Finite Group Databasebeta

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D11×#2001 #14780567

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD11×#2001

Splittings

FittingC11×#2001 ⋊ C2
SylowC11 ⋊ C2×#2001

Subgroups

subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2001C2
socleC23×C11C22×D4
prime radicalC24×D11D4
hypercenter#2001D11
hypocenterC11C2×#2001
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

2182 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, 196362);