Finite Group Databasebeta

C22×#11719417 #16769805

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

Aliases

direct productC22×#11719417

Splittings

FittingC22×C13×#126 ⋊ C2
SylowC13 ⋊ C22×#563

Subgroups

subgroupG/H
centerC24C23×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC22×C13×#126C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC22×#126D13
hypocenterC13C22×#563
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#126

7238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076454);