Finite Group Databasebeta

SD32×D367 #37554608

order23488
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD32×D367

Splittings

FittingSD32×C367 ⋊ C2
SylowC367 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC2D8×D367
commutator, cosocleC8×C367C23
FrattiniC8C22×D367
FittingSD32×C367C2
socleC2×C367C2×D8
prime radicalD8×D367C2
hypercenterSD32D367
hypocenterC367C2×SD32
LCSG ▷ C8×C367 ▷ C4×C367 ▷ C2×C367 ▷ C367
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5872

Conjugacy classes & character table

2035 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 971);