Finite Group Databasebeta

← Group #305337

Character table — Group #305337

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-11-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-111-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111111111-1-11111-1-1-1-1-1-11
χ172222222222-2-222-2-22222-20000-22222000022-2-20000-2-20000000000000000000-20000000
χ182222222222-2-222-2-22222-20000-2-2-2-2-20000-2-2-2-2000022000000000000000000020000000
χ192222222222-2-222-2-2-2-2-2-2-20000-222220000-2-2220000-2-2000000000000000000020000000
χ202222222222-2-222-2-2-2-2-2-2-20000-2-2-2-2-2000022220000220000000000000000000-20000000
χ2122222222-2-222-2-2220000-22222-2000022220000-2-222000000-2-20000000000-20000000000
χ2222222222-2-222-2-2220000-22222-20000-2-2-2-20000-2-2-2-200000022000000000020000000000
χ2322222222-2-222-2-2220000-2-2-2-2-2-200002222000022-2-2000000-2-2000000000020000000000
χ2422222222-2-222-2-2220000-2-2-2-2-2-20000-2-2-2-200002222000000220000000000-20000000000
χ2522-2-22-22-22222-2-2-2-222-2-2222-2-2-200000000002-22-20000000000000000000002-200000000
χ2622-2-22-22-22222-2-2-2-222-2-22-2-222-200000000002-2-22000000000000000000000-2200000000
χ2722-2-22-22-22222-2-2-2-2-2-222222-2-2-20000000000-222-2000000000000000000000-2200000000
χ2822-2-22-22-22222-2-2-2-2-2-2222-2-222-20000000000-22-220000000000000000000002-200000000
χ2922-2-22-22-222-2-2-2-22222-2-2-2000020000000000-220000002i2i−2i−2i00000000002i−2i00000000000
χ3022-2-22-22-222-2-2-2-22222-2-2-2000020000000000-22000000−2i−2i2i2i0000000000−2i2i00000000000
χ3122-2-22-22-222-2-2-2-222-2-222-20000200000000002-20000002i2i−2i−2i0000000000−2i2i00000000000
χ3222-2-22-22-222-2-2-2-222-2-222-20000200000000002-2000000−2i−2i2i2i00000000002i−2i00000000000
χ3322-2-22-22-2-2-22222-2-20000-222-2-22000000000000-2200000000002i2i−2i−2i00000000002i−2i00000
χ3422-2-22-22-2-2-22222-2-20000-222-2-22000000000000-220000000000−2i−2i2i2i0000000000−2i2i00000
χ3522-2-22-22-2-2-22222-2-20000-2-2-22220000000000002-200000000002i2i−2i−2i0000000000−2i2i00000
χ3622-2-22-22-2-2-22222-2-20000-2-2-22220000000000002-20000000000−2i−2i2i2i00000000002i−2i00000
χ3722-2-2-22-222-2002-2002-22-20000002i2i−2i−2ii2i2−i2−i22i−2i000000000000i2−i2i2−i2i2−i222−2−2000000002−2000
χ3822-2-2-22-222-2002-2002-22-20000002i2i−2i−2i−i2−i2i2i22i−2i000000000000−i2i2−i2i2−i2i2−2−22200000000−22000
χ3922-2-2-22-222-2002-2002-22-2000000−2i−2i2i2ii2i2−i2−i2−2i2i000000000000i2−i2i2−i2i2−i2−2−22200000000−22000
χ4022-2-2-22-222-2002-2002-22-2000000−2i−2i2i2i−i2−i2i2i2−2i2i000000000000−i2i2−i2i2−i2i222−2−2000000002−2000
χ4122-2-2-22-222-2002-200-22-220000002i2i−2i−2ii2i2−i2−i2−2i2i000000000000i2−i2−i2i2−i2i222−2−200000000−22000
χ4222-2-2-22-222-2002-200-22-220000002i2i−2i−2i−i2−i2i2i2−2i2i000000000000−i2i2i2−i2i2−i2−2−222000000002−2000
χ4322-2-2-22-222-2002-200-22-22000000−2i−2i2i2ii2i2−i2−i22i−2i000000000000i2−i2−i2i2−i2i2−2−222000000002−2000
χ4422-2-2-22-222-2002-200-22-22000000−2i−2i2i2i−i2−i2i2i22i−2i000000000000−i2i2i2−i2i2−i222−2−200000000−22000
χ452-2-2222-2-2002-2002-2000002i−2i2i−2i0i2−i2i2−i22-22-20000002i−2ii2−i22−22−2000000i2−i2i2−i200000000002−20
χ462-2-2222-2-2002-2002-2000002i−2i2i−2i0i2−i2i2−i2-22-22000000−2i2ii2−i22−22−2000000−i2i2−i2i20000000000−220
χ472-2-2222-2-2002-2002-2000002i−2i2i−2i0−i2i2−i2i22-22-20000002i−2i−i2i2−22−22000000−i2i2−i2i20000000000−220
χ482-2-2222-2-2002-2002-2000002i−2i2i−2i0−i2i2−i2i2-22-22000000−2i2i−i2i2−22−22000000i2−i2i2−i200000000002−20
χ492-2-2222-2-2002-2002-200000−2i2i−2i2i0i2−i2i2−i22-22-2000000−2i2ii2−i2−22−22000000i2−i2i2−i20000000000−220
χ502-2-2222-2-2002-2002-200000−2i2i−2i2i0i2−i2i2−i2-22-220000002i−2ii2−i2−22−22000000−i2i2−i2i200000000002−20
χ512-2-2222-2-2002-2002-200000−2i2i−2i2i0−i2i2−i2i22-22-2000000−2i2i−i2i22−22−2000000−i2i2−i2i200000000002−20
χ522-2-2222-2-2002-2002-200000−2i2i−2i2i0−i2i2−i2i2-22-220000002i−2i−i2i22−22−2000000i2−i2i2−i20000000000−220
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ544444-4-4-4-44-400-44004-4-44000000000000000000000000000000000000000000000000000
χ554444-4-4-4-44-400-4400-444-4000000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-44004-400000000000000000000000000000000000022−22−222200000000000000000
χ574444-4-4-4-4-44004-4000000000000000000000000000000000000−222222−2200000000000000000
χ5844-4-44-44-4-4-4-4-44444000040000-4000000000000000000000000000000000000000000000
χ5944-4-4-44-44-4400-4400000000000000002i22i2−2i2−2i200000000000000−2i22i2000000000000000000000
χ6044-4-4-44-44-4400-440000000000000000−2i2−2i22i22i2000000000000002i2−2i2000000000000000000000
χ614-44-44-4-44004-400-44000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ624-44-44-4-44004-400-4400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ634-44-44-4-4400-44004-400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ644-44-44-4-4400-44004-40000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ654-44-4-444-400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ664-44-4-444-400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ674-44-4-444-4000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ684-44-4-444-4000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ694-4-4444-4-400-4400-4400000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ704-4-4444-4-400-4400-440000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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