Finite Group Databasebeta

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Cayley diagram

C5×#823 #91066

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

Aliases

direct productC5×#823

Splittings

FittingC3×C5×M16 ⋊ C2
HallC3×C5 ⋊ #100
SylowC3 ⋊ C5×#100

Subgroups

subgroupG/H
centerC2×C5(C2×D3)⋊C4
commutatorC22×C3C2×C4×C5
FrattiniC2×C4C2×C5×D3
FittingC3×C5×M16C2
socleC2×C3×C5C22⋊C4
prime radicalC2×C5×D12C2
cosocleC2×C3×C4C22×C5
hypercenterC5×M16D3
hypocenterC3C5×#100
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×M16

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 2 generators on 16 points:

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

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11748178, #11748181, #11748190, …
maximal normal subgroup of#11748178, #11748181, #11748190, …
maximal quotient ofC5×#4464, C5×#4468, C5×#4481, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 142);