Finite Group Databasebeta

D32×D227 #44402030

order29056
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD32×D227

Splittings

FittingD32×C227 ⋊ C2
SylowC227 ⋊ C2×D32

Subgroups

subgroupG/H
centerC2D16×D227
commutator, cosocleC16×C227C23
FrattiniC16C22×D227
FittingD32×C227C2
socleC2×C227C2×D16
hypercenterD32D227
hypocenterC227C2×D32
LCSG ▷ C16×C227 ▷ C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

2185 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 6806);