Finite Group Databasebeta

C2×#13116815 #16016867

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13116815

Splittings

FittingC2×C13×#359 ⋊ C2
SylowC13 ⋊ C2×#2195

Subgroups

subgroupG/H
centerC22#11718434
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#359C2
socleC22×C13#447
prime radicalC2×#11719476C2
hypercenterC2×#359D13
hypocenterC13C2×#2195
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

1078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 323516);