Finite Group Databasebeta

D16×C22⋊D61 #29836662

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD16×C22⋊D61

Splittings

FittingC22×D16×C61 ⋊ C2
SylowC61 ⋊ D4×D16

Subgroups

subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC22×D16×C61C2
socleC22×C61C22×D8
hypercenterC22×D16D61
hypocenterC61D4×D16
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1375 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 326217);