D₂₂₆₁ #17985289

order	4522
automorphism	Aut(G) order 3907008
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₂₂₆₁
unambiguous semidirect product	C₇⋊D₃₂₃
unambiguous semidirect product	C₁₇⋊D₁₃₃
unambiguous semidirect product	C₁₉⋊D₁₁₉

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₇×C₁₉	C₂
LCS	G ▷ C₇×C₁₇×C₁₉
UCS	C₁

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2261

Polycyclic presentation:

2,7,17,19|b^a=b^6,c^a=c^16,d^a=d^18

1132 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4522, 8);