Finite Group Databasebeta

C22×#11718882 #16021272

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×#11718882

Splittings

SylowC13 ⋊ C22×#390

Subgroups

subgroupG/H
centerC25C22×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
Fitting, prime radicalC24×D4×C13C2
socleC25×C13C23
cosocleC23×C13C25
hypercenterC24×D4D13
hypocenterC13C22×#390
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×D4

9534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327921);