Finite Group Databasebeta

← Prev (#44440344) Next (#44440346) →

C11⋊C5×D267 #44440345

order29370
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D267
unambiguous semidirect productC3⋊(C11⋊C5×D89)
unambiguous semidirect productC89⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×D267)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C89 ⋊ C2×C5
HallC3×C11⋊C5×C89 ⋊ C2
HallC11×D267 ⋊ C5
HallC11⋊C5×C89 ⋊ D3
HallC11×C89 ⋊ C5×D3
HallC3×C89 ⋊ C2×C11⋊C5
HallC3×C11⋊C5 ⋊ D89
SylowC89 ⋊ D3×C11⋊C5
HallC3×C11 ⋊ C5×D89
SylowC11 ⋊ C5×D267
SylowC3 ⋊ C11⋊C5×D89

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C89C2×C5
LCSG ▷ C3×C11×C89
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2937

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 30);