Finite Group Databasebeta

#261×#576 #16808369

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

Aliases

direct product#261×#576

Splittings

FittingC13×#576 ⋊ C4
SylowC13 ⋊ C4×#576

Subgroups

subgroupG/H
centerC2C22×D4×#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC13×#576C4
socleC2×C13C22×C4×D4
prime radicalD13×#576C2
cosocleC4×D13C25
hypercenter#576#261
hypocenterC13C4×#576
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ #41 ◁ #576

2826 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, 1115018);