Finite Group Databasebeta

#1851×D83 #35405056

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#1851×D83

Splittings

FittingC83×#1851 ⋊ C2
SylowC83 ⋊ C2×#1851

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1851C2
prime radicalC24×D83C2×C4
cosocleC22×C4×C83C24
hypercenter#1851D83
hypocenterC83C2×#1851
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1851

1702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 170220);