Finite Group Databasebeta

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C9×#3951 #13083779

order1440
isoclinismisoclinic class of #677
automorphism?
homologyAbelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×#3951

Splittings

HallC5×C9 ⋊ #108
SylowC5 ⋊ C9×#108

Subgroups

subgroupG/H
centerC4×C9D20
commutatorC4×C5C2×C4×C9
FrattiniC2×C3×C4C2×C3×D5
FittingC2×C5×C8×C9C2
socleC2×C3×C5C3×C4⋊C4
prime radicalC22×C3×C5C3×Q8
cosocleC2×C3×C4×C5C22×C3
hypercenterC2×C8×C9D5
hypocenterC5C9×#108
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C9 ◁ C2×C4×C9 ◁ C2×C8×C9

90 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)(15,17,19,26,20,27,18,25)(16,21,22,24,23,29,28,30);(11,12)(13,14)(15,16,18,22,20,23,19,28)(17,24,25,29,27,30,26,21)

Conjugacy classes & character table

414 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 96);