Finite Group Databasebeta

← Group #93035

Character table — Group #93035

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order122244442222444422244488888888248888161616161616161616161616161616164444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-1
χ611111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111
χ711111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111
χ811111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1
χ91111-1-1-1-111-1-111-1-1-1111-1-11111-1-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-111-1-1-1111-1-11111-1-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-111-1-111-1-1-1111-1-11111-1-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-111-1-111-1-1-1111-1-11111-1-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ131111-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-111111-111-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ141111-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-111111-111-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ151111-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-111111-111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ161111-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-111111-111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ1822222222222222222-2-22-2-222222222-2-2-2-2-2-200000000000000000000000000000000
χ192222222222-2-2-2-222-222-22200000000-2-2000022−2−222−2−222−2−222−2−20000000000000000
χ202222222222-2-2-2-222-222-22200000000-2-20000−2−222−2−222−2−222−2−2220000000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-200000000220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ222222222222-2-2-2-222-2-2-2-2-2-200000000220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ2322222222-2-2-2-2-2-2-2-22002002i2i−2i−2i2i2i−2i−2i00000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ2422222222-2-2-2-2-2-2-2-22002002i2i−2i−2i2i2i−2i−2i0000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ2522222222-2-2-2-2-2-2-2-2200200−2i−2i2i2i−2i−2i2i2i00000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ2622222222-2-2-2-2-2-2-2-2200200−2i−2i2i2i−2i−2i2i2i0000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ272222-2-2-2-22222-2-2-2-2222-2-2-2000000002-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ282222-2-2-2-22222-2-2-2-2222-2-2-2000000002-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ292222-2-2-2-22222-2-2-2-22-2-2-22200000000-22000022−2−2−2−222−2−22222−2−20000000000000000
χ302222-2-2-2-22222-2-2-2-22-2-2-22200000000-220000−2−22222−2−222−2−2−2−2220000000000000000
χ312222-2-2-2-222-2-222-2-2-2222-2-2-2-2-2-22222-22-2-22200000000000000000000000000000000
χ322222-2-2-2-222-2-222-2-2-2-2-22222222-2-2-2-22-2-2-22200000000000000000000000000000000
χ332222-2-2-2-2-2-222-2-222-2002002i2i−2i−2i−2i−2i2i2i00000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ342222-2-2-2-2-2-222-2-222-2002002i2i−2i−2i−2i−2i2i2i0000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ352222-2-2-2-2-2-222-2-222-200200−2i−2i2i2i2i2i−2i−2i00000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ362222-2-2-2-2-2-222-2-222-200200−2i−2i2i2i2i2i−2i−2i0000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ3722-2-22i−2i2i−2i2-200002i−2i02-202i−2i2−22−2i2−i2i2−i2002−2i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000000000
χ3822-2-22i−2i2i−2i2-200002i−2i02-202i−2i2−22−2i2−i2i2−i2002−2i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000000000
χ3922-2-22i−2i2i−2i2-200002i−2i02-202i−2i−22−22−i2i2−i2i200−22−i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000000000
χ4022-2-22i−2i2i−2i2-200002i−2i02-202i−2i−22−22−i2i2−i2i200−22−i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000000000
χ4122-2-22i−2i2i−2i2-200002i−2i0-220−2i2i2−22−2i2−i2i2−i200−22−i2i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000000000
χ4222-2-22i−2i2i−2i2-200002i−2i0-220−2i2i2−22−2i2−i2i2−i200−22−i2i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000000000
χ4322-2-22i−2i2i−2i2-200002i−2i0-220−2i2i−22−22−i2i2−i2i2002−2i2−i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000000000
χ4422-2-22i−2i2i−2i2-200002i−2i0-220−2i2i−22−22−i2i2−i2i2002−2i2−i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000000000
χ4522-2-2−2i2i−2i2i2-20000−2i2i02-20−2i2i2−22−2−i2i2−i2i2002−2−i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000000000
χ4622-2-2−2i2i−2i2i2-20000−2i2i02-20−2i2i2−22−2−i2i2−i2i2002−2−i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000000000
χ4722-2-2−2i2i−2i2i2-20000−2i2i02-20−2i2i−22−22i2−i2i2−i200−22i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000000000
χ4822-2-2−2i2i−2i2i2-20000−2i2i02-20−2i2i−22−22i2−i2i2−i200−22i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000000000
χ4922-2-2−2i2i−2i2i2-20000−2i2i0-2202i−2i2−22−2−i2i2−i2i200−22i2−i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000000000
χ5022-2-2−2i2i−2i2i2-20000−2i2i0-2202i−2i2−22−2−i2i2−i2i200−22i2−i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000000000
χ5122-2-2−2i2i−2i2i2-20000−2i2i0-2202i−2i−22−22i2−i2i2−i2002−2−i2i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000000000
χ5222-2-2−2i2i−2i2i2-20000−2i2i0-2202i−2i−22−22i2−i2i2−i2002−2−i2i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000000000
χ5344444444-4-44444-4-4-400-4000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4-4-44444400-4000000000000000000000000000000000000000000000000
χ5544-4-44i−4i4i−4i-440000−4i4i0000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000000
χ5644-4-44i−4i4i−4i-440000−4i4i000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000000
χ5744-4-4−4i4i−4i4i-4400004i−4i0000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000000
χ5844-4-4−4i4i−4i4i-4400004i−4i000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000000
χ594-4-4444-4-4004-44-4000000000000000000000000000000000000000000000000002i−2i2i−2i
χ604-4-4444-4-4004-44-400000000000000000000000000000000000000000000000000−2i2i−2i2i
χ614-4-4444-4-400-44-4400000000000000000000000000000000000000000000002i−2i2i−2i0000
χ624-4-4444-4-400-44-440000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ634-4-44-4-444004-4-4400000000000000000000000000000000000000000000002-2-220000
χ644-4-44-4-444004-4-440000000000000000000000000000000000000000000000-222-20000
χ654-4-44-4-44400-444-4000000000000000000000000000000000000000000000000002-2-22
χ664-4-44-4-44400-444-400000000000000000000000000000000000000000000000000-222-2
χ678-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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