Dic₁₅₀₅ #20258221

order	6020
automorphism	Aut(G) order 3034080
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₁₅₀₅
unambiguous semidirect product	C₇⋊Dic₂₁₅
unambiguous semidirect product	C₄₃⋊Dic₃₅

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₅₀₅
commutator, hypocenter	C₅×C₇×C₄₃	C₄
Fitting, socle	C₂×C₅×C₇×C₄₃	C₂
LCS	G ▷ C₅×C₇×C₄₃
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Polycyclic presentation:

2,5,7,43,2|a^2=e,b^a=b^4,c^a=c^6,d^a=d^42

1508 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6020, 9);