Finite Group Databasebeta

← Group #274167

Character table — Group #274167

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444444444444888888884444488888888888822448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ511111111111111111111-1-1-1-11111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1-1-11111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-111-1-111-1-1
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ91111111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-11
χ101111111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111-1
χ111111111111111111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111-1
χ121111111111111111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-11
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1111111-1-111-1-1-1-111-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-111-1-11111-1-11-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-111-1-11111-1-1-1-11-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-1-1-111-1-1-1-11111-11
χ17222222222-2-222-2-2222-2-22222-2-2-2-2-2-2-2-200000000222-2-200000000000000000000000000
χ18222222222-2-222-2-2222-2-2-2-2-2-2-2-2-2-2222200000000-2-222200000000000000000000000000
χ19222222222-2-222-2-22-2-2222222-2-222-2-2-2-200000000-2-2-22200000000000000000000000000
χ20222222222-2-222-2-22-2-222-2-2-2-2-2-22222220000000022-2-2-200000000000000000000000000
χ2122222222-222-2-222-222220000-2-2-2-200002222222200-200-2-2-2-20000000000000000000000
χ2222222222-222-2-222-222220000-2-2-2-20000-2-2-2-2-2-2-2-200-20022220000000000000000000000
χ2322222222-222-2-222-2-2-2-2-20000-2-22200002222-2-2-2-200200-2-2220000000000000000000000
χ2422222222-222-2-222-2-2-2-2-20000-2-2220000-2-2-2-222220020022-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-20000222200000000000000-20000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-20000222200000000000000-2000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222000022-2-20000000000000020000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222000022-2-2000000000000002000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ2922-2-222-2-2200-2-2002002i−2i22-2-2002i−2i0000i2i2−i2−i222−2−20002i−2ii2−i22−2i2−i2i2−i22−22−200000000000000
χ3022-2-222-2-2200-2-2002002i−2i22-2-2002i−2i0000−i2−i2i2i2−2−2220002i−2i−i2i2−22−i2i2−i2i2−22−2200000000000000
χ3122-2-222-2-2200-2-2002002i−2i-2-222002i−2i0000i2i2−i2−i222−2−2000−2i2ii2−i22−2−i2i2−i2i2−22−2200000000000000
χ3222-2-222-2-2200-2-2002002i−2i-2-222002i−2i0000−i2−i2i2i2−2−222000−2i2i−i2i2−22i2−i2i2−i22−22−200000000000000
χ3322-2-222-2-2200-2-200200−2i2i22-2-200−2i2i0000i2i2−i2−i2−2−222000−2i2ii2−i2−22i2−i2i2−i2−22−2200000000000000
χ3422-2-222-2-2200-2-200200−2i2i22-2-200−2i2i0000−i2−i2i2i222−2−2000−2i2i−i2i22−2−i2i2−i2i22−22−200000000000000
χ3522-2-222-2-2200-2-200200−2i2i-2-22200−2i2i0000i2i2−i2−i2−2−2220002i−2ii2−i2−22−i2i2−i2i22−22−200000000000000
χ3622-2-222-2-2200-2-200200−2i2i-2-22200−2i2i0000−i2−i2i2i222−2−20002i−2i−i2i22−2i2−i2i2−i2−22−2200000000000000
χ3722-2-222-2-2-2002200-2002i−2i000000−2i2i2i2i−2i−2ii2i2−i2−i222−2−22-2000−i2i2−222−2−22i2−i2−i2i200000000000000
χ3822-2-222-2-2-2002200-2002i−2i000000−2i2i2i2i−2i−2i−i2−i2i2i2−2−2222-2000i2−i22−2−222−2−i2i2i2−i200000000000000
χ3922-2-222-2-2-2002200-2002i−2i000000−2i2i−2i−2i2i2ii2i2−i2−i222−2−2-22000−i2i2−22−222−2−i2i2i2−i200000000000000
χ4022-2-222-2-2-2002200-2002i−2i000000−2i2i−2i−2i2i2i−i2−i2i2i2−2−222-22000i2−i22−22−2−22i2−i2−i2i200000000000000
χ4122-2-222-2-2-2002200-200−2i2i0000002i−2i2i2i−2i−2ii2i2−i2−i2−2−222-22000−i2i22−22−2−22−i2i2i2−i200000000000000
χ4222-2-222-2-2-2002200-200−2i2i0000002i−2i2i2i−2i−2i−i2−i2i2i222−2−2-22000i2−i2−22−222−2i2−i2−i2i200000000000000
χ4322-2-222-2-2-2002200-200−2i2i0000002i−2i−2i−2i2i2ii2i2−i2−i2−2−2222-2000−i2i22−2−222−2i2−i2−i2i200000000000000
χ4422-2-222-2-2-2002200-200−2i2i0000002i−2i−2i−2i2i2i−i2−i2i2i222−2−22-2000i2−i2−222−2−22−i2i2i2−i200000000000000
χ452-2-22-222-222-22-22-2-200002i−2i2i−2i2-2002i−2i2i−2i0000000000000000000000000002-22i−2i00000000
χ462-2-22-222-222-22-22-2-200002i−2i2i−2i2-2002i−2i2i−2i000000000000000000000000000-22−2i2i00000000
χ472-2-22-222-222-22-22-2-20000−2i2i−2i2i2-200−2i2i−2i2i0000000000000000000000000002-2−2i2i00000000
χ482-2-22-222-222-22-22-2-20000−2i2i−2i2i2-200−2i2i−2i2i000000000000000000000000000-222i−2i00000000
χ492-2-22-222-22-222-2-22-200002i−2i2i−2i-2200−2i2i−2i2i00000000000000000000000002-20000002i−2i0000
χ502-2-22-222-22-222-2-22-200002i−2i2i−2i-2200−2i2i−2i2i0000000000000000000000000-22000000−2i2i0000
χ512-2-22-222-22-222-2-22-20000−2i2i−2i2i-22002i−2i2i−2i00000000000000000000000002-2000000−2i2i0000
χ522-2-22-222-22-222-2-22-20000−2i2i−2i2i-22002i−2i2i−2i0000000000000000000000000-220000002i−2i0000
χ534444-4-4-4-404-400-4400000000000000000000000000000000000000000000000022−22000000
χ544444-4-4-4-404-400-44000000000000000000000000000000000000000000000000−2222000000
χ554444-4-4-4-40-44004-4000000000000000000000000000000000000000000000000000022−2200
χ564444-4-4-4-40-44004-40000000000000000000000000000000000000000000000000000−222200
χ574-44-44-44-4000000004-4000000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000000
χ584-44-44-44-4000000004-400000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000000
χ594-44-44-44-400000000-44000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000
χ604-44-44-44-400000000-4400000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000
χ614-44-4-44-44400-4400-400004i−4i−4i4i00000000000000000000000000000000000000000000000
χ624-44-4-44-44400-4400-40000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ634-44-4-44-44-4004-40040000000000004-4-44000000000000000000000000000000000000000
χ644-44-4-44-44-4004-4004000000000000-444-4000000000000000000000000000000000000000
χ654-4-444-4-4404400-4-40000000000000000000004i−4i−4i4i0000000000000000000000000000000
χ664-4-444-4-4404400-4-4000000000000000000000−4i4i4i−4i0000000000000000000000000000000
χ674-4-444-4-440-4-40044000000000000000004-4-4400000000000000000000000000000000000
χ684-4-444-4-440-4-4004400000000000000000-444-400000000000000000000000000000000000
χ694-4-44-444-4-44-4-444-4400000000-44000000000000000000000000000000000000000000000
χ704-4-44-444-4-4-44-44-444000000004-4000000000000000000000000000000000000000000000
χ7188-8-8-8-888000000000000000000000000000000000000000000000000000000000000000

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