Finite Group Databasebeta

#261×#350 #16789313

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#261×#350

Splittings

FittingC13×#350 ⋊ C4
SylowC13 ⋊ C4×#350

Subgroups

subgroupG/H
centerC8D4×#261
commutatorC4×C13C2×C4×C8
FrattiniC2×C8C22×#261
FittingC13×#350C4
socleC2×C13C4×C22⋊C8
prime radical#41×D13C2×C4
cosocleC2×C8×D13C23
hypercenter#350#261
hypocenterC13C4×#350
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C8 ◁ #350

490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1095962);