Finite Group Databasebeta

C2×#13124569 #16730329

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

Aliases

direct productC2×#13124569

Splittings

FittingC22×C13×#137 ⋊ C2
SylowC13 ⋊ C2×#3069

Subgroups

subgroupG/H
centerC22C2×#88192
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#137C2
socleC22×C13C2×#121
prime radicalC2×#11719527C2
hypercenterC22×#137D13
hypocenterC13C2×#3069
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

2618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036978);