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C3⋊((C11⋊C5)⋊D59) #34085703

order19470
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊D59)
unambiguous semidirect product(C11⋊C5)⋊D177
unambiguous semidirect productC59⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect productD1947⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C59 ⋊ C2×C5
HallC3×C11⋊C5×C59 ⋊ C2
HallD1947 ⋊ C5
HallC11⋊C5×C59 ⋊ D3
HallC11×C59 ⋊ C5×D3
HallC3×C59 ⋊ AGL(1,𝔽11)
HallC3×C11⋊C5 ⋊ D59
SylowC59 ⋊ C3⋊AGL(1,𝔽11)
HallC11⋊C5 ⋊ D177
HallC3×C11 ⋊ C5×D59
SylowC11 ⋊ C5×D177
SylowC3 ⋊ (C11⋊C5)⋊D59

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C59C2×C5
LCSG ▷ C3×C11×C59
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1947

Polycyclic presentation:

2,3,5,11,59|b^a=b^2,d^a=d^10,e^a=e^58,d^c=d^4

Conjugacy classes & character table

627 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19470, 24);