Finite Group Databasebeta

D11×#3055 #15620911

order2816
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD11×#3055

Splittings

FittingC11×#3055 ⋊ C2
SylowC11 ⋊ C2×#3055

Subgroups

subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3055C2
socleC22×C11C23×D4
hypercenter#3055D11
hypocenterC11C2×#3055
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3055

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

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, 1036706);