Finite Group Databasebeta

C22×#11718587 #16726631

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

Aliases

direct productC22×#11718587

Splittings

SylowC13 ⋊ C22×#432

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC23×C42×C13C2
socleC24×C13C22×C4
prime radicalC25×C13C2×C4
cosocleC2×C4×C13C25
hypercenterC23×C42D13
hypocenterC13C22×#432
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C23×C42

2830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033280);