Finite Group Databasebeta

← Group #308505

Character table — Group #308505

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444442222448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-111-1-111-1
χ91111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111
χ101111111111111111-1-1-1-111111111-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-11-11111-1-1-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-11-1-111-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-1-11111-1
χ17222222222-2-22-222-22222-2-2000000-2-200002200-2-222000000000000000-20000000
χ18222222222-2-22-222-22222-2-2000000-2-20000-2-20022-2-200000000000000020000000
χ19222222222-2-22-222-2-2-2-2-2-2-2000000220000220022-2-2000000000000000-20000000
χ20222222222-2-22-222-2-2-2-2-2-2-2000000220000-2-200-2-22200000000000000020000000
χ2122222222-222-22-2-220000-2-222222200-2-2-2-200-2-2000000000000000000200000000
χ2222222222-222-22-2-220000-2-22222-2-200222200-2-2000000000000000000-200000000
χ2322222222-222-22-2-220000-2-2-2-2-2-2220022-2-20022000000000000000000-200000000
χ2422222222-222-22-2-220000-2-2-2-2-2-2-2-200-2-2220022000000000000000000200000000
χ2522-222-2-2-2222-2-22-2-222-2-22-20000002-2000000000000000000002-20000002-200000
χ2622-222-2-2-2222-2-22-2-222-2-22-20000002-200000000000000000000-22000000-2200000
χ2722-222-2-2-2222-2-22-2-2-2-2222-2000000-22000000000000000000002-2000000-2200000
χ2822-222-2-2-2222-2-22-2-2-2-2222-2000000-2200000000000000000000-220000002-200000
χ2922-222-2-2-22-2-2-222-2222-2-2-2200002i−2i-22002i−2i000000000000000000002i−2i000000000
χ3022-222-2-2-22-2-2-222-2222-2-2-220000−2i2i-2200−2i2i00000000000000000000−2i2i000000000
χ3122-222-2-2-22-2-2-222-22-2-222-2200002i−2i2-2002i−2i00000000000000000000−2i2i000000000
χ3222-222-2-2-22-2-2-222-22-2-222-220000−2i2i2-200−2i2i000000000000000000002i−2i000000000
χ3322-222-2-2-2-2-2-222-22200002-200002i−2i0000−2i2i0000000022-2-20000002i−2i00000000000
χ3422-222-2-2-2-2-2-222-22200002-200002i−2i0000−2i2i00000000-2-222000000−2i2i00000000000
χ3522-222-2-2-2-2-2-222-22200002-20000−2i2i00002i−2i0000000022-2-2000000−2i2i00000000000
χ3622-222-2-2-2-2-2-222-22200002-20000−2i2i00002i−2i00000000-2-2220000002i−2i00000000000
χ3722-2-2-222-2200-20-2202-22-200i2i2−i2−i2000000002-2i2−i2002-2i2−i2i2−i2i2i2−i2−i2000000000000i2−i20
χ3822-2-2-222-2200-20-2202-22-200i2i2−i2−i200000000-22i2−i200-22i2−i2i2−i2−i2−i2i2i2000000000000−i2i20
χ3922-2-2-222-2200-20-2202-22-200−i2−i2i2i2000000002-2−i2i2002-2−i2i2−i2i2−i2−i2i2i2000000000000−i2i20
χ4022-2-2-222-2200-20-2202-22-200−i2−i2i2i200000000-22−i2i200-22−i2i2−i2i2i2i2−i2−i2000000000000i2−i20
χ4122-2-2-222-2200-20-220-22-2200i2i2−i2−i2000000002-2i2−i200-22−i2i2−i2i2−i2−i2i2i2000000000000i2−i20
χ4222-2-2-222-2200-20-220-22-2200i2i2−i2−i200000000-22i2−i2002-2−i2i2−i2i2i2i2−i2−i2000000000000−i2i20
χ4322-2-2-222-2200-20-220-22-2200−i2−i2i2i2000000002-2−i2i200-22i2−i2i2−i2i2i2−i2−i2000000000000−i2i20
χ4422-2-2-222-2200-20-220-22-2200−i2−i2i2i200000000-22−i2i2002-2i2−i2i2−i2−i2−i2i2i2000000000000i2−i20
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-4-4440040-4-404-4-44000000000000000000000000000000000000000000000
χ47444-4-4-4-4440040-4-40-444-4000000000000000000000000000000000000000000000
χ48444-4-4-4-44-400-40440000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ49444-4-4-4-44-400-4044000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5044-444-4-4-4-4444-4-44-40000-440000000000000000000000000000000000000000000
χ5144-4-4-444-4-400404-400000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ5244-4-4-444-4-400404-40000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ534-444-44-4-404-40400-4000000000000004-4000000000000000000000000000000000
χ544-444-44-4-404-40400-400000000000000-44000000000000000000000000000000000
χ554-444-44-4-40-440-4004000000000000000000000000000000000000000000002i2−2i2000
χ564-444-44-4-40-440-400400000000000000000000000000000000000000000000−2i22i2000
χ574-44-44-44-40000000000000022−2222−220000000000002i2−2i20000002i−2i2i−2i000000000000000
χ584-44-44-44-40000000000000022−2222−22000000000000−2i22i2000000−2i2i−2i2i000000000000000
χ594-44-44-44-400000000000000−2222−22220000000000002i2−2i2000000−2i2i−2i2i000000000000000
χ604-44-44-44-400000000000000−2222−2222000000000000−2i22i20000002i−2i2i−2i000000000000000
χ614-4-44-4-44404-40-400400000000000000000000000000000022−22−2222000000000000000
χ624-4-44-4-44404-40-4004000000000000000000000000000000−222222−22000000000000000
χ634-4-44-4-4440-440400-40000004i−4i−4i4i000000000000000000000000000000000000000
χ644-4-44-4-4440-440400-4000000−4i4i4i−4i000000000000000000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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