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C9×#3960 #13083789

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

Aliases

direct productC9×#3960

Splittings

FittingC5×C9×Q16 ⋊ C2
HallC5×C9 ⋊ SD32
SylowC5 ⋊ C9×SD32

Subgroups

subgroupG/H
centerC2×C9#686
commutatorC5×C8C22×C9
FrattiniC3×C8C2×C3×D5
FittingC5×C9×Q16C2
socleC2×C3×C5C3×D8
prime radicalC3×D40C2×C3
cosocleC3×C5×C8C22×C3
hypercenterC9×Q16D5
hypocenterC5C9×SD32
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C9 ◁ C4×C9 ◁ C8×C9 ◁ C9×Q16

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)(15,16,19,22)(17,24,26,30)(18,27,25,21)(20,28,29,23);(11,12)(13,14)(16,20)(17,23)(18,25)(21,30)(22,29)(24,27)(26,28)

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, 106);