Finite Group Databasebeta

C2×#13116485 #16015650

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13116485

Splittings

FittingC2×C13×#410 ⋊ C2
SylowC13 ⋊ C2×#2122

Subgroups

subgroupG/H
centerC22C2×#88046
commutatorC23×C13C23×C4
FrattiniC2×D4C23×D13
FittingC2×C13×#410C2
socleC22×C13C2×#99
prime radicalC2×#11719535C2
cosocleC2×D4×C13C24
hypercenterC2×#410D13
hypocenterC13C2×#2122
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

1406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 322299);