Finite Group Databasebeta

#261×#536 #16807551

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#261×#536

Splittings

FittingC13×#536 ⋊ C4
SylowC13 ⋊ C4×#536

Subgroups

subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#536C4
prime radicalC2×#41×D13C22
cosocleC22×D13C25
hypercenter#536#261
hypocenterC13C4×#536
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #536

2962 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114200);