Finite Group Databasebeta

← Group #97508

Character table — Group #97508

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222444444444444444444448888888888888888444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-111-1-11-11-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111-1-1111-1-11-11ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1-1-111-111-1-11−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-11111-1-1-11-111-1−i−iii−i−iiiii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-111-1-11-11-11-1−i−iii−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111-1-1111-1-11-11−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1-1-111-111-1-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-11111-1-1-11-111-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-2-222-222-2-2-2-2-2-20000000000000000222200000000-2-20000000000000000
χ1822222222222222-2-2-222-222-2-2-2-2-2-20000000000000000-2-2-2-200000000220000000000000000
χ1922222222222-2-2-22222-22-2-222-2-2-2-200000000000000000000000022220000-2-2000000000000
χ2022222222222-2-2-22222-22-2-222-2-2-2-2000000000000000000000000-2-2-2-2000022000000000000
χ2122222222222-2-2-2-2-2-22-2-2-2-2-2-222220000000000000000000022-2-2000000-2200000000000000
χ2222222222222-2-2-2-2-2-22-2-2-2-2-2-2222200000000000000000000-2-2220000002-200000000000000
χ2322222222-2-2-2222222-222-2-2-2-222-2-2000000000000000000002222000000-2-200000000000000
χ2422222222-2-2-2222222-222-2-2-2-222-2-200000000000000000000-2-2-2-20000002200000000000000
χ2522222222-2-2-2222-2-2-2-22-2-2-222-2-22200000000000000000000000022-2-20000-22000000000000
χ2622222222-2-2-2222-2-2-2-22-2-2-222-2-222000000000000000000000000-2-22200002-2000000000000
χ2722222222-2-2-2-2-2-2222-2-2222-2-2-2-222000000000000000022-2-200000000-220000000000000000
χ2822222222-2-2-2-2-2-2222-2-2222-2-2-2-2220000000000000000-2-222000000002-20000000000000000
χ292222-2-2-2-222-222-2000-2-202-20000002222−2−2−2−22222−2−2−2−22-22-2000000000000002−22−200000000
χ302222-2-2-2-222-222-2000-2-202-20000002222−2−2−2−22222−2−2−2−2-22-2200000000000000−22−2200000000
χ312222-2-2-2-222-222-2000-2-202-2000000−2−2−2−22222−2−2−2−222222-22-200000000000000−22−2200000000
χ322222-2-2-2-222-222-2000-2-202-2000000−2−2−2−22222−2−2−2−22222-22-22000000000000002−22−200000000
χ332222-2-2-2-2-2-22-2-220002202-2000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22-2-2200000000000000i2−i2−i2i200000000
χ342222-2-2-2-2-2-22-2-220002202-2000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-222-200000000000000−i2i2i2−i200000000
χ352222-2-2-2-2-2-22-2-220002202-2000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22-2-2200000000000000−i2i2i2−i200000000
χ362222-2-2-2-2-2-22-2-220002202-2000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-222-200000000000000i2−i2−i2i200000000
χ3722-2-22-2-220002-222-2-20-2200002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002i−2i2i−2i000000000000002−22−20000
χ3822-2-22-2-220002-222-2-20-2200002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−2i2i−2i2i00000000000000−22−220000
χ3922-2-22-2-220002-222-2-20-2200002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002i−2i2i−2i00000000000000−22−220000
χ4022-2-22-2-220002-222-2-20-2200002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−2i2i−2i2i000000000000002−22−20000
χ4122-2-22-2-22000-22-2-22202-200002-20022−2−222−2−2−2−222−2−22200002i−2i−2i2i00000000000000−i2i2i2−i20000
χ4222-2-22-2-22000-22-2-22202-200002-20022−2−222−2−2−2−222−2−2220000−2i2i2i−2i00000000000000i2−i2−i2i20000
χ4322-2-22-2-22000-22-2-22202-200002-200−2−222−2−22222−2−222−2−200002i−2i−2i2i00000000000000i2−i2−i2i20000
χ4422-2-22-2-22000-22-2-22202-200002-200−2−222−2−22222−2−222−2−20000−2i2i2i−2i00000000000000−i2i2i2−i20000
χ452-22-2-22-222-22000-22-2-202002-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000002i−2i2i−2i000000000000002−22−2
χ462-22-2-22-222-22000-22-2-202002-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000−2i2i−2i2i00000000000000−22−22
χ472-22-2-22-222-22000-22-2-202002-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000002i−2i2i−2i00000000000000−22−22
χ482-22-2-22-222-22000-22-2-202002-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000−2i2i−2i2i000000000000002−22−2
χ492-22-2-22-22-22-20002-2220-2002-200002−22−22−22−2−22−22−22−22000000002i−2i−2i2i00000000000000−i2i2i2−i2
χ502-22-2-22-22-22-20002-2220-2002-200002−22−22−22−2−22−22−22−2200000000−2i2i2i−2i00000000000000i2−i2−i2i2
χ512-22-2-22-22-22-20002-2220-2002-20000−22−22−22−222−22−22−22−2000000002i−2i−2i2i00000000000000i2−i2−i2i2
χ522-22-2-22-22-22-20002-2220-2002-20000−22−22−22−222−22−22−22−200000000−2i2i2i−2i00000000000000−i2i2i2−i2
χ534444-4-4-4-444-4-4-44000-440-440000000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4444-40004-40-440000000000000000000000000000000000000000000000000000
χ5544-4-44-4-440004-44-4440-4-40000-44000000000000000000000000000000000000000000000000
χ5644-4-44-4-44000-44-44-4-40440000-44000000000000000000000000000000000000000000000000
χ5744-4-4-444-40004-4-4000040000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ5844-4-4-444-40004-4-400004000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ5944-4-4-444-4000-4440000-400000000022-2-2-2-222-2-22222-2-2000000000000000000000000000000
χ6044-4-4-444-4000-4440000-4000000000-2-22222-2-222-2-2-2-222000000000000000000000000000000
χ614-44-44-44-44-4-4000000400000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ624-44-44-44-44-4-400000040000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ634-44-44-44-4-444000000-400000000002-22-2-22-22-22-222-22-2000000000000000000000000000000
χ644-44-44-44-4-444000000-40000000000-22-222-22-22-22-2-22-22000000000000000000000000000000
χ654-44-4-44-444-440004-44-40-400-4400000000000000000000000000000000000000000000000000
χ664-44-4-44-44-44-4000-44-440400-4400000000000000000000000000000000000000000000000000
χ674-4-4444-4-40000000000000000004i−4i2ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ684-4-4444-4-40000000000000000004i−4i−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ694-4-4444-4-4000000000000000000−4i4i2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ704-4-4444-4-4000000000000000000−4i4i−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ714-4-44-4-44400000044-400-4000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ724-4-44-4-44400000044-400-400000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ734-4-44-4-444000000-4-44004000000002-2-222-2-222-2-222-2-22000000000000000000000000000000
χ744-4-44-4-444000000-4-4400400000000-222-2-222-2-222-2-222-2000000000000000000000000000000

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