Finite Group Databasebeta

C2×#13116250 #15891655

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

Aliases

direct productC2×#13116250

Splittings

FittingC2×C13×#382 ⋊ C2
SylowC13 ⋊ C2×#2073

Subgroups

subgroupG/H
centerC24C2×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#382C2
socleC24×C13C2×D4
prime radicalC23×D52C22
hypercenterC2×#382D13
hypocenterC13C2×#2073
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#382

1278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 198304);