Finite Group Databasebeta

← Group #310425

Character table — Group #310425

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ311111111111111111111111111-1-11111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-11111-1-11
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-111-1-111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111
χ91111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ101111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111111-1
χ111111111111111111-1-1-1-1111111-1-111-1-11111111111-1-1-1-11111-1-11-1-1-1-1-11111-1-1-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-11111-1-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-111111-1-111-1-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-111-1-1-11111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-111-1-1-111-1-1111
χ17222222222-22-2-222-22222-2-200002200-2-200000022-2-2000000000000000-20000000
χ18222222222-22-2-222-22222-2-20000-2-200-2-2000000-2-22200000000000000020000000
χ19222222222-22-2-222-2-2-2-2-2-2-20000220022000000-2-222000000000000000-20000000
χ20222222222-22-2-222-2-2-2-2-2-2-20000-2-2002200000022-2-200000000000000020000000
χ2122222222-22-222-2-220000-2-2222200220022-2-2-2-200000000000000-2000000000000
χ2222222222-22-222-2-220000-2-2222200-2-200-2-222-2-2000000000000002000000000000
χ2322222222-22-222-2-220000-2-2-2-2-2-2002200-2-2222200000000000000-2000000000000
χ2422222222-22-222-2-220000-2-2-2-2-2-200-2-20022-2-222000000000000002000000000000
χ2522-22-2-22-2-202002-2022-2-200i2i2−i2−i22-200000000i2−i22-200i2i2−i2−i2i2i2−i2−i2000000000000i2−i20
χ2622-22-2-22-2-202002-2022-2-200i2i2−i2−i2-2200000000i2−i2-2200i2i2−i2−i2−i2−i2i2i2000000000000−i2i20
χ2722-22-2-22-2-202002-2022-2-200−i2−i2i2i22-200000000−i2i22-200−i2−i2i2i2−i2−i2i2i2000000000000−i2i20
χ2822-22-2-22-2-202002-2022-2-200−i2−i2i2i2-2200000000−i2i2-2200−i2−i2i2i2i2i2−i2−i2000000000000i2−i20
χ2922-22-2-22-2-202002-20-2-22200i2i2−i2−i22-200000000i2−i2-2200−i2−i2i2i2−i2−i2i2i2000000000000i2−i20
χ3022-22-2-22-2-202002-20-2-22200i2i2−i2−i2-2200000000i2−i22-200−i2−i2i2i2i2i2−i2−i2000000000000−i2i20
χ3122-22-2-22-2-202002-20-2-22200−i2−i2i2i22-200000000−i2i2-2200i2i2−i2−i2i2i2−i2−i2000000000000−i2i20
χ3222-22-2-22-2-202002-20-2-22200−i2−i2i2i2-2200000000−i2i22-200i2i2−i2−i2−i2−i2i2i2000000000000i2−i20
χ3322-2-2-22-2222-2-2-22-222i−2i2i−2i2-2000000002i−2i000000000000000000000002i−2i02-200000
χ3422-2-2-22-2222-2-2-22-222i−2i2i−2i2-2000000002i−2i00000000000000000000000−2i2i0-2200000
χ3522-2-2-22-2222-2-2-22-22−2i2i−2i2i2-200000000−2i2i000000000000000000000002i−2i0-2200000
χ3622-2-2-22-2222-2-2-22-22−2i2i−2i2i2-200000000−2i2i00000000000000000000000−2i2i02-200000
χ3722-2-2-22-222-2-2222-2-22i−2i2i−2i-2200000000−2i2i2i−2i2i−2i000000000000002-20000000000000
χ3822-2-2-22-222-2-2222-2-22i−2i2i−2i-2200000000−2i2i−2i2i−2i2i00000000000000-220000000000000
χ3922-2-2-22-222-2-2222-2-2−2i2i−2i2i-22000000002i−2i2i−2i2i−2i00000000000000-220000000000000
χ4022-2-2-22-222-2-2222-2-2−2i2i−2i2i-22000000002i−2i−2i2i−2i2i000000000000002-20000000000000
χ4122-2-2-22-22-2-2222-22-200002-200000000002i−2i−2i2i0000002i−2i2i−2i00000002-20000000000
χ4222-2-2-22-22-2-2222-22-200002-200000000002i−2i−2i2i000000−2i2i−2i2i0000000-220000000000
χ4322-2-2-22-22-2-2222-22-200002-20000000000−2i2i2i−2i0000002i−2i2i−2i0000000-220000000000
χ4422-2-2-22-22-2-2222-22-200002-20000000000−2i2i2i−2i000000−2i2i−2i2i00000002-20000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-440400-4-400000000000000000000000000022−22−22220000000000000000000
χ47444-44-4-4-440400-4-4000000000000000000000000000−222222−220000000000000000000
χ48444-44-4-4-4-40-4004404i−4i−4i4i000000000000000000000000000000000000000000000
χ49444-44-4-4-4-40-400440−4i4i4i−4i000000000000000000000000000000000000000000000
χ5044-44-4-44-440-400-4400000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ5144-44-4-44-440-400-440000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ5244-4-4-44-44-444-4-4-4440000-440000000000000000000000000000000000000000000
χ534-444-44-4-40000000000000022−2222−22000000000000002i2−2i200002i−2i2i−2i000000000000000
χ544-444-44-4-40000000000000022−2222−2200000000000000−2i22i20000−2i2i−2i2i000000000000000
χ554-444-44-4-400000000000000−2222−2222000000000000002i2−2i20000−2i2i−2i2i000000000000000
χ564-444-44-4-400000000000000−2222−222200000000000000−2i22i200002i−2i2i−2i000000000000000
χ574-44-4-4-4440404-400-4000000000000000000000000000000000000000000002i2−2i2000
χ584-44-4-4-4440404-400-400000000000000000000000000000000000000000000−2i22i2000
χ594-44-4-4-4440-40-440040000000000004-400000000000000000000000000000000000
χ604-44-4-4-4440-40-44004000000000000-4400000000000000000000000000000000000
χ614-4-444-4-44040-4400-40000004i−4i−4i4i000000000000000000000000000000000000000
χ624-4-444-4-44040-4400-4000000−4i4i4i−4i000000000000000000000000000000000000000
χ634-4-444-4-440-404-400400000000000000000000000000000022−22−2222000000000000000
χ644-4-444-4-440-404-4004000000000000000000000000000000−222222−22000000000000000
χ658-8-8-8888-8000000000000000000000000000000000000000000000000000000000

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