Finite Group Databasebeta

SD32×D467 #44470459

order29888
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD32×D467

Splittings

FittingSD32×C467 ⋊ C2
SylowC467 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC2D8×D467
commutator, cosocleC8×C467C23
FrattiniC8C22×D467
FittingSD32×C467C2
socleC2×C467C2×D8
prime radicalD8×D467C2
hypercenterSD32D467
hypocenterC467C2×SD32
LCSG ▷ C8×C467 ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7472

Conjugacy classes & character table

2585 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 971);