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Cayley diagram

C3×#3952 #91022

order480
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×#3952

Splittings

FittingC2×C3×C5×C8 ⋊ C2
HallC3×C5 ⋊ C22⋊C8
SylowC5 ⋊ C3×C22⋊C8

Subgroups

subgroupG/H
centerC2×C3×C4C2×D5
commutatorC2×C5C2×C3×C8
FrattiniC2×C4C2×C3×D5
FittingC2×C3×C5×C8C2
socleC22×C3×C5C2×C4
prime radicalC22×C3×D5C4
cosocleC2×C4×C5C22×C3
hypercenterC2×C3×C8D5
hypocenterC5C3×C22⋊C8
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C8

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 2 generators on 20 points:

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

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11747576, #11747577, #11747587, …
maximal normal subgroup of#11747576, #11747577, #11747587, …
maximal quotient ofC3×#64676, C3×#64679, C3×#64688, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 98);