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C3×#65896 #11755573

order960
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C24

Aliases

direct productC3×#65896

Splittings

FittingC3×C4×C5×D4 ⋊ C2
HallC3×C5 ⋊ #540
SylowC5 ⋊ C3×#540

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C4×C5×D4C2
socleC22×C3×C5C24
hypercenterC3×C4×D4D5
hypocenterC5C3×#540
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3)(4,5,7,8,6)(10,14)(13,16)(17,20,21,19)(18,24,23,22);(10,14)(11,15)(18,23)(22,24);(9,11,12,15)(10,13,14,16)(17,19,21,20)(18,22,23,24);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,22)(20,24)(21,23)

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10611326, C3×#10611543, C3×#10611604, …
maximal normal subgroup ofC3×#10611326, C3×#10611543, C3×#10611604, …
maximal quotient ofC3×#10605491, C3×#10605492, C3×#10614056, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9768);