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C3×#64669 #11746026

order960
isoclinismisoclinic class of D160
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×#64669

Splittings

FittingC3×C5×C32 ⋊ C2
HallC3×C5 ⋊ SD64
SylowC5 ⋊ C3×SD64

Subgroups

subgroupG/H
centerC2×C3D80
commutator, cosocleC5×C16C22×C3
FrattiniC16C2×C3×D5
FittingC3×C5×C32C2
socleC2×C3×C5D16
prime radicalC3×D80C2
hypercenterC3×C32D5
hypocenterC5C3×SD64
LCSG ▷ C5×C16 ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×C16 ◁ C3×C32

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3)(4,5,7,8,6)(9,10,16,28,25,33,37,34,13,18,31,40,24,39,11,15,14,19,20,36,12,17,22,29,26,35,38,32,21,27,23,30);(5,6)(7,8)(10,15)(11,20)(12,24)(13,26)(16,23)(17,32)(18,34)(19,30)(21,25)(22,31)(27,36)(28,39)(29,35)(33,40)(37,38)

Conjugacy classes & character table

249 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×SD64, C2×C3×#64669, #14319180, …
maximal normal subgroup ofC3×D5×SD64, C2×C3×#64669, #14319180, …
maximal quotient ofC3×#10598087, C3×#10598088, C3×#10598083, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 221);