Finite Group Databasebeta

D11×#2011 #14780799

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C28

Aliases

direct productD11×#2011

Splittings

FittingC11×#2011 ⋊ C2
SylowC11 ⋊ C2×#2011

Subgroups

subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2011C2
socleC23×C11C22×D4
hypercenter#2011D11
hypocenterC11C2×#2011
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2011

2942 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, 196594);