Finite Group Databasebeta

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Cayley diagram

C5×#947 #91750

order480
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#947

Splittings

FittingC2×C3×C5×Q8 ⋊ C2
HallC3×C5 ⋊ #124
SylowC3 ⋊ C5×#124

Subgroups

subgroupG/H
centerC22×C5C22×D3
commutator, cosocleC22×C3C23×C5
FrattiniC22C22×C5×D3
FittingC2×C3×C5×Q8C2
socleC22×C3×C5C23
prime radicalC2×C5×D12C2
hypercenterC2×C5×Q8D3
hypocenterC3C5×#124
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C5×Q8

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746013, C5×#4477, #11749188, …
maximal normal subgroup of#11746013, C5×#4477, #11749188, …
maximal quotient ofC5×#4977, C5×#4986, C5×#4988, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 826);