Dic₂₆₀₁ #23780794

order	10404
automorphism	Aut(G) order 8489664
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₂₆₀₁
unambiguous semidirect product	C₉⋊Dic₂₈₉

	subgroup	G/H
center, hypercenter	C₂	D₂₆₀₁
commutator, hypocenter	C₉×C₂₈₉	C₄
Frattini, socle, prime radical	C₂×C₃×C₁₇	D₅₁
Fitting, cosocle	C₂×C₉×C₂₈₉	C₂
LCS	G ▷ C₉×C₂₈₉
UCS	C₁ ◁ C₂

27 conjugacy classes of subgroups.

Polycyclic presentation:

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

2604 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10404, 4);