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AGL(1,𝔽11)×#63271 #44473339

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

Aliases

direct productAGL(1,𝔽11)×#63271
unambiguous semidirect productD11⋊(C5×#63271)
unambiguous semidirect product(C11⋊C5)⋊(C2×#63271)
unambiguous semidirect product(D11×#63271)⋊C5

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C2×C3×C5
HallC11⋊C5×#63271 ⋊ C2
HallC7×C13×AGL(1,𝔽11) ⋊ C3
HallD11×#63271 ⋊ C5
HallC7×C13×C11⋊C5 ⋊ C2×C3
HallC11×#63271 ⋊ C2×C5
HallC7×C13×D11 ⋊ C3×C5
HallC13×AGL(1,𝔽11) ⋊ ΓL(1,𝔽8)
HallC7×AGL(1,𝔽11) ⋊ C13⋊C3
HallC13×C11⋊C5 ⋊ C2×ΓL(1,𝔽8)
HallC7×C11⋊C5 ⋊ C2×C13⋊C3
HallC13×D11 ⋊ C5×ΓL(1,𝔽8)
HallC7×D11 ⋊ C5×C13⋊C3
HallC11×C13 ⋊ C2×C5×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×AGL(1,𝔽11)
HallC7×C11 ⋊ C2×C5×C13⋊C3
HallC11⋊C5 ⋊ C2×#63271
HallD11 ⋊ C5×#63271
SylowC13 ⋊ ΓL(1,𝔽8)×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×#63271
SylowC7 ⋊ C13⋊C3×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C13C2×C3×C5
LCSG ▷ C7×C11×C13
UCSC1

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1001

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 124);