Finite Group Databasebeta

#137×Dic26 #16743522

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct product#137×Dic26

Splittings

SylowC13 ⋊ Q8×#137

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC4×C13×#137C2
socleC22×C13C23×D4
prime radicalC2×C13×#41C23
hypercenterC4×#137D13
hypocenterC13Q8×#137
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

1782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1050171);