Finite Group Databasebeta

D11×#3388 #15634292

order2816
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productD11×#3388

Splittings

FittingC11×#3388 ⋊ C2
SylowC11 ⋊ C2×#3388

Subgroups

subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3388C2
socleC22×C11C23×D4
prime radicalC2×D4×D11C23
hypercenter#3388D11
hypocenterC11C2×#3388
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3388

1822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

203 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1050087);