Finite Group Databasebeta

C22×#11718238 #16796801

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11718238

Splittings

FittingC22×C13×C22⋊C4 ⋊ C4
SylowC13 ⋊ C22×#342

Subgroups

subgroupG/H
centerC23(C2×#261)⋊C4
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC22×C13×C22⋊C4C4
socleC23×C13#95
prime radicalC25×D13C22
cosocleC23×D13C24
hypercenterC22×C22⋊C4#261
hypocenterC13C22×#342
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

4334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103450);