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C9×D40 #10623567

order720
isoclinismisoclinic class of #677
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC9×D40

Splittings

FittingC5×C8×C9 ⋊ C2
HallC5×C9 ⋊ D8
SylowC5 ⋊ C9×D8

Subgroups

subgroupG/H
centerC2×C9D20
commutatorC4×C5C22×C9
FrattiniC3×C4C2×C3×D5
FittingC5×C8×C9C2
socleC2×C3×C5C3×D4
prime radicalC3×D40C3
cosocleC3×C4×C5C22×C3
hypercenterC8×C9D5
hypocenterC5C9×D8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C9 ◁ C4×C9 ◁ C8×C9

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 360

A minimal faithful permutation representation — 2 generators on 22 points:

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

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13083700, #13083701, #13083702, …
maximal normal subgroup of#13083700, #13083701, #13083702, …
maximal quotient ofC9×#3932, C9×D80, C9×Dic40, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 36);