Finite Group Databasebeta

C22×#11719057 #16807442

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C42

Aliases

direct productC22×#11719057
unambiguous semidirect productD13⋊(C2×#376)

Splittings

FittingC22×C42×C13 ⋊ C4
SylowC13 ⋊ C22×#376

Subgroups

subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C23×C42
FrattiniC22C24×#261
FittingC22×C42×C13C4
socleC24×C13C22×C4
prime radicalC24×D13C23
cosocleC22×D13C25
hypercenterC22×C42#261
hypocenterC13C22×#376
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C42

5150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114091);