Finite Group Databasebeta

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C3×#64964 #11749572

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

Aliases

direct productC3×#64964

Splittings

FittingC3×C5×#95 ⋊ C2
HallC3×C5 ⋊ #397
SylowC5 ⋊ C3×#397

Subgroups

subgroupG/H
centerC23×C3C22×D5
commutator, cosocleC23×C5C23×C3
FrattiniC23C22×C3×D5
FittingC3×C5×#95C2
socleC23×C3×C5C23
prime radicalC23×C3×D5C22
hypercenterC3×#95D5
hypocenterC5C3×#397
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#95

340 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

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)(13,14)(15,16)(17,19,20,23)(18,21,22,24);(5,6)(7,8)(14,15)(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×#397, C2×C3×#64964, #14331746, …
maximal normal subgroup ofC3×D5×#397, C2×C3×#64964, #14331746, …
maximal quotient ofC3×#10600221, C3×#10600222, C3×#10600207, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3767);