Finite Group Databasebeta

C22×#11718401 #16726382

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×#11718401

Splittings

FittingC22×C13×#99 ⋊ C2
SylowC13 ⋊ C22×#410

Subgroups

subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC22×C13×#99C2
socleC23×C13C2×C22⋊C4
prime radicalC23×#6129C2
cosocleC23×C13C25
hypercenterC22×#99D13
hypocenterC13C22×#410
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

5278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033031);