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C5×C13⋊C3×C11⋊C5 #24924332

order10725
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C13⋊C3×C11⋊C5
unambiguous semidirect productC11⋊(C52×C13⋊C3)
unambiguous semidirect productC13⋊(C3×C5×C11⋊C5)
unambiguous semidirect product(C5×C11)⋊(C5×C13⋊C3)
unambiguous semidirect product(C5×C13)⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×C13⋊C3)⋊C52
unambiguous semidirect product(C13×C11⋊C5)⋊(C3×C5)
unambiguous semidirect product(C5×C11×C13⋊C3)⋊C5
unambiguous semidirect product(C5×C13×C11⋊C5)⋊C3

Splittings

Fitting, socleC5×C11×C13 ⋊ C3×C5
derived, HallC11×C13 ⋊ C3×C52
HallC5×C13×C11⋊C5 ⋊ C3
HallC11×C13⋊C3 ⋊ C52
SylowC13 ⋊ C3×C5×C11⋊C5
SylowC11 ⋊ C52×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C13⋊C3×C11⋊C5
commutator, cosocle, hypocenterC11×C13C3×C52
FrattiniC1G
Fitting, socleC5×C11×C13C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C5

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×(C13⋊C3)⋊AGL(1,𝔽11), C5×C13⋊C3×AGL(1,𝔽11), C5×C11⋊C5×D13⋊C3, …
maximal normal subgroup ofC5×(C13⋊C3)⋊AGL(1,𝔽11), C5×C13⋊C3×AGL(1,𝔽11), C5×C11⋊C5×D13⋊C3, …
maximal quotient ofC2×C5×C13⋊C3×C11⋊C5, C5×C11⋊C5×C13⋊C9, C3×C5×C13⋊C3×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10725, 6);