Finite Group Databasebeta

#261×#413 #16796987

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct product#261×#413

Splittings

FittingC13×#413 ⋊ C4
SylowC13 ⋊ C4×#413

Subgroups

subgroupG/H
centerC4C22⋊C4×#261
commutatorC22×C13C22×C42
FrattiniC2×C4C23×#261
FittingC13×#413C4
socleC2×C13C2×C4×C22⋊C4
prime radicalC2×#41×D13C22
cosocleC2×C4×D13C24
hypercenter#413#261
hypocenterC13C4×#413
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

1570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

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, 1103636);