Finite Group Databasebeta

← Prev (#91052) Next (#91054) →

Cayley diagram

C5×#810 #91053

order480
isoclinismisoclinic class of #213
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#810

Splittings

HallC3×C5 ⋊ #103
SylowC3 ⋊ C5×#103

Subgroups

subgroupG/H
centerC22×C5#67
commutatorC3×C4C2×C4×C5
FrattiniC2×C4C2×C5×D3
FittingC3×C5×C4⋊C4C2
socle, prime radicalC22×C3×C5D4
cosocleC2×C3×C4C22×C5
hypercenterC5×C4⋊C4D3
hypocenterC3C5×#103
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C5×C4⋊C4

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11747140, #11747145, #11747156, …
maximal normal subgroup of#11747140, #11747145, #11747156, …
maximal quotient ofC5×#4452, C5×#4481, C5×#4484, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 129);