Finite Group Databasebeta

C22×#11718218 #16806743

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11718218

Splittings

FittingC22×C13×C16 ⋊ C4
SylowC13 ⋊ C22×#347

Subgroups

subgroupG/H
centerC22×C4C4×#261
commutatorC4×C13C22×C42
FrattiniC8C23×#261
FittingC22×C13×C16C4
socleC23×C13#97
prime radicalC23×D13M16
cosocleC8×D13C24
hypercenterC22×C16#261
hypocenterC13C22×#347
LCSG ▷ C4×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C16

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113392);