Finite Group Databasebeta

← Group #309949

Character table — Group #309949

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888244444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111-1-111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ411111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-111111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-111-1
χ911111111111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1111
χ1011111111111111111-1-1-1-11111111-1-111-1-111111111-1-1-1-111111-1-1-1-1-1-1-11111-1-1-1
χ1111111111111111111-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-111-1-1111-1-111-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-111-1-1-1-1-111-1-1111
χ1511111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-111-111-1-11111-1
χ1722222222222-2-2-2-22-20000-222222200-2-200-2-2-2-2000000000000200000000000000
χ1822222222222-2-2-2-22-20000-22222-2-200220022-2-2000000000000-200000000000000
χ1922222222222-2-2-2-22-20000-2-2-2-2-222002200-2-222000000000000-200000000000000
χ2022222222222-2-2-2-22-20000-2-2-2-2-2-2-200-2-2002222000000000000200000000000000
χ2122222222-2-2-22222-2-22222-20000002200-2-2000022-2-20000000000000-2000000000
χ2222222222-2-2-22222-2-22222-2000000-2-200-2-20000-2-22200000000000002000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-20000002200220000-2-2220000000000000-2000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2000000-2-20022000022-2-200000000000002000000000
χ252-22-222-2-22-2-222-2-22-20000200002i−2i0000002i−2i00000022-2-2000002i−2i000000000000
χ262-22-222-2-22-2-222-2-22-20000200002i−2i0000002i−2i000000-2-22200000−2i2i000000000000
χ272-22-222-2-22-2-222-2-22-2000020000−2i2i000000−2i2i00000022-2-200000−2i2i000000000000
χ282-22-222-2-22-2-222-2-22-2000020000−2i2i000000−2i2i000000-2-222000002i−2i000000000000
χ292-22-222-2-22-2-2-2-222222i2i−2i−2i-200002i−2i00002i−2i−2i2i000000000000000002-20000000000
χ302-22-222-2-22-2-2-2-222222i2i−2i−2i-20000−2i2i00002i−2i2i−2i00000000000000000-220000000000
χ312-22-222-2-22-2-2-2-22222−2i−2i2i2i-200002i−2i0000−2i2i−2i2i00000000000000000-220000000000
χ322-22-222-2-22-2-2-2-22222−2i−2i2i2i-20000−2i2i0000−2i2i2i−2i000000000000000002-20000000000
χ332-22-222-2-2-222-2-222-2-22i2i−2i−2i20000000000−2i2i00000000000000000000002i−2i2-200000
χ342-22-222-2-2-222-2-222-2-22i2i−2i−2i20000000000−2i2i0000000000000000000000−2i2i-2200000
χ352-22-222-2-2-222-2-222-2-2−2i−2i2i2i200000000002i−2i00000000000000000000002i−2i-2200000
χ362-22-222-2-2-222-2-222-2-2−2i−2i2i2i200000000002i−2i0000000000000000000000−2i2i2-200000
χ372-2-222-22-20002-22-2002-22-20i2i2−i2−i2002i−2i000000i2−i22i−2i00i2−i2i2−i222−2−20000000000002−20
χ382-2-222-22-20002-22-2002-22-20i2i2−i2−i200−2i2i000000i2−i2−2i2i00i2−i2i2−i2−2−222000000000000−220
χ392-2-222-22-20002-22-2002-22-20−i2−i2i2i2002i−2i000000−i2i22i−2i00−i2i2−i2i2−2−222000000000000−220
χ402-2-222-22-20002-22-2002-22-20−i2−i2i2i200−2i2i000000−i2i2−2i2i00−i2i2−i2i222−2−20000000000002−20
χ412-2-222-22-20002-22-200-22-220i2i2−i2−i2002i−2i000000i2−i2−2i2i00−i2i2−i2i2−2−2220000000000002−20
χ422-2-222-22-20002-22-200-22-220i2i2−i2−i200−2i2i000000i2−i22i−2i00−i2i2−i2i222−2−2000000000000−220
χ432-2-222-22-20002-22-200-22-220−i2−i2i2i2002i−2i000000−i2i2−2i2i00i2−i2i2−i222−2−2000000000000−220
χ442-2-222-22-20002-22-200-22-220−i2−i2i2i200−2i2i000000−i2i22i−2i00i2−i2i2−i2−2−2220000000000002−20
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ4644-44-44-4-444-40000-40000004-44-4000000000000000000000000000000000000000
χ4744-44-44-4-444-40000-4000000-44-44000000000000000000000000000000000000000
χ4844-44-44-4-4-4-44000040000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ4944-44-44-4-4-4-4400004000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ5044-4-44-4-440004-4-440000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ5144-4-44-4-440004-4-44000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5244-4-44-4-44000-444-4004i−4i−4i4i00000000000000000000000000000000000000000000
χ5344-4-44-4-44000-444-400−4i4i4i−4i00000000000000000000000000000000000000000000
χ544-444-4-4-44000000000000002i2−2i2−2i22i20000000000000022−2200002i−2i−2i2i000000000000000
χ554-444-4-4-44000000000000002i2−2i2−2i22i200000000000000−22220000−2i2i2i−2i000000000000000
χ564-444-4-4-4400000000000000−2i22i22i2−2i20000000000000022−220000−2i2i2i−2i000000000000000
χ574-444-4-4-4400000000000000−2i22i22i2−2i200000000000000−222200002i−2i−2i2i000000000000000
χ584-44-444-4-4-44444-4-4-440000-40000000000000000000000000000000000000000000
χ594-4-444-44-4000-44-4400000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ604-4-444-44-4000-44-440000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ614-4-4-4-44444-440000-4000000000000004i−4i000000000000000000000000000000000
χ624-4-4-4-44444-440000-400000000000000−4i4i000000000000000000000000000000000
χ634-4-4-4-4444-44-4000040000000000000000000000000000000000000000000022−22000
χ644-4-4-4-4444-44-40000400000000000000000000000000000000000000000000−2222000
χ65888-8-8-88-8000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).