Finite Group Databasebeta

C22×#11719158 #16808408

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11719158

Splittings

SylowC13 ⋊ C22×#446

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC23×Q8×C13C4
socle, prime radicalC24×C13C22×C4
cosocleC2×Dic13C25
hypercenterC23×Q8#261
hypocenterC13C22×#446
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×Q8

2222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

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, 1115057);