Finite Group Databasebeta

#2392×D83 #35570620

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

Aliases

direct product#2392×D83

Splittings

FittingC83×#2392 ⋊ C2
SylowC83 ⋊ C2×#2392

Subgroups

subgroupG/H
centerC22×C4C23×D83
commutator, socle, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC83×#2392C2
prime radical#392×D83C2
hypercenter#2392D83
hypocenterC83C2×#2392
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #2392

4134 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, 335784);