Finite Group Databasebeta

← Group #140313

Character table — Group #140313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122244442244444488888888444444444488888888888816161616161616161616161616161616888888882488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-1-1-111111111-1-1-1-11iiii−i−i−i−i-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-11-1i−i
χ101111-1-1-1-1-1-1-1-111111111-1-1-1-11iiii−i−i−i−i-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii-1-111-11−ii
χ111111-1-1-1-1-1-1-1-111111111-1-1-1-11iiii−i−i−i−i-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-1-11−ii
χ121111-1-1-1-1-1-1-1-111111111-1-1-1-11iiii−i−i−i−i-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iii-1-1111-1i−i
χ131111-1-1-1-1-1-1-1-111111111-1-1-1-11−i−i−i−iiiii-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i-1-1111-1−ii
χ141111-1-1-1-1-1-1-1-111111111-1-1-1-11−i−i−i−iiiii-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iii11-1-1-11i−i
χ151111-1-1-1-1-1-1-1-111111111-1-1-1-11−i−i−i−iiiii-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111-11i−i
χ161111-1-1-1-1-1-1-1-111111111-1-1-1-11−i−i−i−iiiii-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-11-1−ii
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-22-2-2-2-2222222220000000000000000000000000000
χ192222222222-2-22-2-2200000000-222-2-222-2-2-200000000000022−2−222−2−222−2−222−2−2000000000000
χ202222222222-2-22-2-2200000000-222-2-222-2-2-2000000000000−2−222−2−222−2−222−2−222000000000000
χ212222222222-2-22-2-2200000000-2-2-222-2-222-200000000000022−2−222−2−2−2−222−2−222000000000000
χ222222222222-2-22-2-2200000000-2-2-222-2-222-2000000000000−2−222−2−22222−2−222−2−2000000000000
χ2322222222-2-222-222-222222222-200000000-2-2-2-2-20000000000000000000000002-22-200000000
χ2422222222-2-222-222-222222222-200000000-2-2-2-2-2000000000000000000000000-22-2200000000
χ2522222222-2-222-222-2-2-2-2-2-2-2-2-2-200000000-2222200000000000000000000000000002i−2i2i−2i0000
χ2622222222-2-222-222-2-2-2-2-2-2-2-2-2-200000000-222220000000000000000000000000000−2i2i−2i2i0000
χ272222-2-2-2-222-2-2-222-22222-2-2-2-2-2000000002-2-2220000000000000000000000002i−2i−2i2i00000000
χ282222-2-2-2-222-2-2-222-22222-2-2-2-2-2000000002-2-222000000000000000000000000−2i2i2i−2i00000000
χ292222-2-2-2-222-2-2-222-2-2-2-2-22222-200000000222-2-200000000000000000000000000002i−2i−2i2i0000
χ302222-2-2-2-222-2-2-222-2-2-2-2-22222-200000000222-2-20000000000000000000000000000−2i2i2i−2i0000
χ312222-2-2-2-2-2-2222-2-2200000000-22i2i−2i−2i−2i−2i2i2i2000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ322222-2-2-2-2-2-2222-2-2200000000-22i2i−2i−2i−2i−2i2i2i2000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ332222-2-2-2-2-2-2222-2-2200000000-2−2i−2i2i2i2i2i−2i−2i2000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ342222-2-2-2-2-2-2222-2-2200000000-2−2i−2i2i2i2i2i−2i−2i2000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ352222-2-2-2-2-2-2-2-22222-2-2-2-2222222i2i2i2i−2i−2i−2i−2i-2-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ362222-2-2-2-2-2-2-2-22222-2-2-2-222222−2i−2i−2i−2i2i2i2i2i-2-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ372-2-2222-2-22-200-200222−2−222−2−20002i−2i002i−2i02−22−2i2i2−i2−i2i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ382-2-2222-2-22-200-200222−2−222−2−20002i−2i002i−2i02−22−2i2i2−i2−i2i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ392-2-2222-2-22-200-200222−2−222−2−2000−2i2i00−2i2i02−22−2−i2−i2i2i2−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ402-2-2222-2-22-200-200222−2−222−2−2000−2i2i00−2i2i02−22−2−i2−i2i2i2−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ412-2-2222-2-22-200-2002−2−222−2−2220002i−2i002i−2i0−22−22−i2−i2i2i2−i2−i2i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ422-2-2222-2-22-200-2002−2−222−2−2220002i−2i002i−2i0−22−22−i2−i2i2i2−i2−i2i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ432-2-2222-2-22-200-2002−2−222−2−222000−2i2i00−2i2i0−22−22i2i2−i2−i2i2i2−i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ442-2-2222-2-22-200-2002−2−222−2−222000−2i2i00−2i2i0−22−22i2i2−i2−i2i2i2−i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ452-2-22-2-222-2200-200222−2−2−2−2220002-200-2202−2−2222−2−2−2−222ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ462-2-22-2-222-2200-200222−2−2−2−2220002-200-2202−2−2222−2−2−2−222−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ472-2-22-2-222-2200-200222−2−2−2−222000-22002-202−2−22−2−22222−2−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ482-2-22-2-222-2200-200222−2−2−2−222000-22002-202−2−22−2−22222−2−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ492-2-22-2-222-2200-2002−2−22222−2−20002-200-220−222−2−2−22222−2−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ502-2-22-2-222-2200-2002−2−22222−2−20002-200-220−222−2−2−22222−2−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ512-2-22-2-222-2200-2002−2−22222−2−2000-22002-20−222−222−2−2−2−222ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ522-2-22-2-222-2200-2002−2−22222−2−2000-22002-20−222−222−2−2−2−222−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ5344444444-4-4-4-4-4-4-4-40000000040000000040000000000000000000000000000000000000000
χ544444-4-4-4-44444-4-4-4-400000000400000000-40000000000000000000000000000000000000000
χ5544-4-44i−4i4i−4i0000000022−2222−222i2−2i22i2−2i202+2i−2−2i002−2i−2+2i00000002ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ60000000000000000000000000000
χ5644-4-44i−4i4i−4i0000000022−2222−222i2−2i22i2−2i20−2−2i2+2i00−2+2i2−2i0000000−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ60000000000000000000000000000
χ5744-4-44i−4i4i−4i00000000−2222−2222−2i22i2−2i22i202+2i−2−2i002−2i−2+2i0000000−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ60000000000000000000000000000
χ5844-4-44i−4i4i−4i00000000−2222−2222−2i22i2−2i22i20−2−2i2+2i00−2+2i2−2i00000002ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ60000000000000000000000000000
χ5944-4-4−4i4i−4i4i0000000022−2222−22−2i22i2−2i22i202−2i−2+2i002+2i−2−2i0000000−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ20000000000000000000000000000
χ6044-4-4−4i4i−4i4i0000000022−2222−22−2i22i2−2i22i20−2+2i2−2i00−2−2i2+2i00000002ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ20000000000000000000000000000
χ6144-4-4−4i4i−4i4i00000000−2222−22222i2−2i22i2−2i202−2i−2+2i002+2i−2−2i00000002ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ20000000000000000000000000000
χ6244-4-4−4i4i−4i4i00000000−2222−22222i2−2i22i2−2i20−2+2i2−2i00−2−2i2+2i0000000−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ20000000000000000000000000000
χ634-44-44i−4i−4i4i004i−4i04-4000000000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000
χ644-44-44i−4i−4i4i004i−4i04-400000000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000
χ654-44-44i−4i−4i4i00−4i4i0-4404-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000
χ664-44-44i−4i−4i4i00−4i4i0-440-444-4−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ674-44-4−4i4i4i−4i004i−4i0-4404-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ684-44-4−4i4i4i−4i004i−4i0-440-444-44i−4i−4i4i00000000000000000000000000000000000000000000000000
χ694-44-4−4i4i4i−4i00−4i4i04-4000000000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000
χ704-44-4−4i4i4i−4i00−4i4i04-400000000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000
χ714-4-4444-4-4-4400400-42222−22−222222−22−220000000000−2222−2222000000000000000000000000000000000000
χ724-4-4444-4-4-4400400-4−22−222222−22−222222000000000022−2222−22000000000000000000000000000000000000
χ734-4-44-4-4444-400400-42222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000
χ744-4-44-4-4444-400400-4−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.