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C5×C7×C9×C11⋊C5 #31773151

order17325
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C52×C7×C9 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7×C9×C11⋊C5
unambiguous semidirect productC11⋊(C52×C7×C9)
unambiguous semidirect product(C5×C11)⋊(C5×C7×C9)
unambiguous semidirect product(C9×C11)⋊(C52×C7)
unambiguous semidirect product(C5×C9×C11)⋊(C5×C7)
unambiguous semidirect product(C7×C9×C11)⋊C52
unambiguous semidirect product(C5×C7×C9×C11)⋊C5

Splittings

FittingC5×C7×C9×C11 ⋊ C5
derived, SylowC11 ⋊ C52×C7×C9
HallC7×C9×C11 ⋊ C52
HallC9×C11 ⋊ C52×C7
HallC7×C11 ⋊ C52×C9

Subgroups

subgroupG/H
center, hypercenterC5×C7×C9C11⋊C5
commutator, hypocenterC11C52×C7×C9
FrattiniC3C3×C5×C7×C11⋊C5
FittingC5×C7×C9×C11C5
socleC3×C5×C7×C11C3×C5
prime radicalC3×C5×C7×C11⋊C5C3
cosocleC3×C11C3×C52×C7
LCSG ▷ C11
UCSC1 ◁ C5×C7×C9

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

2205 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×C9×AGL(1,𝔽11), C5×C9×C7⋊AGL(1,𝔽11), C5×C9×D7×C11⋊C5, …
maximal normal subgroup ofC5×C7×C9×AGL(1,𝔽11), C5×C9×C7⋊AGL(1,𝔽11), C5×C9×D7×C11⋊C5, …
maximal quotient ofC2×C5×C7×C9×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17325, 11);