Finite Group Databasebeta

C2×#13118165 #16030475

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13118165

Splittings

FittingC2×C13×#385 ⋊ C2
SylowC13 ⋊ C2×#2405

Subgroups

subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#385C2
socleC24×C13C24
prime radicalC24×D52C2
hypercenterC2×#385D13
hypocenterC13C2×#2405
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

7822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 337124);