Finite Group Databasebeta

D16×D593 #49183134

order37952
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD16×D593

Splittings

FittingD16×C593 ⋊ C2
SylowC593 ⋊ C2×D16

Subgroups

subgroupG/H
centerC2D8×D593
commutator, cosocleC8×C593C23
FrattiniC8C22×D593
FittingD16×C593C2
socleC2×C593C2×D8
hypercenterD16D593
hypocenterC593C2×D16
LCSG ▷ C8×C593 ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9488

Conjugacy classes & character table

3278 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37952, 968);