Finite Group Databasebeta

#2076×D83 #35433236

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct product#2076×D83

Splittings

FittingC83×#2076 ⋊ C2
SylowC83 ⋊ C2×#2076

Subgroups

subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2076C2
socleC23×C83C22×D4
prime radicalC24×D83D4
hypercenter#2076D83
hypocenterC83C2×#2076
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2076

1270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

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, 198400);