Finite Group Databasebeta

#1390×D83 #35319341

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct product#1390×D83

Splittings

FittingC83×#1390 ⋊ C2
SylowC83 ⋊ C2×#1390

Subgroups

subgroupG/H
centerC22#99×D83
commutatorC23×C83C2×C42
FrattiniC22×D4C22×D83
FittingC83×#1390C2
socleC22×C83C2×#99
prime radicalC22×D4×D83C22
cosocleC22×D4×C83C23
hypercenter#1390D83
hypocenterC83C2×#1390
LCSG ▷ C23×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

1202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

1118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 84505);