Finite Group Databasebeta

C32×#6308 #14519462

order1944
isoclinismisoclinic class of #6308
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C34

Aliases

direct productC32×#6308

Splittings

SylowC35 ⋊ Q8

Subgroups

subgroupG/H
centerC2×C32C2×C3⋊(C3⋊D3)
commutator, cosocleC2×C33C22×C32
FrattiniC2C2×C32×C3⋊(C3⋊D3)
FittingC35×C4C2
socle, prime radicalC2×C35C22
hypercenterC32×C4C3⋊(C3⋊D3)
hypocenterC33C32×Q8
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C32 ◁ C32×C4

4752 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, 3856);