Finite Group Databasebeta

C42×#6122 #16796727

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43

Aliases

direct productC42×#6122

Splittings

SylowC13 ⋊ C42×M16

Subgroups

subgroupG/H
centerC2×C42C2×#261
commutatorC2×C13C2×C43
FrattiniC23C23×#261
FittingC22×C42×C13C4
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC22×C42#261
hypocenterC13C42×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C22×C42

1734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1103376);