Finite Group Databasebeta

#1914×D83 #35406423

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct product#1914×D83

Splittings

FittingC83×#1914 ⋊ C2
SylowC83 ⋊ C2×#1914

Subgroups

subgroupG/H
centerC2#386×D83
commutatorC23×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1914C2
socleC2×C83C2×#386
prime radical#535×D83C2
cosocleC22×C4×C83C24
hypercenter#1914D83
hypocenterC83C2×#1914
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1914

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1328

Conjugacy classes & character table

1247 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 171587);