Finite Group Databasebeta

← Prev (#11758900) Next (#11758902) →

C9×#1144 #11758901

order1008
isoclinismisoclinic class of #1141
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×#1144

Splittings

HallC7×C9 ⋊ Q16
SylowC7 ⋊ C9×Q16

Subgroups

subgroupG/H
centerC2×C9C22⋊D7
commutatorC4×C7C22×C9
FrattiniC3×C4C2×C3×D7
FittingC7×Q8×C9C2
socle, prime radicalC2×C3×C7C3×D4
cosocleC3×C4×C7C22×C3
hypercenterQ8×C9D7
hypocenterC7C9×Q16
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C9 ◁ C4×C9 ◁ Q8×C9

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1008

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5,6,7,8,9)(10,11,13,15,16,14,12)(17,19,21,27)(18,22,24,31)(20,29,30,26)(23,32,28,25);(11,12)(13,14)(15,16)(17,18,21,24)(19,25,27,32)(20,28,30,23)(22,29,31,26)

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 72);