Finite Group Databasebeta

#261×#563 #16807816

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

Aliases

direct product#261×#563

Splittings

FittingC13×#563 ⋊ C4
SylowC13 ⋊ C4×#563

Subgroups

subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#563C4
prime radicalC2×D4×D13C23
cosocleC22×D13C25
hypercenter#563#261
hypocenterC13C4×#563
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #563

2024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

133 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114465);