Finite Group Databasebeta

← Prev (#11749735) Next (#11749737) →

C3×#65128 #11749736

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

Aliases

direct productC3×#65128

Splittings

FittingC3×C5×C4⋊C8 ⋊ C2
HallC3×C5 ⋊ #424
SylowC5 ⋊ C3×#424

Subgroups

subgroupG/H
centerC2×C3×C4C22×D5
commutatorC22×C5C22×C3×C4
FrattiniC2×C4C22×C3×D5
FittingC3×C5×C4⋊C8C2
socleC22×C3×C5C22×C4
prime radicalC22×C3×D5C2×C4
cosocleC2×C4×C5C23×C3
hypercenterC3×C4⋊C8D5
hypocenterC5C3×#424
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C4⋊C8

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×#424, C2×C3×#65128, #14413069, …
maximal normal subgroup ofC3×D5×#424, C2×C3×#65128, #14413069, …
maximal quotient ofC3×#10599325, C3×#10599365, C3×#10599326, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3931);