Finite Group Databasebeta

C22×#11718145 #16015605

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

Aliases

direct productC22×#11718145

Splittings

SylowC13 ⋊ C22×#349

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic13
commutatorC22×C13C23×C8
FrattiniC2×C8C23×D13
FittingC23×C13×M16C2
socleC23×C13C22⋊C8
prime radicalC25×C13C8
cosocleC2×C8×C13C24
hypercenterC23×M16D13
hypocenterC13C22×#349
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C23×M16

1262 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, 322254);