Finite Group Databasebeta

C22×#11718107 #16015617

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11718107

Splittings

FittingC22×C13×M32 ⋊ C2
SylowC13 ⋊ C22×#350

Subgroups

subgroupG/H
centerC22×C8C22⋊D13
commutatorC4×C13C23×C8
FrattiniC2×C8C23×D13
FittingC22×C13×M32C2
socleC23×C13C22⋊C8
prime radicalC22×#6127C4
cosocleC2×C8×C13C24
hypercenterC22×M32D13
hypocenterC13C22×#350
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C22×M32

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322266);