Finite Group Databasebeta

← Group #100178

Character table — Group #100178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iii
χ172222222222222222-2-2-2-22222-2-2-2-2-2-222-2-2220000-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-200002200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-2-2-222-2-2-2-222-2-2-2-200002200000000000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-222220000-2-200000000000000000000000000000000
χ2122222222-2-2-2-222-2-2222222-2-2-2-222-2-200000000000000000000000022-2-222-2-2000000000000
χ2222222222-2-2-2-222-2-2222222-2-2-2-222-2-2000000000000000000000000-2-222-2-222000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-222-2-222-2-22200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-222-2-222-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2522222222-2-2-2-2-2-2222222-2-222-2-2-2-222000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-222-2-2-2-2220000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-2-22-2-222-22-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2-22-200000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3022-2-22-2-222-22-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2-22-20000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3122-2-22-2-222-22-22i−2i2i−2i−2i−2i2i2i2i−2i2i−2i−2i2i-22-220000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ3222-2-22-2-222-22-22i−2i2i−2i−2i−2i2i2i2i−2i2i−2i−2i2i-22-22000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ3322-2-22-2-222-22-2−2i2i−2i2i2i2i−2i−2i−2i2i−2i2i2i−2i-22-220000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ3422-2-22-2-222-22-2−2i2i−2i2i2i2i−2i−2i−2i2i−2i2i2i−2i-22-22000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ3522-2-22-2-222-22-2−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i−2i2i2-22-200000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ3622-2-22-2-222-22-2−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i−2i2i2-22-20000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ3722-2-22-2-22-22-222i−2i−2i2i2i2i−2i−2i2i−2i−2i2i−2i2i2-2-220000002i2i−2i−2i0022-2-20000000000000000000000000000
χ3822-2-22-2-22-22-222i−2i−2i2i2i2i−2i−2i2i−2i−2i2i−2i2i2-2-22000000−2i−2i2i2i00-2-2220000000000000000000000000000
χ3922-2-22-2-22-22-222i−2i−2i2i−2i−2i2i2i2i−2i−2i2i2i−2i-222-2000000000000000000000000000000002-22i−2i00000000
χ4022-2-22-2-22-22-222i−2i−2i2i−2i−2i2i2i2i−2i−2i2i2i−2i-222-200000000000000000000000000000000-22−2i2i00000000
χ4122-2-22-2-22-22-22−2i2i2i−2i2i2i−2i−2i−2i2i2i−2i−2i2i-222-2000000000000000000000000000000002-2−2i2i00000000
χ4222-2-22-2-22-22-22−2i2i2i−2i2i2i−2i−2i−2i2i2i−2i−2i2i-222-200000000000000000000000000000000-222i−2i00000000
χ4322-2-22-2-22-22-22−2i2i2i−2i−2i−2i2i2i−2i2i2i−2i2i−2i2-2-220000002i2i−2i−2i00-2-2220000000000000000000000000000
χ4422-2-22-2-22-22-22−2i2i2i−2i−2i−2i2i2i−2i2i2i−2i2i−2i2-2-22000000−2i−2i2i2i0022-2-20000000000000000000000000000
χ452-2-2-2-222222-2-222-2-20000-2-2220000002i−2i002i−2i00000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ462-2-2-2-222222-2-222-2-20000-2-2220000002i−2i002i−2i0000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ472-2-2-2-222222-2-222-2-20000-2-222000000−2i2i00−2i2i00000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ482-2-2-2-222222-2-222-2-20000-2-222000000−2i2i00−2i2i0000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ492-2-2-2-222222-2-2-2-222000022-2-20000002i−2i00−2i2i0000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ502-2-2-2-222222-2-2-2-222000022-2-20000002i−2i00−2i2i0000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ512-2-2-2-222222-2-2-2-222000022-2-2000000−2i2i002i−2i0000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ522-2-2-2-222222-2-2-2-222000022-2-2000000−2i2i002i−2i0000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ532-2-2-2-2222-2-22222220000-2-2-2-2000000002-20000002-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ542-2-2-2-2222-2-22222220000-2-2-2-2000000002-20000002-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ552-2-2-2-2222-2-22222220000-2-2-2-200000000-22000000-220000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ562-2-2-2-2222-2-22222220000-2-2-2-200000000-22000000-220000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ572-2-2-2-2222-2-222-2-2-2-200002222000000002-2000000-2200002−2−22−222−22−2−22−222−2000000000000
χ582-2-2-2-2222-2-222-2-2-2-200002222000000002-2000000-220000−222−22−2−22−222−22−2−22000000000000
χ592-2-2-2-2222-2-222-2-2-2-20000222200000000-220000002-200002−2−22−222−2−222−22−2−22000000000000
χ602-2-2-2-2222-2-222-2-2-2-20000222200000000-220000002-20000−222−22−2−222−2−22−222−2000000000000
χ614-444-4-4-444-4-444i−4i−4i4i0000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ624-444-4-4-444-4-44−4i4i4i−4i00004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ634-444-4-4-44-444-44i−4i4i−4i0000−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ644-444-4-4-44-444-4−4i4i−4i4i00004i−4i4i−4i00000000000000000000000000000000000000000000000000
χ654-44-444-4-4000000004-44-400000000000000002i−2i2i−2i002i−2i2i−2i0000000000000000000000000000
χ664-44-444-4-4000000004-44-40000000000000000−2i2i−2i2i00−2i2i−2i2i0000000000000000000000000000
χ674-44-444-4-400000000-44-4400000000000000002i−2i2i−2i00−2i2i−2i2i0000000000000000000000000000
χ684-44-444-4-400000000-44-440000000000000000−2i2i−2i2i002i−2i2i−2i0000000000000000000000000000
χ694-4-444-44-4000000004i−4i−4i4i00000000000000002-2-2200−2i2i2i−2i0000000000000000000000000000
χ704-4-444-44-4000000004i−4i−4i4i0000000000000000-222-2002i−2i−2i2i0000000000000000000000000000
χ714-4-444-44-400000000−4i4i4i−4i00000000000000002-2-22002i−2i−2i2i0000000000000000000000000000
χ724-4-444-44-400000000−4i4i4i−4i0000000000000000-222-200−2i2i2i−2i0000000000000000000000000000
χ73888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ7488-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.