Finite Group Databasebeta

C2×#13115215 #15864420

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

Aliases

direct productC2×#13115215

Splittings

FittingC2×C13×#390 ⋊ C2
SylowC13 ⋊ C2×#1883

Subgroups

subgroupG/H
centerC23#88191
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#390C2
socleC23×C13#120
prime radicalC22×#88186C2
cosocleC22×C4×C13C24
hypercenterC2×#390D13
hypocenterC13C2×#1883
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#390

2018 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, 171069);