Finite Group Databasebeta

← Group #309963

Character table — Group #309963

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-11111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-11111-1-111-1
χ71111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11
χ91111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11
χ101111111111111111-1-1-1-11111111111-1-111-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-111111111-1-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1111-1-111-1-111-1-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1111
χ17222222222-222-2-22-20000-2-22222222200-2-200-2-2000000000000-200000000000000
χ18222222222-222-2-22-20000-2-22222-2-2-2-2002200-2-2000000000000200000000000000
χ19222222222-222-2-22-20000-2-2-2-2-2-222-2-200220022000000000000-200000000000000
χ20222222222-222-2-22-20000-2-2-2-2-2-2-2-22200-2-20022000000000000200000000000000
χ2122222222-22-2-222-222222-2-200000000-2-200220022-2-2000000000-20000000000000
χ2222222222-22-2-222-222222-2-200000000-2-200-2-200-2-22200000000020000000000000
χ2322222222-22-2-222-22-2-2-2-2-2-20000000022002200-2-222000000000-20000000000000
χ2422222222-22-2-222-22-2-2-2-2-2-2000000002200-2-20022-2-200000000020000000000000
χ2522-2-22-22-222-2-2-2-2222i2i−2i−2i2-20000002i−2i2i−2i2i−2i000000000000000000002-2000000000
χ2622-2-22-22-222-2-2-2-2222i2i−2i−2i2-2000000−2i2i2i−2i−2i2i00000000000000000000-22000000000
χ2722-2-22-22-222-2-2-2-222−2i−2i2i2i2-20000002i−2i−2i2i2i−2i00000000000000000000-22000000000
χ2822-2-22-22-222-2-2-2-222−2i−2i2i2i2-2000000−2i2i−2i2i−2i2i000000000000000000002-2000000000
χ2922-2-22-22-22-2-2-2222-20000-220000002i−2i00−2i2i0000000022-2-20000002i−2i00000000000
χ3022-2-22-22-22-2-2-2222-20000-220000002i−2i00−2i2i00000000-2-222000000−2i2i00000000000
χ3122-2-22-22-22-2-2-2222-20000-22000000−2i2i002i−2i0000000022-2-2000000−2i2i00000000000
χ3222-2-22-22-22-2-2-2222-20000-22000000−2i2i002i−2i00000000-2-2220000002i−2i00000000000
χ3322-2-22-22-2-2222-2-2-222i2i−2i−2i-2200000000−2i2i0000000000000000000000002i−2i00002-20
χ3422-2-22-22-2-2222-2-2-222i2i−2i−2i-2200000000−2i2i000000000000000000000000−2i2i0000-220
χ3522-2-22-22-2-2222-2-2-22−2i−2i2i2i-22000000002i−2i0000000000000000000000002i−2i0000-220
χ3622-2-22-22-2-2222-2-2-22−2i−2i2i2i-22000000002i−2i000000000000000000000000−2i2i00002-20
χ372-2222-2-2-20-2002-2022i−2i2i−2i0022−2−2000000002i−2i2−22-200i2−i2i2−i222−2−200000000i2−i200000
χ382-2222-2-2-20-2002-2022i−2i2i−2i0022−2−200000000−2i2i2−2-2200i2−i2i2−i2−2−22200000000−i2i200000
χ392-2222-2-2-20-2002-2022i−2i2i−2i00−2−222000000002i−2i−222-200−i2i2−i2i2−2−22200000000−i2i200000
χ402-2222-2-2-20-2002-2022i−2i2i−2i00−2−22200000000−2i2i−22-2200−i2i2−i2i222−2−200000000i2−i200000
χ412-2222-2-2-20-2002-202−2i2i−2i2i0022−2−2000000002i−2i2−2-2200−i2i2−i2i2−2−22200000000i2−i200000
χ422-2222-2-2-20-2002-202−2i2i−2i2i0022−2−200000000−2i2i2−22-200−i2i2−i2i222−2−200000000−i2i200000
χ432-2222-2-2-20-2002-202−2i2i−2i2i00−2−222000000002i−2i−22-2200i2−i2i2−i222−2−200000000−i2i200000
χ442-2222-2-2-20-2002-202−2i2i−2i2i00−2−22200000000−2i2i−222-200i2−i2i2−i2−2−22200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-4-44404-400-400000004-44-4000000000000000000000000000000000000000
χ47444-4-4-4-44404-400-40000000-44-44000000000000000000000000000000000000000
χ48444-4-4-4-44-40-4400400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ49444-4-4-4-44-40-440040000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ5044-44-44-4-440-4400-4000000000004-40000000000000000000000000000000000000
χ5144-44-44-4-440-4400-400000000000-440000000000000000000000000000000000000
χ5244-44-44-4-4-404-40040000000000000000000000000000000000000000000002i2−2i2000
χ5344-44-44-4-4-404-4004000000000000000000000000000000000000000000000−2i22i2000
χ5444-4-44-44-4-4-44444-4-400004-40000000000000000000000000000000000000000000
χ554-4444-4-4-40400-440-40000002222−22−220000000000−2222000000000000000000000000000
χ564-4444-4-4-40400-440-4000000−22−222222000000000022−22000000000000000000000000000
χ574-44-4-444-40000000000000022−22−2222000000000000002i2−2i200002i−2i−2i2i000000000000000
χ584-44-4-444-40000000000000022−22−222200000000000000−2i22i20000−2i2i2i−2i000000000000000
χ594-44-4-444-400000000000000−222222−22000000000000002i2−2i20000−2i2i2i−2i000000000000000
χ604-44-4-444-400000000000000−222222−2200000000000000−2i22i200002i−2i−2i2i000000000000000
χ614-4-4-444-4404004-40-4000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ624-4-4-444-4404004-40-400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ634-4-4-444-440-400-44044-4-44000000000000000000000000000000000000000000000
χ644-4-4-444-440-400-4404-444-4000000000000000000000000000000000000000000000
χ658-8-88-8-888000000000000000000000000000000000000000000000000000000000

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