Finite Group Databasebeta

#137×C22⋊D13 #16738586

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct product#137×C22⋊D13

Splittings

FittingC22×C13×#137 ⋊ C2
SylowC13 ⋊ D4×#137

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#137C2
socleC22×C13C23×D4
prime radical#41×C22⋊D13C2
hypercenterC22×#137D13
hypocenterC13D4×#137
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

2746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1045235);