Finite Group Databasebeta

← Group #137255

Character table — Group #137255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order122244442244444422444488888888448888161616161616161616161616161616164444444488888888
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
χ51111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-11111-1-11-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-1-1-11111-1-11-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-111-1-1-1-11111-1-11-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-111-1-1-1-11111-1-11-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ131111-1-1-1-111-1-1-1-111-1-1111-11111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-111-1-1-1-111-1-1111-11111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111-1-1-1-111-1-1-1-111-1-1111-11111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-111-1-1-1-111-1-1111-11111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-200000000-2-2000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-2-2-22222-2-200000000-2-20000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-222220000-2-222-2-222-2-20000000000000000000000000000002-22-20000
χ2422222222-2-2-2-222220000-2-222-2-222-2-2000000000000000000000000000000-22-220000
χ2522222222-2-2-2-222220000-2-2-2-222-2-22200000000000000000000000000000000002-22-2
χ2622222222-2-2-2-222220000-2-2-2-222-2-2220000000000000000000000000000000000-22-22
χ272222-2-2-2-222-2-222-2-222-2-2-2200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ282222-2-2-2-222-2-222-2-222-2-2-2200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ292222-2-2-2-222-2-222-2-2-2-222-22000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ302222-2-2-2-222-2-222-2-2-2-222-22000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ312222-2-2-2-222-2-2-2-22222-2-22-2-2-2-2-222222-2-2-22200000000000000000000000000000000
χ322222-2-2-2-222-2-2-2-222-2-2222-2-2-2-2-22222-2222-2-200000000000000000000000000000000
χ332222-2-2-2-2-2-222-2-2220000-2222-2-2-2-2220000000000000000000000000000002i−2i−2i2i0000
χ342222-2-2-2-2-2-222-2-2220000-2222-2-2-2-222000000000000000000000000000000−2i2i2i−2i0000
χ352222-2-2-2-2-2-222-2-2220000-22-2-22222-2-200000000000000000000000000000000002i−2i−2i2i
χ362222-2-2-2-2-2-222-2-2220000-22-2-22222-2-20000000000000000000000000000000000−2i2i2i−2i
χ3722-2-222-2-22-22-200002-22-2002−22−22−22−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ3822-2-222-2-22-22-200002-22-2002−22−22−22−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ3922-2-222-2-22-22-200002-22-200−22−22−22−2200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ4022-2-222-2-22-22-200002-22-200−22−22−22−2200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ4122-2-222-2-22-22-20000-22-22002−22−22−22−200−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ4222-2-222-2-22-22-20000-22-22002−22−22−22−200−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ4322-2-222-2-22-22-20000-22-2200−22−22−22−22002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ4422-2-222-2-22-22-20000-22-2200−22−22−22−22002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ4522-2-2-2-2222-2-2200002-2-22002−22−2−22−22002−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000000000
χ4622-2-2-2-2222-2-2200002-2-22002−22−2−22−22002−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000000000
χ4722-2-2-2-2222-2-2200002-2-2200−22−222−22−200−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ4822-2-2-2-2222-2-2200002-2-2200−22−222−22−200−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ4922-2-2-2-2222-2-220000-222-2002−22−2−22−2200−222−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000000000
χ5022-2-2-2-2222-2-220000-222-2002−22−2−22−2200−222−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000000000
χ5122-2-2-2-2222-2-220000-222-200−22−222−22−2002−2−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ5222-2-2-2-2222-2-220000-222-200−22−222−22−2002−2−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-44444-4-400004-40000000000000000000000000000000000000000000000
χ5544-4-444-4-4-44-44000000000022−22−222222−22−222200000000000000000000000000000000000000
χ5644-4-444-4-4-44-440000000000−222222−22−222222−2200000000000000000000000000000000000000
χ5744-4-4-4-444-444-4000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ5844-4-4-4-444-444-40000000000−222222−2222−22−222200000000000000000000000000000000000000
χ594-44-44i−4i4i−4i00004i−4i4-40000000000000000000000000000000000002-22i−2i000000000000
χ604-44-44i−4i4i−4i00004i−4i4-4000000000000000000000000000000000000-22−2i2i000000000000
χ614-44-44i−4i4i−4i0000−4i4i-4400000000000000000000000000000000000000002-22i−2i00000000
χ624-44-44i−4i4i−4i0000−4i4i-440000000000000000000000000000000000000000-22−2i2i00000000
χ634-44-4−4i4i−4i4i00004i−4i-4400000000000000000000000000000000000000002-2−2i2i00000000
χ644-44-4−4i4i−4i4i00004i−4i-440000000000000000000000000000000000000000-222i−2i00000000
χ654-44-4−4i4i−4i4i0000−4i4i4-40000000000000000000000000000000000002-2−2i2i000000000000
χ664-44-4−4i4i−4i4i0000−4i4i4-4000000000000000000000000000000000000-222i−2i000000000000
χ678-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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