Finite Group Databasebeta

Dic11×#365 #14669159

order2816
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productDic11×#365

Splittings

SylowC11 ⋊ C4×#365

Subgroups

subgroupG/H
centerC22D11×#106
commutatorC8×C11C2×C42
FrattiniC22×C8C22×D11
FittingC2×C11×#365C2
socleC22×C11C2×#106
prime radicalC23×C11C2×SD16
cosocleC22×C8×C11C23
hypercenterC2×#365D11
hypocenterC11C4×#365
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 84954);