# Properties

 Modulus $24$ Structure $$C_{2}\times C_{2}\times C_{2}$$ Order $8$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(24)

pari: g = idealstar(,24,2)

## Character group

 sage: G.order()  pari: g.no Order = 8 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{24}(7,\cdot)$, $\chi_{24}(13,\cdot)$, $\chi_{24}(17,\cdot)$

## Characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$
$$\chi_{24}(1,\cdot)$$ 24.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{24}(5,\cdot)$$ 24.h 2 yes $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$
$$\chi_{24}(7,\cdot)$$ 24.g 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{24}(11,\cdot)$$ 24.f 2 yes $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$
$$\chi_{24}(13,\cdot)$$ 24.d 2 no $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$
$$\chi_{24}(17,\cdot)$$ 24.e 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$
$$\chi_{24}(19,\cdot)$$ 24.b 2 no $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$
$$\chi_{24}(23,\cdot)$$ 24.c 2 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$