Finite Group Databasebeta

SD32×D359 #37526865

order22976
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD32×D359

Splittings

FittingSD32×C359 ⋊ C2
SylowC359 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC2D8×D359
commutator, cosocleC8×C359C23
FrattiniC8C22×D359
FittingSD32×C359C2
socleC2×C359C2×D8
prime radicalD8×D359C2
hypercenterSD32D359
hypocenterC359C2×SD32
LCSG ▷ C8×C359 ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5744

Conjugacy classes & character table

1991 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 971);