Finite Group Databasebeta

← Group #118006

Character table — Group #118006

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ911-1-1-1-11111-1-1-1-11111-1-1-111-11-11-1-11iiii−i−i−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−i
χ1011-1-1-1-11111-1-1-1-11111-1-1-111-11-11-1-11iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iii
χ1111-1-1-1-11111-1-1-1-11111-1-1-111-11-11-1-11iiii−i−i−i−i-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−i
χ1211-1-1-1-11111-1-1-1-11111-1-1-111-11-11-1-11iiii−i−i−i−i-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iii
χ1311-1-1-1-11111-1-1-1-11111-1-1-111-11-11-1-11−i−i−i−iiiii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii
χ1411-1-1-1-11111-1-1-1-11111-1-1-111-11-11-1-11−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i
χ1511-1-1-1-11111-1-1-1-11111-1-1-111-11-11-1-11−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii
χ1611-1-1-1-11111-1-1-1-11111-1-1-111-11-11-1-11−i−i−i−iiiii-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i
χ1722222222222222-2-2-2-2-2-2-222-222-2-2-2-20000000000000000000000000000000000002-22-20000
χ1822222222222222-2-2-2-2-2-2-222-222-2-2-2-2000000000000000000000000000000000000-22-220000
χ19222222222222-2-22222222-2-22-2-2-2-2-2-20000000022-2-222-2-20000000000000000000000000000
χ20222222222222-2-22222222-2-22-2-2-2-2-2-200000000-2-222-2-2220000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-2000000000000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-222000000000000000000000000000000000000
χ2322222222-2-2-2-22222-2-222-222-2-2-2-22-2200000000000000000000000022-2-222-2-2000000000000
χ2422222222-2-2-2-22222-2-222-222-2-2-2-22-22000000000000000000000000-2-222-2-222000000000000
χ2522222222-2-2-2-222-2-222-2-22222-2-22-22-200000000000000000000000000000000000000002-22-2
χ2622222222-2-2-2-222-2-222-2-22222-2-22-22-20000000000000000000000000000000000000000-22-22
χ2722222222-2-2-2-2-2-222-2-222-2-2-2-2222-22-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2822222222-2-2-2-2-2-222-2-222-2-2-2-2222-22-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2922222222-2-2-2-2-2-2-2-222-2-22-2-2222-22-22000000000000000000000000000000002-22-200000000
χ3022222222-2-2-2-2-2-2-2-222-2-22-2-2222-22-2200000000000000000000000000000000-22-2200000000
χ3122-2-2-2-22222-2-2222222-2-2-2-2-2-2-22-222-20000000022-2-2-2-2220000000000000000000000000000
χ3222-2-2-2-22222-2-2222222-2-2-2-2-2-2-22-222-200000000-2-22222-2-20000000000000000000000000000
χ3322-2-2-2-22222-2-222-2-2-2-2222-2-22-222-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ3422-2-2-2-22222-2-222-2-2-2-2222-2-22-222-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ3522-2-2-2-22222-2-2-2-2-2-2-2-22222222-2-222-20000000000000000000000000000000000002i−2i−2i2i0000
χ3622-2-2-2-22222-2-2-2-2-2-2-2-22222222-2-222-2000000000000000000000000000000000000−2i2i2i−2i0000
χ3722-2-2-2-222-2-2222222-2-2-2-22-2-222-222-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ3822-2-2-2-222-2-2222222-2-2-2-22-2-222-222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ3922-2-2-2-222-2-22222-2-22222-2-2-2-22-2-2-222000000000000000000000000000000002i−2i−2i2i00000000
χ4022-2-2-2-222-2-22222-2-22222-2-2-2-22-2-2-22200000000000000000000000000000000−2i2i2i−2i00000000
χ4122-2-2-2-222-2-222-2-222-2-2-2-22222-22-2-22200000000000000000000000022-2-2-2-222000000000000
χ4222-2-2-2-222-2-222-2-222-2-2-2-22222-22-2-222000000000000000000000000-2-22222-2-2000000000000
χ4322-2-2-2-222-2-222-2-2-2-22222-222-2-2222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ4422-2-2-2-222-2-222-2-2-2-22222-222-2-2222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ452-222-2-22-22-22-2002-22-22-2-200200000000000000002i−2i002i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ462-222-2-22-22-22-2002-22-22-2-200200000000000000002i−2i002i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ472-222-2-22-22-22-2002-22-22-2-20020000000000000000−2i2i00−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ482-222-2-22-22-22-2002-22-22-2-20020000000000000000−2i2i00−2i2i−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ492-222-2-22-2-22-22002-2-222-2200-2000000000000002-2002-200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ502-222-2-22-2-22-22002-2-222-2200-2000000000000002-2002-200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ512-222-2-22-2-22-22002-2-222-2200-200000000000000-2200-2200i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ522-222-2-22-2-22-22002-2-222-2200-200000000000000-2200-2200−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ532-2-2-2222-22-2-22002-22-2-22200-200000000000000002i−2i00−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ542-2-2-2222-22-2-22002-22-2-22200-200000000000000002i−2i00−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ552-2-2-2222-22-2-22002-22-2-22200-20000000000000000−2i2i002i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ562-2-2-2222-22-2-22002-22-2-22200-20000000000000000−2i2i002i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ572-2-2-2222-2-222-2002-2-22-22-2002000000000000002-200-2200i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ582-2-2-2222-2-222-2002-2-22-22-2002000000000000002-200-2200−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ592-2-2-2222-2-222-2002-2-22-22-200200000000000000-22002-200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ602-2-2-2222-2-222-2002-2-22-22-200200000000000000-22002-200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ614-444-4-44-44-44-400-44-44-44400-400000000000000000000000000000000000000000000000000
χ624-444-4-44-4-44-4400-444-4-44-400400000000000000000000000000000000000000000000000000
χ634-44-44-4-4400004i−4i00000004i−4i00000002-22i−2i2-22i−2i000000000000000000000000000000000000
χ644-44-44-4-4400004i−4i00000004i−4i0000000-22−2i2i-22−2i2i000000000000000000000000000000000000
χ654-44-44-4-440000−4i4i0000000−4i4i00000002-2−2i2i2-2−2i2i000000000000000000000000000000000000
χ664-44-44-4-440000−4i4i0000000−4i4i0000000-222i−2i-222i−2i000000000000000000000000000000000000
χ674-4-44-44-4400004i−4i0000000−4i4i00000002i−2i2-2−2i2i-22000000000000000000000000000000000000
χ684-4-44-44-4400004i−4i0000000−4i4i0000000−2i2i-222i−2i2-2000000000000000000000000000000000000
χ694-4-44-44-440000−4i4i00000004i−4i00000002i−2i-22−2i2i2-2000000000000000000000000000000000000
χ704-4-44-44-440000−4i4i00000004i−4i0000000−2i2i2-22i−2i-22000000000000000000000000000000000000
χ714-4-4-4444-44-4-4400-44-444-4-400400000000000000000000000000000000000000000000000000
χ724-4-4-4444-4-444-400-444-44-4400-400000000000000000000000000000000000000000000000000
χ73888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000000
χ7488-888-8-8-8000000000000000000000000000000000000000000000000000000000000000000

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