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C2×C3×C11×(C31⋊C3)⋊C5 #44501773

order30690
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C11×(C31⋊C3)⋊C5
unambiguous semidirect product(C2×C31⋊C3)⋊(C3×C5×C11)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C32×C11)
unambiguous semidirect product(C2×C3×C31⋊C3)⋊(C5×C11)
unambiguous semidirect product(C2×C3×ΓL(1,𝔽32))⋊(C3×C11)
unambiguous semidirect product(C2×C11×ΓL(1,𝔽32))⋊C32
unambiguous semidirect product(C2×C3×C11×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socleC2×C3×C11×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C2×C32×C5×C11
HallC2×C3×C11×C31⋊C3 ⋊ C5
HallC2×C11×ΓL(1,𝔽32) ⋊ C32
HallC3×C11×C31⋊C3 ⋊ C2×C5
HallC11×ΓL(1,𝔽32) ⋊ C2×C32
HallC2×C11×C31 ⋊ C32×C5
HallC2×C3×C31⋊C3 ⋊ C5×C11
HallC11×C31 ⋊ C2×C32×C5
HallC2×ΓL(1,𝔽32) ⋊ C32×C11
HallC3×C31⋊C3 ⋊ C2×C5×C11
HallΓL(1,𝔽32) ⋊ C2×C32×C11
HallC2×C31 ⋊ C32×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C2×C32×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C3×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2046

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 140);