Finite Group Databasebeta

C2×#13115251 #15864567

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

Aliases

direct productC2×#13115251

Splittings

FittingC2×C13×#407 ⋊ C2
SylowC13 ⋊ C2×#1891

Subgroups

subgroupG/H
centerC2×C4#88191
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#407C2
socleC22×C13#386
prime radicalC2×#11719496C2
cosocleC22×C4×C13C24
hypercenterC2×#407D13
hypocenterC13C2×#1891
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

1870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 171216);