Finite Group Databasebeta

← Group #309088

Character table — Group #309088

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-11-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1111-111-1-11-1
χ91111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-11-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-11-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111-1111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-11-1-1-1111-1
χ172222222222-22-2-2-222222-2-20000000022-2-200-2-2002200000000-2-20000000000000000
χ182222222222-22-2-2-222222-2-200000000-2-2-2-2002200-2-200000000220000000000000000
χ192222222222-22-2-2-22-2-2-2-2-2-200000000222200-2-200-2-200000000220000000000000000
χ202222222222-22-2-2-22-2-2-2-2-2-200000000-2-2220022002200000000-2-20000000000000000
χ2122222222-2-22-2222-20000-2-22222-2-2-2-2000022002200000000000000000000-2-2000000
χ2222222222-2-22-2222-20000-2-22222-2-2-2-20000-2-200-2-20000000000000000000022000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-2222200002200-2-2000000000000000000002-2000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-222220000-2-2002200000000000000000000-22000000
χ252222-2-2-2-22-202000-222-2-20022−2−222−2−22-2000000002-222−2−222−2−20022−2−2000000000000
χ262222-2-2-2-22-202000-222-2-20022−2−222−2−2-2200000000-2222−2−2−2−22200−2−222000000000000
χ272222-2-2-2-22-202000-222-2-200−2−222−2−2222-2000000002-2−2−222−2−22200−2−222000000000000
χ282222-2-2-2-22-202000-222-2-200−2−222−2−222-2200000000-22−2−22222−2−20022−2−2000000000000
χ292222-2-2-2-22-202000-2-2-2220022−2−222−2−22-200000000-22−2−22222−2−200−2−222000000000000
χ302222-2-2-2-22-202000-2-2-2220022−2−222−2−2-22000000002-2−2−222−2−2220022−2−2000000000000
χ312222-2-2-2-22-202000-2-2-22200−2−222−2−2222-200000000-2222−2−2−2−2220022−2−2000000000000
χ322222-2-2-2-22-202000-2-2-22200−2−222−2−222-22000000002-222−2−222−2−200−2−222000000000000
χ3322-2-222-2-222-2-222-2-200002-22-22-22-22-2000000000000000000000000002-22-200000000
χ3422-2-222-2-222-2-222-2-200002-22-22-22-22-200000000000000000000000000-22-2200000000
χ3522-2-222-2-222-2-222-2-200002-2-22-22-22-22000000000000000000000000002-2-2200000000
χ3622-2-222-2-222-2-222-2-200002-2-22-22-22-2200000000000000000000000000-222-200000000
χ3722-2-222-2-2-2-222-2-2222i−2i2i−2i2-200000000002i−2i0000000000002-22-2002i−2i2i−2i000000000000
χ3822-2-222-2-2-2-222-2-2222i−2i2i−2i2-200000000002i−2i000000000000-22-2200−2i2i−2i2i000000000000
χ3922-2-222-2-2-2-222-2-222−2i2i−2i2i2-20000000000−2i2i0000000000002-22-200−2i2i−2i2i000000000000
χ4022-2-222-2-2-2-222-2-222−2i2i−2i2i2-20000000000−2i2i000000000000-22-22002i−2i2i−2i000000000000
χ4122-2-222-2-2-2-2-2222-222i−2i2i−2i-222-22-2-22-2200−2i2i000000002i−2i2i−2i0000000000000000000000
χ4222-2-222-2-2-2-2-2222-222i−2i2i−2i-22-22-222-22-200−2i2i00000000−2i2i−2i2i0000000000000000000000
χ4322-2-222-2-2-2-2-2222-22−2i2i−2i2i-222-22-2-22-22002i−2i00000000−2i2i−2i2i0000000000000000000000
χ4422-2-222-2-2-2-2-2222-22−2i2i−2i2i-22-22-222-22-2002i−2i000000002i−2i2i−2i0000000000000000000000
χ4522-2-2-2-222-2202000-22i−2i−2i2i002−2−22−222−20000002-20000i2−i2−i2i22−2−222i−2ii2−i2−i2i2000000000000
χ4622-2-2-2-222-2202000-22i−2i−2i2i002−2−22−222−2000000-220000i2−i2−i2i2−222−2−2i2i−i2i2i2−i2000000000000
χ4722-2-2-2-222-2202000-22i−2i−2i2i00−222−22−2−220000002-20000−i2i2i2−i2−222−22i−2i−i2i2i2−i2000000000000
χ4822-2-2-2-222-2202000-22i−2i−2i2i00−222−22−2−22000000-220000−i2i2i2−i22−2−22−2i2ii2−i2−i2i2000000000000
χ4922-2-2-2-222-2202000-2−2i2i2i−2i002−2−22−222−20000002-20000−i2i2i2−i22−2−22−2i2i−i2i2i2−i2000000000000
χ5022-2-2-2-222-2202000-2−2i2i2i−2i002−2−22−222−2000000-220000−i2i2i2−i2−222−22i−2ii2−i2−i2i2000000000000
χ5122-2-2-2-222-2202000-2−2i2i2i−2i00−222−22−2−220000002-20000i2−i2−i2i2−222−2−2i2ii2−i2−i2i2000000000000
χ5222-2-2-2-222-2202000-2−2i2i2i−2i00−222−22−2−22000000-220000i2−i2−i2i22−2−222i−2i−i2i2i2−i2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ544444-4-4-4-4-440-400040000002222−22−22−22−22222200000000000000000000000000000000000000
χ554444-4-4-4-4-440-40004000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5644-4-444-4-4444-4-4-44-40000-440000000000000000000000000000000000000000000000
χ5744-4-4-4-4444-40-4000400000022−22−222222−22−222200000000000000000000000000000000000000
χ5844-4-4-4-4444-40-40004000000−222222−22−222222−2200000000000000000000000000000000000000
χ594-44-44-44-400404-4-400000000000000000004-400000000000000000000000000000000
χ604-44-44-44-400404-4-40000000000000000000-4400000000000000000000000000000000
χ614-44-44-44-400-40-444000000000000000000000000000000000000000000000002i2−2i20000
χ624-44-44-44-400-40-44400000000000000000000000000000000000000000000000−2i22i20000
χ634-4-444-4-440040-44-400000000000000000000000000000000000000000000000002i2−2i200
χ644-4-444-4-440040-44-40000000000000000000000000000000000000000000000000−2i22i200
χ654-4-444-4-4400-404-44000000000000000000000004-40000000000000000000000000000
χ664-4-444-4-4400-404-4400000000000000000000000-440000000000000000000000000000
χ678-88-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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