Finite Group Databasebeta

D16×C47⋊C8 #26128000

order12032
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD16×C47⋊C8

Splittings

SylowC47 ⋊ C8×D16

Subgroups

subgroupG/H
centerC2×C4D8×D47
commutatorC8×C47C22×C8
FrattiniC4×C8C22×D47
FittingC4×D16×C47C2
socleC22×C47C4×D8
prime radicalC2×D16×C47C4
cosocleC4×C8×C47C23
hypercenterC4×D16D47
hypocenterC47C8×D16
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D16

258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 81290);