Finite Group Databasebeta

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Cayley diagram

C3×#3954 #91024

order480
isoclinismisoclinic class of #686
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#3954

Splittings

HallC3×C5 ⋊ #108
SylowC5 ⋊ C3×#108

Subgroups

subgroupG/H
centerC3×C4C22⋊D5
commutatorC4×C5C2×C3×C4
FrattiniC2×C4C2×C3×D5
FittingC3×C5×M16C2
socleC2×C3×C5C4⋊C4
prime radicalC22×C3×C5Q8
cosocleC2×C4×C5C22×C3
hypercenterC3×M16D5
hypocenterC5C3×#108
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×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:

(1,2,4,5,3)(6,17,10,8,11,19,9,18)(7,16,14,12,15,21,13,20)(22,23,24);(2,3)(4,5)(6,14,9,7,11,13,10,15)(8,20,19,16,18,12,17,21)

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#3954, #11748170, #11748172, …
maximal normal subgroup ofD3×#3954, #11748170, #11748172, …
maximal quotient ofC3×#64699, C3×#64700, C3×#64778, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 100);