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C3×D11×(C31⋊C3)⋊C5 #44501748

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

Aliases

direct productC3×D11×(C31⋊C3)⋊C5
unambiguous semidirect product(D11×ΓL(1,𝔽32))⋊C32
unambiguous semidirect product(C3×D11×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socleC3×C11×C31 ⋊ C2×C3×C5
derived, HallC11×C31 ⋊ C2×C32×C5
HallC3×C11×(C31⋊C3)⋊C5 ⋊ C2
HallC3×D11×C31⋊C3 ⋊ C5
HallD11×ΓL(1,𝔽32) ⋊ C32
HallC3×C11×C31⋊C3 ⋊ C2×C5
HallC11×ΓL(1,𝔽32) ⋊ C2×C32
HallD11×C31 ⋊ C32×C5
HallC3×C31⋊C3 ⋊ C5×D11
HallΓL(1,𝔽32) ⋊ C32×D11
SylowC31 ⋊ C32×C5×D11
SylowC11 ⋊ C2×C3×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC3D11×(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1023

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 115);