Finite Group Databasebeta

#1513×D83 #35371655

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

Aliases

direct product#1513×D83

Splittings

FittingC83×#1513 ⋊ C2
SylowC83 ⋊ C2×#1513

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1513C2
socleC22×C83C22×C22⋊C4
prime radical#525×D83C2
cosocleC22×C4×C83C24
hypercenter#1513D83
hypocenterC83C2×#1513
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

1510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

1118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 136819);