Finite Group Databasebeta

D16×D577 #49148368

order36928
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD16×D577

Splittings

FittingD16×C577 ⋊ C2
SylowC577 ⋊ C2×D16

Subgroups

subgroupG/H
centerC2D8×D577
commutator, cosocleC8×C577C23
FrattiniC8C22×D577
FittingD16×C577C2
socleC2×C577C2×D8
hypercenterD16D577
hypocenterC577C2×D16
LCSG ▷ C8×C577 ▷ C4×C577 ▷ C2×C577 ▷ C577
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9232

Conjugacy classes & character table

3190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36928, 968);