Finite Group Databasebeta

C22×#11718270 #16806794

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11718270

Splittings

SylowC13 ⋊ C22×#350

Subgroups

subgroupG/H
centerC22×C4C22⋊#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC22×C13×M16C4
socleC23×C13C22⋊C8
prime radicalC22×#6127C4
cosocleC2×#1055C24
hypercenterC22×M16#261
hypocenterC13C22×#350
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113443);