Finite Group Databasebeta

C2×C9×Dic22 #13096968

order1584
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C23×C9 · Schur multiplier (H2) = C22

Aliases

direct productC2×C9×Dic22
unambiguous semidirect product(C2×C11)⋊(Q8×C9)

Splittings

HallC9×C11 ⋊ C2×Q8
SylowC11 ⋊ C2×Q8×C9

Subgroups

subgroupG/H
centerC22×C9C2×D11
commutatorC2×C11C23×C9
FrattiniC2×C3C22×C3×D11
FittingC2×C4×C9×C11C2
socle, prime radicalC22×C3×C11C22×C3
cosocleC2×C3×C11C23×C3
hypercenterC2×C4×C9D11
hypocenterC11C2×Q8×C9
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C9 ◁ C2×C4×C9

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1584

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 132);