Finite Group Databasebeta

C22×#11719631 #16809633

order3328
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×#11719631
unambiguous semidirect productD13⋊(C2×#520)

Splittings

FittingC22×C13×#41 ⋊ C4
SylowC13 ⋊ C22×#520

Subgroups

subgroupG/H
centerC23C23×#261
commutatorC2×C13C25×C4
FrattiniC2C25×#261
FittingC22×C13×#41C4
socleC23×C13C23×C4
prime radicalC22×#41×D13C2
cosocleC2×D13C26
hypercenterC22×#41#261
hypocenterC13C22×#520
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×#41

12270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1116282);