Finite Group Databasebeta

SD32×D193 #27135681

order12352
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD32×D193

Splittings

FittingSD32×C193 ⋊ C2
SylowC193 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC2D8×D193
commutator, cosocleC8×C193C23
FrattiniC8C22×D193
FittingSD32×C193C2
socleC2×C193C2×D8
prime radicalD8×D193C2
hypercenterSD32D193
hypocenterC193C2×SD32
LCSG ▷ C8×C193 ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1078 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 971);