Finite Group Databasebeta

#261×#447 #16799769

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct product#261×#447

Splittings

FittingC13×#447 ⋊ C4
SylowC13 ⋊ C4×#447

Subgroups

subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#447C4
socleC22×C13C2×C4×D4
prime radicalD13×#447C2
cosocleC2×C4×D13C24
hypercenter#447#261
hypocenterC13C4×#447
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

1964 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

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, 1106418);