Finite Group Databasebeta

C22×#11719106 #16808350

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11719106
unambiguous semidirect productD13⋊(C2×#440)

Splittings

FittingC22×C13×SD16 ⋊ C4
SylowC13 ⋊ C22×#440

Subgroups

subgroupG/H
centerC23D4×#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC22×C13×SD16C4
socleC23×C13C4×D4
prime radicalC22×D4×D13C22
cosocleC4×D13C25
hypercenterC22×SD16#261
hypocenterC13C22×#440
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

3222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114999);