Finite Group Databasebeta

D11×#1294 #14643755

order2816
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productD11×#1294

Splittings

FittingC11×#1294 ⋊ C2
SylowC11 ⋊ C2×#1294

Subgroups

subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11C2×#1294
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 59550);