Finite Group Databasebeta

#2359×D83 #35563899

order21248
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#2359×D83

Splittings

FittingC83×#2359 ⋊ C2
SylowC83 ⋊ C2×#2359

Subgroups

subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2359C2
socle, cosocleC23×C83C25
prime radicalC22×D4×D83C22
hypercenter#2359D83
hypocenterC83C2×#2359
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2359

3830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

2150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 329063);