Finite Group Databasebeta

#2008×D83 #35431393

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct product#2008×D83

Splittings

FittingC83×#2008 ⋊ C2
SylowC83 ⋊ C2×#2008

Subgroups

subgroupG/H
centerC2#392×D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2008C2
socleC2×C83C2×#392
hypercenter#2008D83
hypocenterC83C2×#2008
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2008

2118 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, 196557);