Finite Group Databasebeta

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C9×#3959 #13083788

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

Aliases

direct productC9×#3959

Splittings

HallC5×C9 ⋊ SD32
SylowC5 ⋊ C9×SD32

Subgroups

subgroupG/H
centerC2×C9#686
commutatorC5×C8C22×C9
FrattiniC3×C8C2×C3×D5
FittingC5×C9×D8C2
socleC2×C3×C5C3×D8
prime radicalC3×C5×D8C2×C3
cosocleC3×C5×C8C22×C3
hypercenterC9×D8D5
hypocenterC5C9×SD32
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C9 ◁ C4×C9 ◁ C8×C9 ◁ C9×D8

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 720

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7,8,9)(10,11,13,14,12)(16,20)(17,24)(18,25)(21,22)(23,29)(26,30)(27,28);(11,12)(13,14)(15,16,19,23)(17,20,26,29)(18,27,25,22)(21,30,28,24)

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, 105);