Finite Group Databasebeta

C2×#13114679 #15860756

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13114679

Splittings

FittingC2×C13×#341 ⋊ C2
SylowC13 ⋊ C2×#1765

Subgroups

subgroupG/H
centerC22×C4D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC2×C13×#341C2
socleC23×C13C4×D4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC2×#341D13
hypocenterC13C2×#1765
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#341

1518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167405);