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C3⋊D561 #16809883

order3366
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊D561
unambiguous semidirect productC11⋊(C3⋊D51)
unambiguous semidirect productC17⋊(C3⋊D33)

Splittings

Fitting, socle, derived, HallC32×C11×C17 ⋊ C2
HallC11×C17 ⋊ C3⋊D3
HallC32×C17 ⋊ D11
HallC32×C11 ⋊ D17
SylowC17 ⋊ C3⋊D33
SylowC11 ⋊ C3⋊D51
SylowC32 ⋊ D187

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C17C2
LCSG ▷ C32×C11×C17
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1683

Polycyclic presentation:

2,3^2,11,17|b^a=b^2,c^a=c^2,d^a=d^10,e^a=e^16

Conjugacy classes & character table

843 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3⋊(C3⋊(C17⋊AGL(1,𝔽11))), C3⋊D2805, C5×C3⋊D561, …
maximal normal subgroup ofC3⋊(C3⋊(C17⋊AGL(1,𝔽11))), C5×C3⋊D561, C7×C3⋊D561, …
maximal quotient ofC3⋊D2805, C5×C3⋊D561, C7×C3⋊D561, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3366, 20);