Finite Group Databasebeta

← Group #310294

Character table — Group #310294

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888882
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1
χ411111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1111-111-1-111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-111-1
χ91111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ101111111111111111-1-1-1-11111111111-1-111-1-1111111-1-1-1-11111-1-1-11-1-1-1-11111-1-1-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111111-1-1-111-1-111-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111111-1-1111-1-111-1-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111111-1-1-1-11111-1
χ17222222222-222-2-2-220000-2-22222222200-2-200-2-2000000000000000-200000000000
χ18222222222-222-2-2-220000-2-22222-2-2-2-2002200-2-2000000000000000200000000000
χ19222222222-222-2-2-220000-2-2-2-2-2-222-2-200-2-20022000000000000000200000000000
χ20222222222-222-2-2-220000-2-2-2-2-2-2-2-22200220022000000000000000-200000000000
χ2122222222-22-2-2222-22222-2-200000000-2-200220022-2-200000000-200000000000000
χ2222222222-22-2-2222-22222-2-200000000-2-200-2-200-2-22200000000200000000000000
χ2322222222-22-2-2222-2-2-2-2-2-2-20000000022002200-2-22200000000-200000000000000
χ2422222222-22-2-2222-2-2-2-2-2-2-2000000002200-2-20022-2-200000000200000000000000
χ2522-22-2-2-2222-2-2-22-222i2i−2i−2i2-2000000002i−2i00000000000000000002i−2i000002-200000
χ2622-22-2-2-2222-2-2-22-222i2i−2i−2i2-2000000002i−2i0000000000000000000−2i2i00000-2200000
χ2722-22-2-2-2222-2-2-22-22−2i−2i2i2i2-200000000−2i2i00000000000000000002i−2i00000-2200000
χ2822-22-2-2-2222-2-2-22-22−2i−2i2i2i2-200000000−2i2i0000000000000000000−2i2i000002-200000
χ2922-22-2-2-22-2222-22-2-22i2i−2i−2i-2200002i−2i00−2i2i2i−2i000000000000000000002-2000000000
χ3022-22-2-2-22-2222-22-2-22i2i−2i−2i-220000−2i2i00−2i2i−2i2i00000000000000000000-22000000000
χ3122-22-2-2-22-2222-22-2-2−2i−2i2i2i-2200002i−2i002i−2i2i−2i00000000000000000000-22000000000
χ3222-22-2-2-22-2222-22-2-2−2i−2i2i2i-220000−2i2i002i−2i−2i2i000000000000000000002-2000000000
χ3322-22-2-2-22-2-2222-22-200002-200002i−2i0000−2i2i000000002i2i−2i−2i00000000002-20000000
χ3422-22-2-2-22-2-2222-22-200002-200002i−2i0000−2i2i00000000−2i−2i2i2i0000000000-220000000
χ3522-22-2-2-22-2-2222-22-200002-20000−2i2i00002i−2i000000002i2i−2i−2i0000000000-220000000
χ3622-22-2-2-22-2-2222-22-200002-20000−2i2i00002i−2i00000000−2i−2i2i2i00000000002-20000000
χ372-2222-2-2-20-200-22202-22-20022−2−2000000002i−2i2−22i−2i002−22−2i2i2−i2−i2000000000000i2−i20
χ382-2222-2-2-20-200-22202-22-20022−2−200000000−2i2i2−2−2i2i002−22−2−i2−i2i2i2000000000000−i2i20
χ392-2222-2-2-20-200-22202-22-200−2−222000000002i−2i−222i−2i00−22−22−i2−i2i2i2000000000000−i2i20
χ402-2222-2-2-20-200-22202-22-200−2−22200000000−2i2i−22−2i2i00−22−22i2i2−i2−i2000000000000i2−i20
χ412-2222-2-2-20-200-2220-22-220022−2−2000000002i−2i2−2−2i2i00−22−22−i2−i2i2i2000000000000i2−i20
χ422-2222-2-2-20-200-2220-22-220022−2−200000000−2i2i2−22i−2i00−22−22i2i2−i2−i2000000000000−i2i20
χ432-2222-2-2-20-200-2220-22-2200−2−222000000002i−2i−22−2i2i002−22−2i2i2−i2−i2000000000000−i2i20
χ442-2222-2-2-20-200-2220-22-2200−2−22200000000−2i2i−222i−2i002−22−2−i2−i2i2i2000000000000i2−i20
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-44-4404-4000-40000000000000000000000000000000000000000000022−22000
χ47444-4-4-44-4404-4000-400000000000000000000000000000000000000000000−2222000
χ48444-4-4-44-4-40-4400040000000000004i−4i00000000000000000000000000000000000
χ49444-4-4-44-4-40-440004000000000000−4i4i00000000000000000000000000000000000
χ5044-44-4-4-444-4-4-44-4440000-440000000000000000000000000000000000000000000
χ5144-4-444-4-440-44000-40000004-44-4000000000000000000000000000000000000000
χ5244-4-444-4-440-44000-4000000-44-44000000000000000000000000000000000000000
χ5344-4-444-4-4-404-400040000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ5444-4-444-4-4-404-40004000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ554-4444-4-4-404004-4-400000002222−22−220000000000−2222000000000000000000000000000
χ564-4444-4-4-404004-4-40000000−22−222222000000000022−22000000000000000000000000000
χ574-4-44-444-40400-4-440000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ584-4-44-444-40400-4-44000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ594-4-44-444-40-40044-404i−4i−4i4i000000000000000000000000000000000000000000000
χ604-4-44-444-40-40044-40−4i4i4i−4i000000000000000000000000000000000000000000000
χ614-4-4-44-4440000000000000022−22−22220000000000000022−2200002-2-22000000000000000
χ624-4-4-44-4440000000000000022−22−222200000000000000−22220000-222-2000000000000000
χ634-4-4-44-44400000000000000−222222−220000000000000022−220000-222-2000000000000000
χ644-4-4-44-44400000000000000−222222−2200000000000000−222200002-2-22000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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