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C5×#127⋊C9 #13084341

order1440
isoclinismisoclinic class of #127⋊C3
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C4

Aliases

direct productC5×#127⋊C9
unambiguous semidirect product#127⋊(C5×C9)
unambiguous semidirect product(C5×#127)⋊C9

Splittings

derivedC42 ⋊ C2×C5×C9
HallC5×#127 ⋊ C9
Sylow#127 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5#127⋊C3
commutator, hypocenterC42C2×C5×C9
FrattiniC22×C3C2×C5×A4
Fitting, prime radicalC3×C5×#127C3
socleC22×C3×C5C2×A4
cosocleC3×C42C2×C3×C5
LCSG ▷ C42
UCSC1 ◁ C3×C5

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 180

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5)(6,7,10)(8,16,15,13,11,17)(9,12,14)(18,22,26,20,25,21,23,19,24);(6,13,9,8)(10,15,14,17)

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, 658);