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C9×#3961 #13083790

order1440
isoclinismisoclinic class of #3958
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×#3961

Splittings

HallC5×C9 ⋊ Q32
SylowC5 ⋊ C9×Q32

Subgroups

subgroupG/H
centerC2×C9#686
commutatorC5×C8C22×C9
FrattiniC3×C8C2×C3×D5
FittingC5×C9×Q16C2
socle, prime radicalC2×C3×C5C3×D8
cosocleC3×C5×C8C22×C3
hypercenterC9×Q16D5
hypocenterC5C9×Q32
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C9 ◁ C4×C9 ◁ C8×C9 ◁ C9×Q16

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 1440

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2,3,4,5,6,7,8,9)(10,11,13,14,12)(15,17,20,28)(16,21,24,38)(18,30,33,46)(19,35,31,27)(22,40,41,45)(23,42,34,37)(25,43,44,29)(26,39,36,32);(11,12)(13,14)(15,16,20,24)(17,25,28,44)(18,29,33,43)(19,34,31,23)(21,36,38,26)(22,39,41,32)(27,45,35,40)(30,42,46,37)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 107);