Finite Group Databasebeta

C32×#6229 #14518914

order1944
isoclinismisoclinic class of #6229
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C3

Aliases

direct productC32×#6229

Splittings

SylowC32×H(3,𝔽3) ⋊ Q8

Subgroups

subgroupG/H
center, socleC2×C33C2×C3⋊D3
commutator, cosocleC2×H(3,𝔽3)C22×C32
FrattiniC2×C3C2×C32×C3⋊D3
FittingC32×C4×H(3,𝔽3)C2
prime radicalC2×C32×H(3,𝔽3)C22
hypercenterC33×C4C3⋊D3
hypocenterH(3,𝔽3)C32×Q8
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C33 ◁ C33×C4

1332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 648

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3308);