Finite Group Databasebeta

SD32×D41 #14580758

order2624
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD32×D41

Splittings

FittingSD32×C41 ⋊ C2
SylowC41 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC2D8×D41
commutator, cosocleC8×C41C23
FrattiniC8C22×D41
FittingSD32×C41C2
socleC2×C41C2×D8
prime radicalD8×D41C2
hypercenterSD32D41
hypocenterC41C2×SD32
LCSG ▷ C8×C41 ▷ C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 656

Conjugacy classes & character table

242 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 971);