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C5×#120⋊C9 #13084339

order1440
isoclinismisoclinic class of #120⋊C3
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C22

Aliases

direct productC5×#120⋊C9
unambiguous semidirect product#120⋊(C5×C9)
unambiguous semidirect product(C5×#120)⋊C9

Splittings

derivedC24 ⋊ C2×C5×C9
HallC5×#120 ⋊ C9
Sylow#120 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5#120⋊C3
commutator, hypocenterC24C2×C5×C9
FrattiniC22×C3C2×C5×A4
Fitting, prime radicalC3×C5×#120C3
socleC22×C3×C5C2×A4
cosocleC24×C3C2×C3×C5
LCSG ▷ C24
UCSC1 ◁ C3×C5

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 180

A minimal faithful permutation representation — 2 generators on 22 points:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 656);