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C3×#65908 #11755585

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

Aliases

direct productC3×#65908

Splittings

FittingC3×C4×C5×Q8 ⋊ C2
HallC3×C5 ⋊ #520
SylowC5 ⋊ C3×#520

Subgroups

subgroupG/H
centerC22×C3C23×D5
commutatorC2×C5C23×C3×C4
FrattiniC22C23×C3×D5
FittingC3×C4×C5×Q8C2
socleC22×C3×C5C24
prime radicalC2×C3×#713C2
cosocleC22×C5C24×C3
hypercenterC3×C4×Q8D5
hypocenterC5C3×#520
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8

588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10611378, C3×#10611506, #14417059, …
maximal normal subgroup ofC3×#10611378, C3×#10611506, #14417059, …
maximal quotient ofC3×#10605481, C3×#10605482, C3×#10614181, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9780);