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C11⋊C5×C3⋊AGL(1,𝔽7) #20294155

order6930
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×C3⋊AGL(1,𝔽7)
unambiguous semidirect productC3⋊(AGL(1,𝔽7)×C11⋊C5)
unambiguous semidirect productΓL(1,𝔽8)⋊(D3×C11⋊C5)
unambiguous semidirect productD21⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×C3⋊AGL(1,𝔽7))⋊C5
unambiguous semidirect product(D21×C11⋊C5)⋊C3

Splittings

Fitting, socle, derivedC3×C7×C11 ⋊ C2×C3×C5
HallC3×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallC11×C3⋊AGL(1,𝔽7) ⋊ C5
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C5
HallC7×C11⋊C5 ⋊ C3×D3
HallC7×C11 ⋊ C3×C5×D3
HallC3×ΓL(1,𝔽8) ⋊ C2×C11⋊C5
SylowC11 ⋊ C5×C3⋊AGL(1,𝔽7)
SylowC7 ⋊ C3×D3×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C7×C11C2×C3×C5
LCSG ▷ C3×C7×C11
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×C3⋊AGL(1,𝔽7), (C3⋊AGL(1,𝔽7))⋊AGL(1,𝔽11), D3×AGL(1,𝔽7)×C11⋊C5, …
maximal normal subgroup ofAGL(1,𝔽11)×C3⋊AGL(1,𝔽7), (C3⋊AGL(1,𝔽7))⋊AGL(1,𝔽11), D3×AGL(1,𝔽7)×C11⋊C5, …
maximal quotient ofC11⋊C5×C3⋊(ΓL(1,𝔽8)⋊C4), C2×C11⋊C5×C3⋊AGL(1,𝔽7), C3⋊AGL(1,𝔽7)×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 42);