Finite Group Databasebeta

← Group #310253

Character table — Group #310253

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888244444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11-11111-1-111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-111-1
χ91111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ101111111111111111-1-1-1-111111111-1-11111-1-1111111-1-1-1-11111-11-1-1-1-1-1-11111-1-1-1
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
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-1111111111-111-1-111-1-111-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111111-1-1-1-11111-1
χ17222222222-22-2-222-22222-2-2000000-2-200002200-2-22200000000-200000000000000
χ18222222222-22-2-222-22222-2-2000000-2-20000-2-20022-2-200000000200000000000000
χ19222222222-22-2-222-2-2-2-2-2-2-2000000220000220022-2-200000000-200000000000000
χ20222222222-22-2-222-2-2-2-2-2-2-2000000220000-2-200-2-22200000000200000000000000
χ2122222222-22-222-2-220000-2-222222200-2-2-2-200-2-2000000000000020000000000000
χ2222222222-22-222-2-220000-2-22222-2-200222200-2-20000000000000-20000000000000
χ2322222222-22-222-2-220000-2-2-2-2-2-22200-2-22200220000000000000-20000000000000
χ2422222222-22-222-2-220000-2-2-2-2-2-2-2-20022-2-20022000000000000020000000000000
χ2522-22-2-22-2-20-2002202i2i−2i−2i0022−2−2000000002i−2i2−2002-2i2i2−i2−i222−2−2000000000000i2−i20
χ2622-22-2-22-2-20-2002202i2i−2i−2i0022−2−200000000−2i2i2−200-22i2i2−i2−i2−2−222000000000000−i2i20
χ2722-22-2-22-2-20-2002202i2i−2i−2i00−2−222000000002i−2i−22002-2−i2−i2i2i2−2−222000000000000−i2i20
χ2822-22-2-22-2-20-2002202i2i−2i−2i00−2−22200000000−2i2i−2200-22−i2−i2i2i222−2−2000000000000i2−i20
χ2922-22-2-22-2-20-200220−2i−2i2i2i0022−2−2000000002i−2i2−200-22−i2−i2i2i2−2−222000000000000i2−i20
χ3022-22-2-22-2-20-200220−2i−2i2i2i0022−2−200000000−2i2i2−2002-2−i2−i2i2i222−2−2000000000000−i2i20
χ3122-22-2-22-2-20-200220−2i−2i2i2i00−2−222000000002i−2i−2200-22i2i2−i2−i222−2−2000000000000−i2i20
χ3222-22-2-22-2-20-200220−2i−2i2i2i00−2−22200000000−2i2i−22002-2i2i2−i2−i2−2−222000000000000i2−i20
χ3322-2-2-22-2222-2-2-22-222i−2i2i−2i2-20000002i−2i00000000000000000000002i−2i00002-200000
χ3422-2-2-22-2222-2-2-22-222i−2i2i−2i2-20000002i−2i0000000000000000000000−2i2i0000-2200000
χ3522-2-2-22-2222-2-2-22-22−2i2i−2i2i2-2000000−2i2i00000000000000000000002i−2i0000-2200000
χ3622-2-2-22-2222-2-2-22-22−2i2i−2i2i2-2000000−2i2i0000000000000000000000−2i2i00002-200000
χ3722-2-2-22-222-2-2222-2-22i−2i2i−2i-2200002i−2i−2i2i2i−2i00000000000000000000002-2000000000
χ3822-2-2-22-222-2-2222-2-22i−2i2i−2i-220000−2i2i−2i2i−2i2i0000000000000000000000-22000000000
χ3922-2-2-22-222-2-2222-2-2−2i2i−2i2i-2200002i−2i2i−2i2i−2i0000000000000000000000-22000000000
χ4022-2-2-22-222-2-2222-2-2−2i2i−2i2i-220000−2i2i2i−2i−2i2i00000000000000000000002-2000000000
χ4122-2-2-22-22-2-2222-22-200002-200002i−2i00−2i2i00000000002i−2i2i−2i00000000002-20000000
χ4222-2-2-22-22-2-2222-22-200002-200002i−2i00−2i2i0000000000−2i2i−2i2i0000000000-220000000
χ4322-2-2-22-22-2-2222-22-200002-20000−2i2i002i−2i00000000002i−2i2i−2i0000000000-220000000
χ4422-2-2-22-22-2-2222-22-200002-20000−2i2i002i−2i0000000000−2i2i−2i2i00000000002-20000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-440-400-4400000000000000000000000000022−22−22220000000000000000000
χ47444-44-4-4-440-400-44000000000000000000000000000−222222−220000000000000000000
χ48444-44-4-4-4-404004-404-4-44000000000000000000000000000000000000000000000
χ49444-44-4-4-4-404004-40-444-4000000000000000000000000000000000000000000000
χ5044-44-4-44-440400-4-400000002222−22−220000000000−2222000000000000000000000000000
χ5144-44-4-44-440400-4-40000000−22−222222000000000022−22000000000000000000000000000
χ5244-4-4-44-44-444-4-4-4440000-440000000000000000000000000000000000000000000
χ534-44-4-4-4440404-400-40000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ544-44-4-4-4440404-400-4000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ554-44-4-4-4440-40-440040000004-44-4000000000000000000000000000000000000000
χ564-44-4-4-4440-40-44004000000-44-44000000000000000000000000000000000000000
χ574-4-444-4-44040-4400-400000000000000004i−4i0000000000000000000000000000000
χ584-4-444-4-44040-4400-40000000000000000−4i4i0000000000000000000000000000000
χ594-4-444-4-440-404-40040000000000000000000000000000000000000000000022−22000
χ604-4-444-4-440-404-400400000000000000000000000000000000000000000000−2222000
χ614-4-4-4444-40000000000000022−22−22220000000000002i2−2i20000002i−2i−2i2i000000000000000
χ624-4-4-4444-40000000000000022−22−2222000000000000−2i22i2000000−2i2i2i−2i000000000000000
χ634-4-4-4444-400000000000000−222222−220000000000002i2−2i2000000−2i2i2i−2i000000000000000
χ644-4-4-4444-400000000000000−222222−22000000000000−2i22i20000002i−2i−2i2i000000000000000
χ658-888-88-8-8000000000000000000000000000000000000000000000000000000000

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