Finite Group Databasebeta

C2×#13123477 #16726654

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#13123477

Splittings

FittingC2×C13×#433 ⋊ C2
SylowC13 ⋊ C2×#2922

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C13×#433C2
socleC23×C13C23×C4
prime radicalC22×#6127C22
cosocleC2×C4×C13C25
hypercenterC2×#433D13
hypocenterC13C2×#2922
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#433

2222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033303);