Finite Group Databasebeta

C2×#13123356 #16726462

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13123356

Splittings

FittingC23×C13×M16 ⋊ C2
SylowC13 ⋊ C2×#2896

Subgroups

subgroupG/H
centerC22×C4C2×D52
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC23×C13×M16C2
socleC23×C13C22×D4
prime radicalC23×#6127C2
cosocleC2×C4×C13C25
hypercenterC23×M16D13
hypocenterC13C2×#2896
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×M16

5198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033111);