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C3⋊(C3⋊((C11⋊C5)⋊#595)) #46778017

order33660
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊((C11⋊C5)⋊#595))
unambiguous semidirect product(C11⋊C5)⋊(C3⋊(C3⋊#595))
unambiguous semidirect product(C3⋊(C3⋊(C11⋊#595)))⋊C5

Splittings

Fitting, socle, derived, HallC32×C11×C17 ⋊ C4×C5
HallC32×C17×C11⋊C5 ⋊ C4
HallC3⋊(C3⋊(C11⋊#595)) ⋊ C5
HallC17×C11⋊C5 ⋊ C3⋊Dic3
HallC32×C11⋊C5 ⋊ #595
HallC11×C17 ⋊ C5×C3⋊Dic3
HallC32×C17 ⋊ Dic11⋊C5
HallC32×C11 ⋊ C5×#595
HallC11⋊C5 ⋊ C3⋊(C3⋊#595)
SylowC17 ⋊ C3⋊(C3⋊(Dic11⋊C5))
SylowC11 ⋊ C5×C3⋊(C3⋊#595)
SylowC32 ⋊ (C11⋊C5)⋊#595

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C11×C17C4×C5
prime radicalC32×D17×C11⋊C5C2
cosocleC32×C11×D17C2×C5
LCSG ▷ C32×C11×C17
UCSC1

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 1683

A minimal faithful permutation representation — 3 generators on 34 points:

(2,3)(5,6)(8,12,13,11,16,9,10,17,14,15)(19,20,21,23)(22,25,26,30)(24,29,27,28)(31,33,34,32);(4,5,6)(7,8,11,16,10,13,17,12,15,14,9)(18,19,22,27,23,28,32,34,30,25,31,33,29,20,24,26,21);(1,2,3)

Polycyclic presentation:

2,5,2,3^2,11,17|a^2=c,d^a=d^2,e^a=e^2,f^a=f^10,g^a=g^13,f^b=f^4,g^c=g^16

Conjugacy classes & character table

330 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 185);