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(C11⋊C5)⋊(#261⋊C9) #38787807

order25740
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊(#261⋊C9)
unambiguous semidirect product((C11⋊C5)⋊#261)⋊C9
unambiguous semidirect product(C11⋊(#261⋊C9))⋊C5

Splittings

derived, HallC11×C13 ⋊ C4×C5×C9
HallC11⋊C5×C13⋊C9 ⋊ C4
HallC11⋊(#261⋊C9) ⋊ C5
Hall(C11⋊C5)⋊#261 ⋊ C9
HallC11×C13⋊C9 ⋊ C4×C5
HallC13×C11⋊C5 ⋊ C4×C9
HallC11⋊#261 ⋊ C5×C9
HallC13⋊C9 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ #261⋊C9
SylowC13 ⋊ C9×Dic11⋊C5
SylowC11 ⋊ C5×#261⋊C9

Subgroups

subgroupG/H
center, Frattini, hypercenterC3(C11⋊C5)⋊AGL(1,𝔽13)
commutator, hypocenterC11×C13C4×C5×C9
Fitting, socleC3×C11×C13C3×C4×C5
prime radicalC3×D13×C11⋊C5C2×C3
cosocleC3×C11×D13C2×C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1287

Polycyclic presentation:

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

Conjugacy classes & character table

219 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 38);