Finite Group Databasebeta

C2×#13124238 #16729653

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×#13124238

Splittings

FittingC2×C13×#585 ⋊ C2
SylowC13 ⋊ C2×#3027

Subgroups

subgroupG/H
centerC22C2×#88207
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#585C2
socleC22×C13C2×#120
hypercenterC2×#585D13
hypocenterC13C2×#3027
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#585

5110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036302);