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C3⋊((C11⋊C5)⋊#261) #22575075

order8580
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊#261)
unambiguous semidirect product(C11⋊C5)⋊(C3⋊#261)
unambiguous semidirect product(C3⋊(C11⋊#261))⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C13 ⋊ C4×C5
HallC3×C13×C11⋊C5 ⋊ C4
HallC3⋊(C11⋊#261) ⋊ C5
HallC13×C11⋊C5 ⋊ Dic3
HallC3×C11⋊C5 ⋊ #261
HallC11×C13 ⋊ C5×Dic3
HallC11⋊C5 ⋊ C3⋊#261
HallC3×C13 ⋊ Dic11⋊C5
HallC3×C11 ⋊ C5×#261
SylowC13 ⋊ C3⋊(Dic11⋊C5)
SylowC11 ⋊ C5×C3⋊#261
SylowC3 ⋊ (C11⋊C5)⋊#261

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C11×C13C4×C5
LCSG ▷ C3×C11×C13
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9⋊((C11⋊C5)⋊#261), C3⋊((C11⋊C5)⋊AGL(1,𝔽13)), C3×C3⋊((C11⋊C5)⋊#261), …
maximal normal subgroup ofC3⋊((C11⋊C5)⋊AGL(1,𝔽13)), C3×C3⋊((C11⋊C5)⋊#261)
maximal quotient ofC9⋊((C11⋊C5)⋊#261), C3×C3⋊((C11⋊C5)⋊#261), C3⋊(C3⋊((C11⋊C5)⋊#261))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 47);