Finite Group Databasebeta

← Prev (#44501718) Next (#44501720) →

AGL(1,𝔽11)×C31⋊C9 #44501719

order30690
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽11)×C31⋊C9
unambiguous semidirect productD11⋊(C5×C31⋊C9)
unambiguous semidirect product(C11⋊C5)⋊(C2×C31⋊C9)
unambiguous semidirect product(C31×AGL(1,𝔽11))⋊C9

Splittings

derived, HallC11×C31 ⋊ C2×C5×C9
HallC11⋊C5×C31⋊C9 ⋊ C2
HallD11×C31⋊C9 ⋊ C5
HallC31×AGL(1,𝔽11) ⋊ C9
HallC11×C31⋊C9 ⋊ C2×C5
HallC31×C11⋊C5 ⋊ C2×C9
HallD11×C31 ⋊ C5×C9
HallC11⋊C5 ⋊ C2×C31⋊C9
SylowC31 ⋊ C9×AGL(1,𝔽11)
HallD11 ⋊ C5×C31⋊C9
SylowC11 ⋊ C2×C5×C31⋊C9

Subgroups

subgroupG/H
center, Frattini, hypercenterC3C31⋊C3×AGL(1,𝔽11)
commutator, hypocenterC11×C31C2×C5×C9
Fitting, socle, cosocleC3×C11×C31C2×C3×C5
prime radicalC3×C31×AGL(1,𝔽11)C3
LCSG ▷ C11×C31
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 86);