Finite Group Databasebeta

C22×#11719205 #16769689

order3328
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×#11719205

Splittings

SylowC13 ⋊ C22×#544

Subgroups

subgroupG/H
centerC24C23×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC23×C13×C4⋊C4C2
socleC24×C13C24
prime radicalC25×C13C23
hypercenterC23×C4⋊C4D13
hypocenterC13C22×#544
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4⋊C4

7630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1076338);