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C3×C5×ΓL(1,𝔽8)×C11⋊C5 #31773156

order17325
automorphism?
homologyAbelianization (H1) = C32×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C5×ΓL(1,𝔽8)×C11⋊C5
unambiguous semidirect productC7⋊(C32×C5×C11⋊C5)
unambiguous semidirect productC11⋊(C3×C52×ΓL(1,𝔽8))
unambiguous semidirect product(C3×C7)⋊(C3×C5×C11⋊C5)
unambiguous semidirect product(C3×C11)⋊(C52×ΓL(1,𝔽8))
unambiguous semidirect product(C5×C7)⋊(C32×C11⋊C5)
unambiguous semidirect product(C5×C11)⋊(C3×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C3×C5×C7)⋊(C3×C11⋊C5)
unambiguous semidirect product(C3×C5×C11)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C11×ΓL(1,𝔽8))⋊(C3×C52)
unambiguous semidirect product(C7×C11⋊C5)⋊(C32×C5)
unambiguous semidirect product(C3×C11×ΓL(1,𝔽8))⋊C52
unambiguous semidirect product(C3×C7×C11⋊C5)⋊(C3×C5)
unambiguous semidirect product(C5×C11×ΓL(1,𝔽8))⋊(C3×C5)
unambiguous semidirect product(C5×C7×C11⋊C5)⋊C32
unambiguous semidirect product(C3×C5×C11×ΓL(1,𝔽8))⋊C5
unambiguous semidirect product(C3×C5×C7×C11⋊C5)⋊C3

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C3×C5
derived, HallC7×C11 ⋊ C32×C52
HallC5×C7×C11⋊C5 ⋊ C32
HallC3×C11×ΓL(1,𝔽8) ⋊ C52
SylowC11 ⋊ C3×C52×ΓL(1,𝔽8)
SylowC7 ⋊ C32×C5×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)×C11⋊C5
commutator, cosocle, hypocenterC7×C11C32×C52
FrattiniC1G
Fitting, socleC3×C5×C7×C11C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

525 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C3×C5×AGL(1,𝔽7)×C11⋊C5, C3×C5×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal normal subgroup ofC3×C5×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C3×C5×AGL(1,𝔽7)×C11⋊C5, C3×C5×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal quotient ofC2×C3×C5×ΓL(1,𝔽8)×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17325, 16);