Finite Group Databasebeta

#261×#568 #16808021

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct product#261×#568

Splittings

FittingC13×#568 ⋊ C4
SylowC13 ⋊ C4×#568

Subgroups

subgroupG/H
center, FrattiniC4C24×#261
commutator, socleC2×C13C23×C42
FittingC13×#568C4
prime radicalC2×#41×D13C22
cosocleC4×D13C25
hypercenter#568#261
hypocenterC13C4×#568
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ #568

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114670);