Finite Group Databasebeta

C22×#11719147 #16808039

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

Aliases

direct productC22×#11719147

Splittings

SylowC13 ⋊ C22×#408

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC23×D4×C13C4
socleC24×C13C22×C4
prime radicalC23×#6129C2
cosocleC2×Dic13C25
hypercenterC23×D4#261
hypocenterC13C22×#408
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×D4

5326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114688);