Finite Group Databasebeta

C22×#11718336 #16029128

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11718336

Splittings

FittingC22×C13×#95 ⋊ C2
SylowC13 ⋊ C22×#397

Subgroups

subgroupG/H
centerC25C22×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#95C2
socleC25×C13C23
prime radicalC25×D13C22
hypercenterC22×#95D13
hypocenterC13C22×#397
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C25 ◁ C22×#95

5230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 335777);