Finite Group Databasebeta

#1289×D83 #35294274

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

Aliases

direct product#1289×D83

Splittings

FittingC83×#1289 ⋊ C2
SylowC83 ⋊ C2×#1289

Subgroups

subgroupG/H
centerC22#95×D83
commutatorC2×C4×C83C2×C42
FrattiniC23×C4C22×D83
FittingC83×#1289C2
socleC22×C83C2×#95
prime radicalC24×D83D4
cosocleC23×C4×C83C23
hypercenter#1289D83
hypocenterC83C2×#1289
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

1130 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, 59438);