Finite Group Databasebeta

#3266×D83 #36279377

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct product#3266×D83

Splittings

FittingC83×#3266 ⋊ C2
SylowC83 ⋊ C2×#3266

Subgroups

subgroupG/H
centerC22C22×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC83×#3266C2
socleC22×C83C23×D4
prime radical#546×D83C2
hypercenter#3266D83
hypocenterC83C2×#3266
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3266

2882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

1247 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1044541);