Finite Group Databasebeta

#1976×D83 #35408374

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct product#1976×D83

Splittings

FittingC83×#1976 ⋊ C2
SylowC83 ⋊ C2×#1976

Subgroups

subgroupG/H
centerC4#121×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1976C2
socleC2×C83C2×#390
prime radicalC2×#135×D83C2
cosocleC22×C4×C83C24
hypercenter#1976D83
hypocenterC83C2×#1976
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1976

1474 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, 173538);