Finite Group Databasebeta

#2143×D83 #35557329

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

Aliases

direct product#2143×D83

Splittings

FittingC83×#2143 ⋊ C2
SylowC83 ⋊ C2×#2143

Subgroups

subgroupG/H
centerC4C2×D8×D83
commutatorC8×C83C23×C4
FrattiniC2×C8C23×D83
FittingC83×#2143C2
socleC2×C83C22×#102
prime radicalC2×#135×D83C2
cosocleC2×C8×C83C24
hypercenter#2143D83
hypocenterC83C2×#2143
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2143

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 322493);