Dic₁₄₆₃ #19154409

order	5852
automorphism	Aut(G) order 3160080
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₁₄₆₃
unambiguous semidirect product	C₇⋊Dic₂₀₉
unambiguous semidirect product	C₁₁⋊Dic₁₃₃
unambiguous semidirect product	C₁₉⋊Dic₇₇

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₄₆₃
commutator, hypocenter	C₇×C₁₁×C₁₉	C₄
Fitting, socle	C₂×C₇×C₁₁×C₁₉	C₂
LCS	G ▷ C₇×C₁₁×C₁₉
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Polycyclic presentation:

2,7,11,19,2|a^2=e,b^a=b^6,c^a=c^10,d^a=d^18

1466 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5852, 8);