Finite Group Databasebeta

C22×#11718289 #16796802

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11718289

Splittings

FittingC24×C4×C13 ⋊ C4
SylowC13 ⋊ C22×#342

Subgroups

subgroupG/H
centerC24C22⋊#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC24×C4×C13C4
socleC24×C13C22⋊C4
prime radicalC25×D13C22
cosocleC23×D13C24
hypercenterC24×C4#261
hypocenterC13C22×#342
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C25 ◁ C24×C4

4334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103451);