Finite Group Databasebeta

C2×#13127969 #16769422

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13127969

Splittings

FittingC2×C13×#508 ⋊ C2
SylowC13 ⋊ C2×#3414

Subgroups

subgroupG/H
centerC2×C4D8×D13
commutator, cosocleC8×C13C25
FrattiniC8C24×D13
FittingC2×C13×#508C2
socleC22×C13C22×D8
hypercenterC2×#508D13
hypocenterC13C2×#3414
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

2098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076071);