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C7×C3⋊(C3⋊AGL(1,𝔽11)) #20294166

order6930
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×C3⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect productC3⋊(C7×C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C7×C3⋊D3)
unambiguous semidirect product(C3⋊D33)⋊(C5×C7)
unambiguous semidirect product(C7×C3⋊D33)⋊C5

Splittings

Fitting, socle, HallC32×C7×C11 ⋊ C2×C5
derived, HallC32×C11 ⋊ C2×C5×C7
HallC32×C7×C11⋊C5 ⋊ C2
HallC7×C3⋊D33 ⋊ C5
HallC32×C11⋊C5 ⋊ C2×C7
HallC7×C11⋊C5 ⋊ C3⋊D3
HallC3⋊D33 ⋊ C5×C7
HallC7×C11 ⋊ C5×C3⋊D3
HallC32×C7 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C7×C3⋊D3
SylowC11 ⋊ C5×C7×C3⋊D3
SylowC32 ⋊ C7×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C3⋊AGL(1,𝔽11))
commutator, hypocenterC32×C11C2×C5×C7
FrattiniC1G
Fitting, socleC32×C7×C11C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

273 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C3⋊D3×AGL(1,𝔽11), D7×C3⋊(C3⋊AGL(1,𝔽11)), (C7⋊AGL(1,𝔽11))⋊(C3⋊D3), …
maximal normal subgroup ofC7×C3⋊D3×AGL(1,𝔽11), D7×C3⋊(C3⋊AGL(1,𝔽11)), (C7⋊AGL(1,𝔽11))⋊(C3⋊D3), …
maximal quotient ofC7×C3⋊(C3⋊(Dic11⋊C5)), C2×C7×C3⋊(C3⋊AGL(1,𝔽11)), C7×C3⋊(C3⋊(D11⋊C25)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 53);