Finite Group Databasebeta

← Prev (#91061) Next (#91063) →

Cayley diagram

C5×#819 #91062

order480
isoclinismisoclinic class of #204
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#819

Splittings

HallC3×C5 ⋊ #108
SylowC3 ⋊ C5×#108

Subgroups

subgroupG/H
centerC4×C5D12
commutatorC3×C4C2×C4×C5
FrattiniC2×C4C2×C5×D3
FittingC2×C3×C5×C8C2
socleC2×C3×C5C4⋊C4
prime radicalC22×C3×C5Q8
cosocleC2×C3×C4C22×C5
hypercenterC2×C5×C8D3
hypocenterC3C5×#108
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C2×C5×C8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3)(4,16,8,14,9,6,7,15)(5,18,11,19,12,10,17,13)(20,21,22,23,24);(2,3)(4,12,7,17,9,5,8,11)(6,19,14,10,16,13,15,18)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745903, #11745908, #11745915, …
maximal normal subgroup of#11745903, #11745908, #11745915, …
maximal quotient ofC5×#4457, C5×#4458, C5×#4552, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 138);