Finite Group Databasebeta

D11×SD16⋊C8 #14723154

order2816
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productD11×SD16⋊C8

Splittings

FittingC11×SD16⋊C8 ⋊ C2
SylowC11 ⋊ C2×SD16⋊C8

Subgroups

subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC11×SD16⋊C8C2
socleC22×C11C2×C4×D4
prime radicalC2×D4×D11C2×C4
cosocleC42×C11C24
hypercenterSD16⋊C8D11
hypocenterC11C2×SD16⋊C8
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 138949);