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C3×#65862 #11755539

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

Aliases

direct productC3×#65862

Splittings

FittingC3×C5×#117 ⋊ C2
HallC3×C5 ⋊ #529
SylowC5 ⋊ C3×#529

Subgroups

subgroupG/H
centerC2×C3×C4C22×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×#117C2
socleC22×C3×C5C24
prime radicalC3×#4030C2
hypercenterC3×#117D5
hypocenterC5C3×#529
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×#117

468 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)(19,23)(21,24);(9,11,12,15)(10,13,14,16)(17,19)(18,21)(20,23)(22,24);(17,18,20,22)(19,21,23,24);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10610287, C3×#10611097, #14419217, …
maximal normal subgroup ofC3×#10610287, C3×#10611097, #14419217, …
maximal quotient ofC3×#10605144, C3×#10613999, C3×#10605145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9734);