Finite Group Databasebeta

#1867×D83 #35405482

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct product#1867×D83

Splittings

FittingC83×#1867 ⋊ C2
SylowC83 ⋊ C2×#1867

Subgroups

subgroupG/H
centerC22#120×D83
commutatorC23×C83C23×C4
FrattiniC24C23×D83
FittingC83×#1867C2
socleC22×C83C2×#120
prime radicalC22×D4×D83C22
cosocleC24×C83C24
hypercenter#1867D83
hypocenterC83C2×#1867
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C24 ◁ #1867

1994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

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, 170646);