Finite Group Databasebeta

C22×#11718568 #16769384

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

Aliases

direct productC22×#11718568

Splittings

FittingC22×C13×M32 ⋊ C2
SylowC13 ⋊ C22×#504

Subgroups

subgroupG/H
centerC22×C8C22×D13
commutatorC2×C13C24×C8
FrattiniC8C24×D13
FittingC22×C13×M32C2
socleC23×C13C22×C8
prime radicalC22×#6127C4
cosocleC8×C13C25
hypercenterC22×M32D13
hypocenterC13C22×#504
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C22×M32

2118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076033);