Finite Group Databasebeta

C2×#13115279 #15864672

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

Aliases

direct productC2×#13115279

Splittings

FittingC23×C42×C13 ⋊ C2
SylowC13 ⋊ C2×#1896

Subgroups

subgroupG/H
centerC22×C4C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC23×C42×C13C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#11719496C2
cosocleC22×C4×C13C24
hypercenterC23×C42D13
hypocenterC13C2×#1896
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×C42

2514 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 171321);