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D3×ΓL(1,𝔽8)×C11⋊C5 #20294157

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

Aliases

direct productD3×ΓL(1,𝔽8)×C11⋊C5
unambiguous semidirect productC3⋊(C2×ΓL(1,𝔽8)×C11⋊C5)
unambiguous semidirect product(D3×C7)⋊(C3×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(D3×C11×ΓL(1,𝔽8))⋊C5
unambiguous semidirect product(D3×C7×C11⋊C5)⋊C3

Splittings

Fitting, socle, derivedC3×C7×C11 ⋊ C2×C3×C5
HallC3×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallD3×C11×ΓL(1,𝔽8) ⋊ 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×D3×ΓL(1,𝔽8)
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

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×ΓL(1,𝔽8)⋊AGL(1,𝔽11), D3×AGL(1,𝔽7)×C11⋊C5, D3×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal normal subgroup ofD3×ΓL(1,𝔽8)⋊AGL(1,𝔽11), D3×AGL(1,𝔽7)×C11⋊C5, D3×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal quotient ofDic3×ΓL(1,𝔽8)×C11⋊C5, C2×D3×ΓL(1,𝔽8)×C11⋊C5, D3×ΓL(1,𝔽8)×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 44);