Finite Group Databasebeta

D16×D383 #37588770

order24512
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD16×D383

Splittings

FittingD16×C383 ⋊ C2
SylowC383 ⋊ C2×D16

Subgroups

subgroupG/H
centerC2D8×D383
commutator, cosocleC8×C383C23
FrattiniC8C22×D383
FittingD16×C383C2
socleC2×C383C2×D8
hypercenterD16D383
hypocenterC383C2×D16
LCSG ▷ C8×C383 ▷ C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6128

Conjugacy classes & character table

2123 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24512, 968);