Finite Group Databasebeta

Dic11×#379 #14674980

order2816
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productDic11×#379

Splittings

SylowC11 ⋊ C4×#379

Subgroups

subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#379C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11C4×#379
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

6734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 90775);