Projective special linear group:PSL(2,17)

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Definition

This group is defined as the projective special linear group of degree two over field:F17.

Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	2448	groups with same order	As $P S L (2, q), q = 17$ , $q$ odd: $(q^{3} - q) / 2 = q (q + 1) (q - 1) / 2 = (1 7^{3} - 17) / 2 = (17) (16) (18) / 2 = 2448$ . See element structure of projective special linear group of degree two.
exponent of a group	1224	groups with same order and exponent of a group \| groups with same exponent of a group	As $P S L (2, q), q = 17$ , $q$ odd: $(q^{3} - q) / 4 = q (q + 1) (q - 1) / 4 = (1 7^{3} - 17) / 4 = (17) (18) (16) / 4 = 1224$ . See element structure of projective special linear group of degree two.

Arithmetic functions of a counting nature

Function	Value	Explanation
number of conjugacy classes	11	As $P S L (2, q), q = 17$ , $q$ odd: $(q + 5) / 2 = (17 + 5) / 2 = 11$ . See element structure of projective special linear group of degree two
number of conjugacy classes of subgroups	22
number of subgroups	2420

Group properties

Property	Satisfied?	Explanation
abelian group	No
nilpotent group	No
solvable group	No
simple group, simple non-abelian group	Yes	projective special linear group of degree two is simple (small exceptions exist)
minimal simple group	Yes	See classification of finite minimal simple groups

GAP implementation

Description	Functions used
`PSL(2,17)`	PSL