Finite Group Databasebeta

#2239×D83 #35559291

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

Aliases

direct product#2239×D83

Splittings

FittingC83×#2239 ⋊ C2
SylowC83 ⋊ C2×#2239

Subgroups

subgroupG/H
centerC2#481×D83
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingC83×#2239C2
socleC2×C83C2×#481
prime radicalC23×D83SD16
hypercenter#2239D83
hypocenterC83C2×#2239
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2239

552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 324455);