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C3×#65897 #11755574

order960
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×#65897

Splittings

FittingC3×C4×C5×D4 ⋊ C2
HallC3×C5 ⋊ #555
SylowC5 ⋊ C3×#555

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C4×C5×D4C2
socleC22×C3×C5C24
hypercenterC3×C4×D4D5
hypocenterC5C3×#555
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4

472 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)(17,19,20,24)(18,22,21,23);(10,14)(11,16)(18,21)(22,23);(9,11)(10,13)(12,16)(14,15)(18,21)(22,23);(5,6)(7,8)(9,10)(11,15)(12,14)(13,16)(17,18)(19,23)(20,21)(22,24)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10601810, C3×#10598992, #14289070, …
maximal normal subgroup ofC3×#10601810, C3×#10598992, #14289070, …
maximal quotient ofC3×#10605364, C3×#10605190, C3×#10605369, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9769);