Finite Group Databasebeta

Dic11×#568 #15617187

order2816
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productDic11×#568

Splittings

SylowC11 ⋊ C4×#568

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D11
commutatorC2×C11C23×C42
FittingC2×C11×#568C2
socleC22×C11C24×C4
prime radicalC22×C11×#41C22
cosocleC2×C4×C11C25
hypercenterC2×#568D11
hypocenterC11C4×#568
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#568

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1032982);