Finite Group Databasebeta

#1602×D83 #35376483

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

Aliases

direct product#1602×D83

Splittings

FittingC83×#1602 ⋊ C2
SylowC83 ⋊ C2×#1602

Subgroups

subgroupG/H
centerC22#120×D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#1602C2
socleC22×C83C2×#120
prime radicalC24×D83D4
hypercenter#1602D83
hypocenterC83C2×#1602
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1602

1308 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

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, 141647);