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C3×C5×ΓL(1,𝔽8)×D11 #20294172

order6930
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×ΓL(1,𝔽8)×D11
unambiguous semidirect product(C5×C7×D11)⋊C32
unambiguous semidirect product(C3×C5×C7×D11)⋊C3

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C32×C5
HallC3×C5×C11×ΓL(1,𝔽8) ⋊ C2
HallC5×C7×D11 ⋊ C32
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C5
HallC5×C7×C11 ⋊ C2×C32
HallC7×D11 ⋊ C32×C5
HallC5×C11 ⋊ C2×C3×ΓL(1,𝔽8)
HallC5×C7 ⋊ C32×D11
SylowC11 ⋊ C2×C3×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C32×C5×D11

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

525 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×D11×AGL(1,𝔽7), C3×D11×C5⋊AGL(1,𝔽7), C3×D5×ΓL(1,𝔽8)×D11, …
maximal normal subgroup ofC3×C5×D11×AGL(1,𝔽7), C3×D11×C5⋊AGL(1,𝔽7), C3×D5×ΓL(1,𝔽8)×D11, …
maximal quotient ofC3×C5×ΓL(1,𝔽8)×Dic11, C2×C3×C5×ΓL(1,𝔽8)×D11, C3×ΓL(1,𝔽8)×D11×C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 59);