Finite Group Databasebeta

C22×#11718901 #16726384

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

Aliases

direct productC22×#11718901

Splittings

SylowC13 ⋊ C22×#410

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
Fitting, prime radicalC23×C13×#41C2
socleC23×C13C2×C22⋊C4
cosocleC23×C13C25
hypercenterC23×#41D13
hypocenterC13C22×#410
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×#41

5278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033033);