Finite Group Databasebeta

#261×#535 #16807550

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct product#261×#535

Splittings

FittingC13×#535 ⋊ C4
SylowC13 ⋊ C4×#535

Subgroups

subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#535C4
prime radicalD13×#535C2
cosocleC22×D13C25
hypercenter#535#261
hypocenterC13C4×#535
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #535

3602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#261×#3484, #261×#3498
maximal normal subgroup of#261×#3484, #261×#3498

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114199);