Finite Group Databasebeta

C22×#11718125 #15860371

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11718125

Splittings

SylowC13 ⋊ C22×#344

Subgroups

subgroupG/H
centerC22×C4#6103
commutatorC22×C13C22×C42
FrattiniC22×C4C23×D13
FittingC22×C13×#117C2
socleC23×C13#95
prime radicalC25×C13C2×C4
cosocleC22×C4×C13C24
hypercenterC22×#117D13
hypocenterC13C22×#344
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×#117

2190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 167020);