Finite Group Databasebeta

C2×#13123370 #16726478

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

Aliases

direct productC2×#13123370

Splittings

FittingC22×C13×#131 ⋊ C2
SylowC13 ⋊ C2×#2898

Subgroups

subgroupG/H
centerC23C22×D52
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#131C2
socleC23×C13C22×D4
prime radicalC22×#88257C2
cosocleC2×C4×C13C25
hypercenterC22×#131D13
hypocenterC13C2×#2898
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×#131

4882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1033127);