Dic₁₅₃₃ #20259481

order	6132
automorphism	Aut(G) order 2649024
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₁₅₃₃
unambiguous semidirect product	C₃⋊Dic₅₁₁
unambiguous semidirect product	C₇⋊Dic₂₁₉

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₅₃₃
commutator, hypocenter	C₃×C₇×C₇₃	C₄
Fitting, socle	C₂×C₃×C₇×C₇₃	C₂
LCS	G ▷ C₃×C₇×C₇₃
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Polycyclic presentation:

2,3,7,73,2|a^2=e,b^a=b^2,c^a=c^6,d^a=d^72

1536 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6132, 12);