Finite Group Databasebeta

C2×#13116540 #16015798

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13116540

Splittings

FittingC2×C13×#357 ⋊ C2
SylowC13 ⋊ C2×#2138

Subgroups

subgroupG/H
centerC23D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC2×C13×#357C2
socleC23×C13C2×D8
prime radicalC22×#88166C2
cosocleC2×C8×C13C24
hypercenterC2×#357D13
hypocenterC13C2×#2138
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

1190 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, 322447);