Finite Group Databasebeta

C22×#11718216 #16806712

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11718216

Splittings

FittingC22×C13×C16 ⋊ C4
SylowC13 ⋊ C22×#346

Subgroups

subgroupG/H
centerC22×C8C2×#261
commutatorC2×C13C22×C4×C8
FrattiniC8C23×#261
FittingC22×C13×C16C4
socleC23×C13C4×C8
prime radicalC23×D13C2×C8
cosocleC8×D13C24
hypercenterC22×C16#261
hypocenterC13C22×#346
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C22×C16

942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113361);