Finite Group Databasebeta

← Prev (#46803273) Next (#46803275) →

D11×D777 #46803274

order34188
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD11×D777
unambiguous semidirect product(C3×D11)⋊D259
unambiguous semidirect product(C7×D11)⋊D111
unambiguous semidirect product(D11×C37)⋊D21

Splittings

Fitting, socle, derived, HallC3×C7×C11×C37 ⋊ C22
HallC7×C11×C37 ⋊ C2×D3
HallC3×C11×C37 ⋊ C2×D7
HallC3×C7×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×D21
HallC7×C37 ⋊ D3×D11
HallC3×C7×C11 ⋊ C2×D37
HallC3×C37 ⋊ D7×D11
HallC7×C11 ⋊ C2×D111
SylowC37 ⋊ D11×D21
HallC3×C11 ⋊ C2×D259
HallC3×C7 ⋊ D11×D37
SylowC11 ⋊ C2×D777
SylowC7 ⋊ D11×D111
SylowC3 ⋊ D11×D259

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C37C22
LCSG ▷ C3×C7×C11×C37
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8547

Conjugacy classes & character table

2730 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 146);