Finite Group Databasebeta

#2121×D83 #35557127

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

Aliases

direct product#2121×D83

Splittings

FittingC83×#2121 ⋊ C2
SylowC83 ⋊ C2×#2121

Subgroups

subgroupG/H
centerC2C2×#99×D83
commutatorC23×C83C23×C4
FrattiniC2×D4C23×D83
FittingC83×#2121C2
socleC2×C83C22×#99
prime radical#534×D83C2
cosocleC2×D4×C83C24
hypercenter#2121D83
hypocenterC83C2×#2121
LCSG ▷ C23×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #2121

1494 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, 322291);