Finite Group Databasebeta

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C3×#64946 #11749554

order960
isoclinismisoclinic class of #64945
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×#64946

Splittings

HallC3×C5 ⋊ #398
SylowC5 ⋊ C3×#398

Subgroups

subgroupG/H
centerC23×C3C22×D5
commutator, cosocleC23×C5C23×C3
FrattiniC23C22×C3×D5
FittingC3×C5×#95C2
socle, prime radicalC23×C3×C5C23
hypercenterC3×#95D5
hypocenterC5C3×#398
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#95

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×#398, C2×C3×#64946, #14331803, …
maximal normal subgroup ofC3×D5×#398, C2×C3×#64946, #14331803, …
maximal quotient ofC3×#10600202, C3×#10600204, C3×#10600205, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3749);