Finite Group Databasebeta

#261×#509 #16807195

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#261×#509

Splittings

FittingC13×#509 ⋊ C4
SylowC13 ⋊ C4×#509

Subgroups

subgroupG/H
centerC2C2×D8×#261
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC13×#509C4
socleC2×C13C2×C4×D8
prime radicalD13×#509C2
cosocleC8×D13C24
hypercenter#509#261
hypocenterC13C4×#509
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113844);