Finite Group Databasebeta

D11×#2973 #15618496

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productD11×#2973

Splittings

FittingC11×#2973 ⋊ C2
SylowC11 ⋊ C2×#2973

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2973C2
prime radicalC22×D4×D11C4
cosocleC2×C4×C11C25
hypercenter#2973D11
hypocenterC11C2×#2973
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2973

2610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

308 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1034291);