Finite Group Databasebeta

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C3×C7×C13×AGL(1,𝔽11) #44473258

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C13×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×C7×C13)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C7×C13)
unambiguous semidirect product(C3×D11)⋊(C5×C7×C13)
unambiguous semidirect product(C3×C7×D11)⋊(C5×C13)
unambiguous semidirect product(C3×C13×D11)⋊(C5×C7)
unambiguous semidirect product(C3×C7×C13×D11)⋊C5

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C5×C7×C13
HallC3×C7×C13×C11⋊C5 ⋊ C2
HallC3×C7×C13×D11 ⋊ C5
HallC7×C13×C11⋊C5 ⋊ C2×C3
HallC3×C13×C11⋊C5 ⋊ C2×C7
HallC7×C13×D11 ⋊ C3×C5
HallC3×C7×C11⋊C5 ⋊ C2×C13
HallC7×C11×C13 ⋊ C2×C3×C5
HallC3×C13×D11 ⋊ C5×C7
HallC13×C11⋊C5 ⋊ C2×C3×C7
HallC3×C7×D11 ⋊ C5×C13
HallC3×C11×C13 ⋊ C2×C5×C7
HallC7×C11⋊C5 ⋊ C2×C3×C13
HallC13×D11 ⋊ C3×C5×C7
HallC3×C7×C11 ⋊ C2×C5×C13
HallC3×C11⋊C5 ⋊ C2×C7×C13
HallC7×D11 ⋊ C3×C5×C13
HallC11×C13 ⋊ C2×C3×C5×C7
HallC7×C11 ⋊ C2×C3×C5×C13
HallC3×D11 ⋊ C5×C7×C13
HallC11⋊C5 ⋊ C2×C3×C7×C13
HallC3×C11 ⋊ C2×C5×C7×C13
HallD11 ⋊ C3×C5×C7×C13

Subgroups

subgroupG/H
center, hypercenterC3×C7×C13AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C5×C7×C13
FrattiniC1G
Fitting, socleC3×C7×C11×C13C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C7×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

3003 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 43);