Finite Group Databasebeta

#1945×D83 #35407809

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#1945×D83

Splittings

FittingC83×#1945 ⋊ C2
SylowC83 ⋊ C2×#1945

Subgroups

subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1945C2
socleC22×C83C2×C4×D4
prime radicalC23×D83#41
cosocleC22×C4×C83C24
hypercenter#1945D83
hypocenterC83C2×#1945
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1945

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

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, 172973);