Finite Group Databasebeta

#1616×D83 #35376624

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct product#1616×D83

Splittings

FittingC83×#1616 ⋊ C2
SylowC83 ⋊ C2×#1616

Subgroups

subgroupG/H
centerC22#120×D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#1616C2
socleC22×C83C2×#120
prime radical#537×D83C2
hypercenter#1616D83
hypocenterC83C2×#1616
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1616

1264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 141788);