Finite Group Databasebeta

D16×D457 #44417196

order29248
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD16×D457

Splittings

FittingD16×C457 ⋊ C2
SylowC457 ⋊ C2×D16

Subgroups

subgroupG/H
centerC2D8×D457
commutator, cosocleC8×C457C23
FrattiniC8C22×D457
FittingD16×C457C2
socleC2×C457C2×D8
hypercenterD16D457
hypocenterC457C2×D16
LCSG ▷ C8×C457 ▷ C4×C457 ▷ C2×C457 ▷ C457
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7312

Conjugacy classes & character table

2530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 968);