Finite Group Databasebeta

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Cayley diagram

C5×#822 #91065

order480
isoclinismisoclinic class of #213
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#822

Splittings

HallC3×C5 ⋊ #108
SylowC3 ⋊ C5×#108

Subgroups

subgroupG/H
centerC4×C5#67
commutatorC3×C4C2×C4×C5
FrattiniC2×C4C2×C5×D3
FittingC3×C5×M16C2
socleC2×C3×C5C4⋊C4
prime radicalC22×C3×C5Q8
cosocleC2×C3×C4C22×C5
hypercenterC5×M16D3
hypocenterC3C5×#108
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C5×M16

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#822, #11748170, #11748171, …
maximal normal subgroup ofD5×#822, #11748170, #11748171, …
maximal quotient ofC5×#4479, C5×#4480, C5×#4558, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 141);