Finite Group Databasebeta

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C3×#64709 #11746066

order960
isoclinismisoclinic class of #3958
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#64709

Splittings

HallC3×C5 ⋊ #366
SylowC5 ⋊ C3×#366

Subgroups

subgroupG/H
centerC22×C3#686
commutatorC5×C8C2×C3×C4
FrattiniC2×C8C2×C3×D5
FittingC3×C5×#107C2
socle, prime radicalC22×C3×C5D8
cosocleC2×C5×C8C22×C3
hypercenterC3×#107D5
hypocenterC5C3×#366
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#107

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,3)(4,5,7,8,6)(9,10,11,12)(14,18)(15,22)(16,23)(19,20)(21,26)(24,28)(25,27);(5,6)(7,8)(13,14,15,19,23,27,28,26,17,21,24,25,16,20,22,18)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×#366, C2×C3×#64709, #14314552, …
maximal normal subgroup ofC3×D5×#366, C2×C3×#64709, #14314552, …
maximal quotient ofC3×#10597960, C3×#10598213, C3×#10598066, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 261);