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 \! PSL(2,q), q = 17, q odd: \! (q^3 - q)/2 = q(q+1)(q-1)/2 = (17^3 - 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 \! PSL(2,q), q = 17, q odd: (q^3 - q)/4 = q(q+1)(q-1)/4 = (17^3-17)/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 PSL(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