Finite Group Databasebeta

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C11×C3⋊AGL(1,𝔽31) #44501749

order30690
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊AGL(1,𝔽31)
unambiguous semidirect productC3⋊(C11×AGL(1,𝔽31))
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(D3×C11)
unambiguous semidirect product(C3⋊(D31⋊C3))⋊(C5×C11)
unambiguous semidirect product(C3⋊(D31⋊C5))⋊(C3×C11)
unambiguous semidirect product(C11×C3⋊(D31⋊C5))⋊C3

Splittings

Fitting, socleC3×C11×C31 ⋊ C2×C3×C5
derivedC3×C31 ⋊ C2×C3×C5×C11
HallC3×C11×(C31⋊C3)⋊C5 ⋊ C2
HallC11×C3⋊(D31⋊C3) ⋊ C5
HallC3×C11×C31⋊C3 ⋊ C2×C5
HallC11×ΓL(1,𝔽32) ⋊ C3×D3
HallC3×(C31⋊C3)⋊C5 ⋊ C2×C11
HallC3⋊(D31⋊C3) ⋊ C5×C11
HallC11×C31 ⋊ C3×C5×D3
HallC3×C31⋊C3 ⋊ C2×C5×C11
HallΓL(1,𝔽32) ⋊ C3×D3×C11
SylowC31 ⋊ C3×C5×D3×C11

Subgroups

subgroupG/H
center, hypercenterC11C3⋊AGL(1,𝔽31)
commutator, cosocle, hypocenterC3×C31C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C11×C31C2×C3×C5
LCSG ▷ C3×C31
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1023

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 116);