Finite Group Databasebeta

C22×#11719162 #16809615

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11719162

Splittings

SylowC13 ⋊ C22×#504

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C24×C8
FrattiniC4C24×#261
Fitting, prime radicalC22×C13×#41C4
socleC23×C13C22×C8
cosocle#1055C25
hypercenterC22×#41#261
hypocenterC13C22×#504
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×#41

2118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1116264);