Finite Group Databasebeta

← Prev (#11746024) Next (#11746026) →

C3×D160 #11746025

order960
isoclinismisoclinic class of D160
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D160

Splittings

FittingC3×C5×C32 ⋊ C2
HallC3×C5 ⋊ D32
SylowC5 ⋊ C3×D32

Subgroups

subgroupG/H
centerC2×C3D80
commutator, cosocleC5×C16C22×C3
FrattiniC16C2×C3×D5
FittingC3×C5×C32C2
socleC2×C3×C5D16
hypercenterC3×C32D5
hypocenterC5C3×D32
LCSG ▷ C5×C16 ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×C16 ◁ C3×C32

68 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)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35)(36,37,38,39,40);(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)(37,40)(38,39)

Conjugacy classes & character table

249 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10598098, C3×D320, #14279811, …
maximal normal subgroup ofC3×#10598098, C3×D320, #14279811, …
maximal quotient ofC3×#10598087, C3×#10598082, C3×D320, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 220);