Finite Group Databasebeta

C2×C11×#687 #13183151

order1760
isoclinismisoclinic class of #686
automorphism?
homologyAbelianization (H1) = C23×C11 · Schur multiplier (H2) = C22

Aliases

direct productC2×C11×#687

Splittings

HallC5×C11 ⋊ C2×SD16
SylowC5 ⋊ C2×C11×SD16

Subgroups

subgroupG/H
centerC22×C11C22⋊D5
commutator, cosocleC4×C5C23×C11
FrattiniC4C22×D5×C11
Fitting, prime radicalC2×C5×D4×C11C2
socleC22×C5×C11D4
hypercenterC2×D4×C11D5
hypocenterC5C2×C11×SD16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C11 ◁ C2×C4×C11 ◁ C2×D4×C11

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 880

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 960);