Finite Group Databasebeta

Dic11×#536 #14912817

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productDic11×#536

Splittings

SylowC11 ⋊ C4×#536

Subgroups

subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#536C2
socle, cosocleC23×C11C25
prime radicalC22×C11×#41C22
hypercenterC2×#536D11
hypocenterC11C4×#536
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#536

2962 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

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, 328612);