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C7×C3⋊D3×C11⋊C5 #20294167

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

Aliases

direct productC7×C3⋊D3×C11⋊C5
unambiguous semidirect productC3⋊(D3×C7×C11⋊C5)
unambiguous semidirect product(C11×C3⋊D3)⋊(C5×C7)
unambiguous semidirect product(C7×C11×C3⋊D3)⋊C5

Splittings

Fitting, socle, HallC32×C7×C11 ⋊ C2×C5
derived, HallC32×C11 ⋊ C2×C5×C7
HallC32×C7×C11⋊C5 ⋊ C2
HallC7×C11×C3⋊D3 ⋊ C5
HallC32×C11⋊C5 ⋊ C2×C7
HallC11×C3⋊D3 ⋊ C5×C7
HallC7×C11 ⋊ C5×C3⋊D3
HallC32×C7 ⋊ C2×C11⋊C5
SylowC11 ⋊ C5×C7×C3⋊D3
SylowC32 ⋊ C2×C7×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC7C3⋊D3×C11⋊C5
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

294 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C3⋊D3×AGL(1,𝔽11), C3⋊D3×C7⋊AGL(1,𝔽11), D7×C3⋊D3×C11⋊C5, …
maximal normal subgroup ofC7×C3⋊D3×AGL(1,𝔽11), C3⋊D3×C7⋊AGL(1,𝔽11), D7×C3⋊D3×C11⋊C5, …
maximal quotient ofC7×C3⋊Dic3×C11⋊C5, C2×C7×C3⋊D3×C11⋊C5, C7×C3⋊D3×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 54);