Finite Group Databasebeta

← Group #17860

Character table — Group #17860

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111111122222222444444444444444444888811111111222222224444444444444444448888
order1222444444448888444488888888888888248822224444444488884444888888888888882488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ41111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-1-1-111-1-1ii−i−i11-1-1i−iii−i−i11-1-1ii−i−i1-1i−i1111-1-1-1-111-1-1ii−i−i11-1-1i−iii−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-111-1-1ii−i−i11-1-1i−iii−i−i-1-111−i−iii-11−ii1111-1-1-1-111-1-1ii−i−i11-1-1i−iii−i−i-1-111−i−iii-11−ii
χ111111-1-1-1-111-1-1ii−i−i-1-111i−i−i−iii11-1-1ii−i−i-11−ii1111-1-1-1-111-1-1ii−i−i-1-111i−i−i−iii11-1-1ii−i−i-11−ii
χ121111-1-1-1-111-1-1ii−i−i-1-111i−i−i−iii-1-111−i−iii1-1i−i1111-1-1-1-111-1-1ii−i−i-1-111i−i−i−iii-1-111−i−iii1-1i−i
χ131111-1-1-1-111-1-1−i−iii11-1-1−ii−i−iii11-1-1−i−iii1-1−ii1111-1-1-1-111-1-1−i−iii11-1-1−ii−i−iii11-1-1−i−iii1-1−ii
χ141111-1-1-1-111-1-1−i−iii11-1-1−ii−i−iii-1-111ii−i−i-11i−i1111-1-1-1-111-1-1−i−iii11-1-1−ii−i−iii-1-111ii−i−i-11i−i
χ151111-1-1-1-111-1-1−i−iii-1-111−iiii−i−i11-1-1−i−iii-11i−i1111-1-1-1-111-1-1−i−iii-1-111−iiii−i−i11-1-1−i−iii-11i−i
χ161111-1-1-1-111-1-1−i−iii-1-111−iiii−i−i-1-111ii−i−i1-1−ii1111-1-1-1-111-1-1−i−iii-1-111−iiii−i−i-1-111ii−i−i1-1−ii
χ1722222222-2-2-2-222220000-2-2000000000000000022222222-2-2-2-222220000-2-20000000000000000
χ1822222222-2-2-2-2-2-2-2-2000022000000000000000022222222-2-2-2-2-2-2-2-20000220000000000000000
χ192222-2-2-2-2-2-2222i2i−2i−2i0000−2i2i00000000000000002222-2-2-2-2-2-2222i2i−2i−2i0000−2i2i0000000000000000
χ202222-2-2-2-2-2-222−2i−2i2i2i00002i−2i00000000000000002222-2-2-2-2-2-222−2i−2i2i2i00002i−2i0000000000000000
χ2122-2-222-2-200002-22-20000000000i2−i2i2−i2i2−i2i2−i2000022-2-222-2-200002-22-20000000000i2−i2i2−i2i2−i2i2−i20000
χ2222-2-222-2-200002-22-20000000000−i2i2−i2i2−i2i2−i2i2000022-2-222-2-200002-22-20000000000−i2i2−i2i2−i2i2−i2i20000
χ2322-2-222-2-20000-22-220000000000i2−i2i2−i2−i2i2−i2i2000022-2-222-2-20000-22-220000000000i2−i2i2−i2−i2i2−i2i20000
χ2422-2-222-2-20000-22-220000000000−i2i2−i2i2i2−i2i2−i2000022-2-222-2-20000-22-220000000000−i2i2−i2i2i2−i2i2−i20000
χ2522-2-2-2-22200002i−2i−2i2i0000000000i2−i2−i2i2−222−2000022-2-2-2-22200002i−2i−2i2i0000000000i2−i2−i2i2−222−20000
χ2622-2-2-2-22200002i−2i−2i2i0000000000−i2i2i2−i22−2−22000022-2-2-2-22200002i−2i−2i2i0000000000−i2i2i2−i22−2−220000
χ2722-2-2-2-2220000−2i2i2i−2i0000000000i2−i2−i2i22−2−22000022-2-2-2-2220000−2i2i2i−2i0000000000i2−i2−i2i22−2−220000
χ2822-2-2-2-2220000−2i2i2i−2i0000000000−i2i2i2−i2−222−2000022-2-2-2-2220000−2i2i2i−2i0000000000−i2i2i2−i2−222−20000
χ292-22-22i−2i2i−2i2-22i−2i00000000002ζ−2ζ2ζ3−2ζ30000000000002-22-22i−2i2i−2i2-22i−2i00000000002ζ−2ζ2ζ3−2ζ3000000000000
χ302-22-22i−2i2i−2i2-22i−2i0000000000−2ζ2ζ−2ζ32ζ30000000000002-22-22i−2i2i−2i2-22i−2i0000000000−2ζ2ζ−2ζ32ζ3000000000000
χ312-22-22i−2i2i−2i-22−2i2i00002-22i−2i0000000000000000002-22-22i−2i2i−2i-22−2i2i00002-22i−2i000000000000000000
χ322-22-22i−2i2i−2i-22−2i2i0000-22−2i2i0000000000000000002-22-22i−2i2i−2i-22−2i2i0000-22−2i2i000000000000000000
χ332-22-2−2i2i−2i2i2-2−2i2i00000000002ζ3−2ζ32ζ−2ζ0000000000002-22-2−2i2i−2i2i2-2−2i2i00000000002ζ3−2ζ32ζ−2ζ000000000000
χ342-22-2−2i2i−2i2i2-2−2i2i0000000000−2ζ32ζ3−2ζ2ζ0000000000002-22-2−2i2i−2i2i2-2−2i2i0000000000−2ζ32ζ3−2ζ2ζ000000000000
χ352-22-2−2i2i−2i2i-222i−2i00002-2−2i2i0000000000000000002-22-2−2i2i−2i2i-222i−2i00002-2−2i2i000000000000000000
χ362-22-2−2i2i−2i2i-222i−2i0000-222i−2i0000000000000000002-22-2−2i2i−2i2i-222i−2i0000-222i−2i000000000000000000
χ374-4-444i−4i−4i4i0000000000000000000000000000004-4-444i−4i−4i4i000000000000000000000000000000
χ384-4-44−4i4i4i−4i0000000000000000000000000000004-4-44−4i4i4i−4i000000000000000000000000000000
χ3911111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4011111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ411111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ421111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1
χ43111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-111
χ44111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1
χ45111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ46111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111
χ471111-1-1-1-111-1-1ii−i−i11-1-1i−iii−i−i11-1-1ii−i−i1-1i−i-1-1-1-11111-1-111−i−iii-1-111−ii−i−iii-1-111−i−iii-11−ii
χ481111-1-1-1-111-1-1ii−i−i11-1-1i−iii−i−i-1-111−i−iii-11−ii-1-1-1-11111-1-111−i−iii-1-111−ii−i−iii11-1-1ii−i−i1-1i−i
χ491111-1-1-1-111-1-1ii−i−i-1-111i−i−i−iii11-1-1ii−i−i-11−ii-1-1-1-11111-1-111−i−iii11-1-1−iiii−i−i-1-111−i−iii1-1i−i
χ501111-1-1-1-111-1-1ii−i−i-1-111i−i−i−iii-1-111−i−iii1-1i−i-1-1-1-11111-1-111−i−iii11-1-1−iiii−i−i11-1-1ii−i−i-11−ii
χ511111-1-1-1-111-1-1−i−iii11-1-1−ii−i−iii11-1-1−i−iii1-1−ii-1-1-1-11111-1-111ii−i−i-1-111i−iii−i−i-1-111ii−i−i-11i−i
χ521111-1-1-1-111-1-1−i−iii11-1-1−ii−i−iii-1-111ii−i−i-11i−i-1-1-1-11111-1-111ii−i−i-1-111i−iii−i−i11-1-1−i−iii1-1−ii
χ531111-1-1-1-111-1-1−i−iii-1-111−iiii−i−i11-1-1−i−iii-11i−i-1-1-1-11111-1-111ii−i−i11-1-1i−i−i−iii-1-111ii−i−i1-1−ii
χ541111-1-1-1-111-1-1−i−iii-1-111−iiii−i−i-1-111ii−i−i1-1−ii-1-1-1-11111-1-111ii−i−i11-1-1i−i−i−iii11-1-1−i−iii-11i−i
χ5522222222-2-2-2-222220000-2-20000000000000000-2-2-2-2-2-2-2-22222-2-2-2-20000220000000000000000
χ5622222222-2-2-2-2-2-2-2-20000220000000000000000-2-2-2-2-2-2-2-2222222220000-2-20000000000000000
χ572222-2-2-2-2-2-2222i2i−2i−2i0000−2i2i0000000000000000-2-2-2-2222222-2-2−2i−2i2i2i00002i−2i0000000000000000
χ582222-2-2-2-2-2-222−2i−2i2i2i00002i−2i0000000000000000-2-2-2-2222222-2-22i2i−2i−2i0000−2i2i0000000000000000
χ5922-2-222-2-200002-22-20000000000i2−i2i2−i2i2−i2i2−i20000-2-222-2-2220000-22-220000000000−i2i2−i2i2−i2i2−i2i20000
χ6022-2-222-2-200002-22-20000000000−i2i2−i2i2−i2i2−i2i20000-2-222-2-2220000-22-220000000000i2−i2i2−i2i2−i2i2−i20000
χ6122-2-222-2-20000-22-220000000000i2−i2i2−i2−i2i2−i2i20000-2-222-2-22200002-22-20000000000−i2i2−i2i2i2−i2i2−i20000
χ6222-2-222-2-20000-22-220000000000−i2i2−i2i2i2−i2i2−i20000-2-222-2-22200002-22-20000000000i2−i2i2−i2−i2i2−i2i20000
χ6322-2-2-2-22200002i−2i−2i2i0000000000i2−i2−i2i2−222−20000-2-22222-2-20000−2i2i2i−2i0000000000−i2i2i2−i22−2−220000
χ6422-2-2-2-22200002i−2i−2i2i0000000000−i2i2i2−i22−2−220000-2-22222-2-20000−2i2i2i−2i0000000000i2−i2−i2i2−222−20000
χ6522-2-2-2-2220000−2i2i2i−2i0000000000i2−i2−i2i22−2−220000-2-22222-2-200002i−2i−2i2i0000000000−i2i2i2−i2−222−20000
χ6622-2-2-2-2220000−2i2i2i−2i0000000000−i2i2i2−i2−222−20000-2-22222-2-200002i−2i−2i2i0000000000i2−i2−i2i22−2−220000
χ672-22-22i−2i2i−2i2-22i−2i00000000002ζ−2ζ2ζ3−2ζ3000000000000-22-22−2i2i−2i2i-22−2i2i0000000000−2ζ2ζ−2ζ32ζ3000000000000
χ682-22-22i−2i2i−2i2-22i−2i0000000000−2ζ2ζ−2ζ32ζ3000000000000-22-22−2i2i−2i2i-22−2i2i00000000002ζ−2ζ2ζ3−2ζ3000000000000
χ692-22-22i−2i2i−2i-22−2i2i00002-22i−2i000000000000000000-22-22−2i2i−2i2i2-22i−2i0000-22−2i2i000000000000000000
χ702-22-22i−2i2i−2i-22−2i2i0000-22−2i2i000000000000000000-22-22−2i2i−2i2i2-22i−2i00002-22i−2i000000000000000000
χ712-22-2−2i2i−2i2i2-2−2i2i00000000002ζ3−2ζ32ζ−2ζ000000000000-22-222i−2i2i−2i-222i−2i0000000000−2ζ32ζ3−2ζ2ζ000000000000
χ722-22-2−2i2i−2i2i2-2−2i2i0000000000−2ζ32ζ3−2ζ2ζ000000000000-22-222i−2i2i−2i-222i−2i00000000002ζ3−2ζ32ζ−2ζ000000000000
χ732-22-2−2i2i−2i2i-222i−2i00002-2−2i2i000000000000000000-22-222i−2i2i−2i2-2−2i2i0000-222i−2i000000000000000000
χ742-22-2−2i2i−2i2i-222i−2i0000-222i−2i000000000000000000-22-222i−2i2i−2i2-2−2i2i00002-2−2i2i000000000000000000
χ754-4-444i−4i−4i4i000000000000000000000000000000-444-4−4i4i4i−4i000000000000000000000000000000
χ764-4-44−4i4i4i−4i000000000000000000000000000000-444-44i−4i−4i4i000000000000000000000000000000

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