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(C11⋊C5)⋊#10597480 #46777992

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

Aliases

unambiguous semidirect product(C11⋊C5)⋊#10597480
unambiguous semidirect product(C11⋊#10597480)⋊C5

Splittings

Fitting, socle, derived, HallC32×C11×C17 ⋊ C4×C5
HallC32×C17×C11⋊C5 ⋊ C4
HallC11⋊#10597480 ⋊ C5
HallC17×C11⋊C5 ⋊ #157
HallC32×C11⋊C5 ⋊ Dic17
HallC11×C17 ⋊ C5×#157
HallC32×C17 ⋊ Dic11⋊C5
HallC32×C11 ⋊ C5×Dic17
HallC11⋊C5 ⋊ #10597480
SylowC17 ⋊ (C11⋊C5)⋊#157
SylowC11 ⋊ C5×#10597480
SylowC32 ⋊ (C11⋊C5)⋊Dic17

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C11×C17C4×C5
prime radicalC17×C3⋊D3×C11⋊C5C2
cosocleC11×C17×C3⋊D3C2×C5
LCSG ▷ C32×C11×C17
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1122

Polycyclic presentation:

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

Conjugacy classes & character table

372 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 160);