Finite Group Databasebeta

SD32×D397 #38762944

order25408
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD32×D397

Splittings

FittingSD32×C397 ⋊ C2
SylowC397 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC2D8×D397
commutator, cosocleC8×C397C23
FrattiniC8C22×D397
FittingSD32×C397C2
socleC2×C397C2×D8
prime radicalD8×D397C2
hypercenterSD32D397
hypocenterC397C2×SD32
LCSG ▷ C8×C397 ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6352

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 971);