Finite Group Databasebeta

#1294×D83 #35294386

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

Aliases

direct product#1294×D83

Splittings

FittingC83×#1294 ⋊ C2
SylowC83 ⋊ C2×#1294

Subgroups

subgroupG/H
centerC23C22⋊C4×D83
commutatorC2×C4×C83C2×C42
FrattiniC23×C4C22×D83
FittingC83×#1294C2
socleC23×C83C2×C22⋊C4
prime radicalC24×D83D4
cosocleC23×C4×C83C23
hypercenter#1294D83
hypocenterC83C2×#1294
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

1634 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 59550);