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C11⋊(#63122⋊C3) #22575093

order8580
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊(#63122⋊C3)
unambiguous semidirect product(C11⋊#63122)⋊C3

Splittings

Fitting, socle, derived, HallC5×C11×C13 ⋊ C3×C4
HallC11⋊#63122 ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C4
HallC11×C13⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C13⋊C3 ⋊ Dic11
HallC11×C13 ⋊ C3×AGL(1,𝔽5)
HallC5×C13 ⋊ C3×Dic11
HallC5×C11 ⋊ AGL(1,𝔽13)
HallC13⋊C3 ⋊ C11⋊AGL(1,𝔽5)
SylowC13 ⋊ C3×C11⋊AGL(1,𝔽5)
SylowC11 ⋊ #63122⋊C3
SylowC5 ⋊ C11⋊AGL(1,𝔽13)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C11×C13C3×C4
LCSG ▷ C5×C11×C13
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,2,5,11,13|a^2=c,d^a=d^2,e^a=e^10,f^a=f^5,f^b=f^3,d^c=d^4,f^c=f^12

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊(#63122⋊C3), C3⋊(C11⋊(#63122⋊C3))
maximal normal subgroup ofC3×C11⋊(#63122⋊C3)
maximal quotient ofC11⋊(#63122⋊C9), C3×C11⋊(#63122⋊C3), C3⋊(C11⋊(#63122⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 65);