Finite Group Databasebeta

D16×C22⋊D17 #17190973

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD16×C22⋊D17

Splittings

FittingC22×C17×D16 ⋊ C2
SylowC17 ⋊ D4×D16

Subgroups

subgroupG/H
centerC22C2×D8×D17
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC22×C17×D16C2
socleC22×C17C22×D8
hypercenterC22×D16D17
hypocenterC17D4×D16
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 326217);