Finite Group Databasebeta

C22×#11718244 #16793284

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11718244

Splittings

SylowC13 ⋊ C22×Q8⋊C8

Subgroups

subgroupG/H
centerC24C22⋊#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC22×C13×C4⋊C4C4
socle, prime radicalC24×C13C22⋊C4
cosocleC4×Dic13C24
hypercenterC22×C4⋊C4#261
hypocenterC13C22×Q8⋊C8
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

1454 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, 1099933);