Finite Group Databasebeta

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C3×#64944 #11749552

order960
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×#64944

Splittings

HallC3×C5 ⋊ #387
SylowC5 ⋊ C3×#387

Subgroups

subgroupG/H
centerC23×C3C22×D5
commutatorC22×C5C22×C3×C4
FrattiniC23C22×C3×D5
FittingC3×C5×#95C2
socle, prime radicalC23×C3×C5C23
cosocleC23×C5C23×C3
hypercenterC3×#95D5
hypocenterC5C3×#387
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#95

308 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)(9,11,12,10)(13,14,15,16)(18,22)(21,24);(9,10,12,11)(14,16)(17,19,20,23)(18,21,22,24);(5,6)(7,8)(9,10,12,11)(17,18)(19,21)(20,22)(23,24)

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×#387, C2×C3×#64944, #14320423, …
maximal normal subgroup ofC3×D5×#387, C2×C3×#64944, #14320423, …
maximal quotient ofC3×#10600196, C3×#10600199, C3×#10600200, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3747);