Finite Group Databasebeta

#2081×D83 #35433337

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#2081×D83

Splittings

FittingC83×#2081 ⋊ C2
SylowC83 ⋊ C2×#2081

Subgroups

subgroupG/H
centerC2#397×D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2081C2
socleC2×C83C2×#397
prime radicalC22×D4×D83C22
hypercenter#2081D83
hypocenterC83C2×#2081
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2081

1006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1328

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, 198501);