Finite Group Databasebeta

SD32×D491 #44537147

order31424
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD32×D491

Splittings

FittingSD32×C491 ⋊ C2
SylowC491 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC2D8×D491
commutator, cosocleC8×C491C23
FrattiniC8C22×D491
FittingSD32×C491C2
socleC2×C491C2×D8
prime radicalD8×D491C2
hypercenterSD32D491
hypocenterC491C2×SD32
LCSG ▷ C8×C491 ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7856

Conjugacy classes & character table

2717 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 971);