Finite Group Databasebeta

SD32×D172 #25253272

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productSD32×D172

Splittings

FittingC4×SD32×C43 ⋊ C2
SylowC43 ⋊ D4×SD32

Subgroups

subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC4×SD32×C43C2
socleC22×C43C22×D8
prime radicalD8×D172C2
hypercenterC4×SD32D43
hypocenterC43D4×SD32
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

738 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

979 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 326243);