Finite Group Databasebeta

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C5×D3×C7×C11⋊C5 #26040490

order11550
automorphism?
homologyAbelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC5×D3×C7×C11⋊C5
unambiguous semidirect productC3⋊(C2×C5×C7×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊(C52×C7)
unambiguous semidirect product(C5×D3×C11)⋊(C5×C7)
unambiguous semidirect product(D3×C7×C11)⋊C52
unambiguous semidirect product(C5×D3×C7×C11)⋊C5

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C52×C7
HallC3×C5×C7×C11⋊C5 ⋊ C2
HallC3×C5×C11⋊C5 ⋊ C2×C7
HallD3×C7×C11 ⋊ C52
HallC3×C7×C11 ⋊ C2×C52
HallC7×C11 ⋊ C52×D3
HallD3×C11 ⋊ C52×C7
HallC3×C7 ⋊ C2×C5×C11⋊C5
SylowC11 ⋊ C52×D3×C7
SylowC3 ⋊ C2×C5×C7×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC5×C7D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C52×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C5×C7

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

735 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×C7×AGL(1,𝔽11), C5×D3×C7⋊AGL(1,𝔽11), C5×D3×D7×C11⋊C5, …
maximal normal subgroup ofC5×D3×C7×AGL(1,𝔽11), C5×D3×C7⋊AGL(1,𝔽11), C5×D3×D7×C11⋊C5, …
maximal quotient ofC5×C7×Dic3×C11⋊C5, C2×C5×D3×C7×C11⋊C5, C5×C7×D9×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 54);