Finite Group Databasebeta

D16×D409 #39909666

order26176
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD16×D409

Splittings

FittingD16×C409 ⋊ C2
SylowC409 ⋊ C2×D16

Subgroups

subgroupG/H
centerC2D8×D409
commutator, cosocleC8×C409C23
FrattiniC8C22×D409
FittingD16×C409C2
socleC2×C409C2×D8
hypercenterD16D409
hypocenterC409C2×D16
LCSG ▷ C8×C409 ▷ C4×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6544

Conjugacy classes & character table

2266 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 968);