Finite Group Databasebeta

C2×#13131087 #16806808

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13131087

Splittings

FittingC24×C4×C13 ⋊ C4
SylowC13 ⋊ C2×#2120

Subgroups

subgroupG/H
centerC2×C4#88119
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC24×C4×C13C4
socleC22×C13C2×#99
prime radicalC2×#11719496C2
cosocleC2×C22⋊D13C24
hypercenterC24×C4#261
hypocenterC13C2×#2120
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

244 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113457);