Finite Group Databasebeta

C9×D108 #14515930

order1944
isoclinismisoclinic class of Dic54
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC9×D108
unambiguous semidirect productC4⋊(C9×D27)

Splittings

FittingC4×C9×C27 ⋊ C2
SylowC9×C27 ⋊ D4

Subgroups

subgroupG/H
centerC2×C9C2×D27
commutatorC2×C27C22×C9
FrattiniC2×C3×C9C2×C3×D3
FittingC4×C9×C27C2
socleC2×C32C2×C3×D9
prime radicalC3×D108C3
cosocleC2×C3×C27C22×C3
hypercenterC4×C9D27
hypocenterC27D4×C9
LCSG ▷ C2×C27 ▷ C27
UCSC1 ◁ C2×C9 ◁ C4×C9

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 324);