Finite Group Databasebeta

C2×#13113759 #15834995

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

Aliases

direct productC2×#13113759

Splittings

FittingC2×C13×#543 ⋊ C2
SylowC13 ⋊ C2×#1596

Subgroups

subgroupG/H
centerC23#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#543C2
socleC23×C13#120
prime radicalC2×#11718621C2
hypercenterC2×#543D13
hypocenterC13C2×#1596
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#543

1696 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, 141644);