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C9×Dic20 #10623568

order720
isoclinismisoclinic class of #677
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×Dic20

Splittings

HallC5×C9 ⋊ Q16
SylowC5 ⋊ C9×Q16

Subgroups

subgroupG/H
centerC2×C9D20
commutatorC4×C5C22×C9
FrattiniC3×C4C2×C3×D5
FittingC5×C8×C9C2
socle, prime radicalC2×C3×C5C3×D4
cosocleC3×C4×C5C22×C3
hypercenterC8×C9D5
hypocenterC5C9×Q16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C9 ◁ C4×C9 ◁ C8×C9

54 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)(10,11,12,13,14,15,16,17)(18,25,24,23,22,21,20,19)(26,27,28,29,30);(10,18,14,22)(11,19,15,23)(12,20,16,24)(13,21,17,25)(27,30)(28,29)

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13083704, #13083705, #13083706, …
maximal normal subgroup of#13083704, #13083705, #13083706, …
maximal quotient ofC9×#3950, C9×#3948, C2×C9×Dic20

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 37);