Finite Group Databasebeta

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Cayley diagram

C5×#835 #91078

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

Aliases

direct productC5×#835

Splittings

HallC3×C5 ⋊ #103
SylowC3 ⋊ C5×#103

Subgroups

subgroupG/H
centerC22×C5#67
commutatorC3×C4C2×C4×C5
FrattiniC2×C4C2×C5×D3
FittingC2×C3×C5×Q8C2
socle, prime radicalC22×C3×C5D4
cosocleC2×C3×C4C22×C5
hypercenterC2×C5×Q8D3
hypocenterC3C5×#103
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×Q8

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11749189, #11749190, D5×#835, …
maximal normal subgroup of#11749189, #11749190, D5×#835, …
maximal quotient ofC5×#4529, C5×#4535, C5×#4538, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 154);