C3×#10604861, #14315227, …
maximal normal subgroup ofC3×#10603999, C3×#10604861, #14315227, …
maximal quotient ofC3×#10604366, C3×#10605007, C3×#10604367, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 6519);