Finite Group Databasebeta

← Prev (#11755594) Next (#11755596) →

C3×#65918 #11755595

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

Aliases

direct productC3×#65918

Splittings

FittingC3×C4×C5×Q8 ⋊ C2
HallC3×C5 ⋊ #556
SylowC5 ⋊ C3×#556

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C4×C5×Q8C2
socleC22×C3×C5C24
prime radicalC2×C3×D20C22
hypercenterC3×C4×Q8D5
hypocenterC5C3×#556
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8

424 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)(9,12,13,11)(10,14,15,16)(17,19,20,23)(18,21,22,24);(17,18,20,22)(19,24,23,21);(9,11,13,12)(10,14,15,16);(5,6)(7,8)(9,10)(11,16)(12,14)(13,15)(19,23)(21,24)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10601822, C3×#10599038, #14289325, …
maximal normal subgroup ofC3×#10601822, C3×#10599038, #14289325, …
maximal quotient ofC3×#10605365, C3×#10605369, C3×#10614193, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9790);