Finite Group Databasebeta

← Prev (#14518857) Next (#14518859) →

C32×C9⋊SL(2,𝔽3) #14518858

order1944
isoclinismisoclinic class of C9⋊SL(2,𝔽3)
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC32×C9⋊SL(2,𝔽3)

Splittings

FittingC32×Q8×C9 ⋊ C3
SylowQ8 ⋊ C32×3−1+2

Subgroups

subgroupG/H
center, socleC2×C33C3×A4
commutator, cosocleC3×Q8C34
FrattiniC2×C3C33×A4
FittingC32×Q8×C9C3
prime radicalC33×SL(2,𝔽3)C3
hypercenterC2×C32×C9A4
hypocenterQ8C32×3−1+2
LCSG ▷ C3×Q8 ▷ Q8
UCSC1 ◁ C2×C33 ◁ C2×C32×C9

914 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 648

Conjugacy classes & character table

279 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3252);