Finite Group Databasebeta

← Prev (#11755555) Next (#11755557) →

C3×#65879 #11755556

order960
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#65879

Splittings

FittingC3×C4×C5×D4 ⋊ C2
HallC3×C5 ⋊ #518
SylowC5 ⋊ C3×#518

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutatorC2×C5C23×C3×C4
FrattiniC22C23×C3×D5
FittingC3×C4×C5×D4C2
socleC22×C3×C5C24
prime radicalC2×C3×D4×D5C2
cosocleC22×C5C24×C3
hypercenterC3×C4×D4D5
hypocenterC5C3×#518
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×D4

676 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10611318, C3×#10611378, C3×#10611597, …
maximal normal subgroup ofC3×#10611318, C3×#10611378, C3×#10611597, …
maximal quotient ofC3×#10605291, C3×#10605481, C3×#10605167, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9751);