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C3×#65858 #11755535

order960
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×#65858

Splittings

FittingC3×C5×#117 ⋊ C2
HallC3×C5 ⋊ #525
SylowC5 ⋊ C3×#525

Subgroups

subgroupG/H
centerC2×C3×C4C22×D5
commutator, cosocleC22×C5C24×C3
FrattiniC22C23×C3×D5
FittingC3×C5×#117C2
socleC22×C3×C5C24
hypercenterC3×#117D5
hypocenterC5C3×#525
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×#117

660 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);(13,15,16,19)(14,17,18,20);(13,14)(15,17)(16,18)(19,20);(5,6)(7,8)(10,12)

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10604346, #14282827, C3×#10604347, …
maximal normal subgroup ofC3×#10604346, #14282827, C3×#10604347, …
maximal quotient ofC3×#10613998, C3×#10605145, C3×#10613958, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9730);