Finite Group Databasebeta

C2×#13115281 #15864675

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13115281

Splittings

FittingC22×C13×#104 ⋊ C2
SylowC13 ⋊ C2×#1897

Subgroups

subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#104C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#11719533C2
cosocleC22×C4×C13C24
hypercenterC22×#104D13
hypocenterC13C2×#1897
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

1954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 171324);