Finite Group Databasebeta

SD32×D461 #44442498

order29504
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD32×D461

Splittings

FittingSD32×C461 ⋊ C2
SylowC461 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC2D8×D461
commutator, cosocleC8×C461C23
FrattiniC8C22×D461
FittingSD32×C461C2
socleC2×C461C2×D8
prime radicalD8×D461C2
hypercenterSD32D461
hypocenterC461C2×SD32
LCSG ▷ C8×C461 ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7376

Conjugacy classes & character table

2552 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 971);