Finite Group Databasebeta

← Group #97491

Character table — Group #97491

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222222244444444444444448888888888888888444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-11-111111-1-1-1-1-1-1-1-1
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
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-11-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1-1-111-11-111-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-11111-1-1-111-1-11−i−iiiii−i−i−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1iiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-111-1-11-1-1-111−i−iii−i−iiiii−i−i
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111-1-1111-111-1-1ii−i−i−i−iii−i−iii
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1-1-111-11-111-1−i−iii−i−iii−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-11111-1-1-111-1-11ii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-111-1-11-1-1-111ii−i−iii−i−i−i−iii
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111-1-1111-111-1-1−i−iiiii−i−iii−i−i
χ1722222222222222-2-222-2-222-2-2-2-2-2-20000000000000000222200000000-2-20000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-20000000000000000-2-2-2-200000000220000000000000000
χ19222222222222-2-222-2-222-2-2-2-2-222-2000000000000000000002222000000-20-20000000000000
χ20222222222222-2-222-2-222-2-2-2-2-222-200000000000000000000-2-2-2-20000002020000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2222-2-2200000000000000000000000022-2-200020-2000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2222-2-22000000000000000000000000-2-222000-202000000000000
χ2322222222-2-2-2-222222222-2-222-2-2-2-20000000000000000000000002222000-20-2000000000000
χ2422222222-2-2-2-222222222-2-222-2-2-2-2000000000000000000000000-2-2-2-2000202000000000000
χ2522222222-2-2-2-222-2-222-2-2-2-2-2-222220000000000000000000022-2-200000020-20000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-2-2-2222200000000000000000000-2-222000000-2020000000000000
χ2722222222-2-2-2-2-2-222-2-22222-2-22-2-22000000000000000022-2-2000000002-20000000000000000
χ2822222222-2-2-2-2-2-222-2-22222-2-22-2-220000000000000000-2-22200000000-220000000000000000
χ292222-2-2-2-222-2-22200-2-2002-20000002222−2−2−2−22222−2−2−2−22-22-20000000000000000002−22−20000
χ302222-2-2-2-222-2-22200-2-2002-20000002222−2−2−2−22222−2−2−2−2-22-22000000000000000000−22−220000
χ312222-2-2-2-222-2-22200-2-2002-2000000−2−2−2−22222−2−2−2−222222-22-2000000000000000000−22−220000
χ322222-2-2-2-222-2-22200-2-2002-2000000−2−2−2−22222−2−2−2−22222-22-220000000000000000002−22−20000
χ332222-2-2-2-2-2-222-2-20022002-2000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22-2-22000000000000000000i2−i2−i2i20000
χ342222-2-2-2-2-2-222-2-20022002-2000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-222-2000000000000000000−i2i2i2−i20000
χ352222-2-2-2-2-2-222-2-20022002-2000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22-2-22000000000000000000−i2i2i2−i20000
χ362222-2-2-2-2-2-222-2-20022002-2000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-222-2000000000000000000i2−i2−i2i20000
χ3722-2-2-22-222-22-200-2-20022000002-20i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002i−2i2i−2i0000000000000000002−22−2
χ3822-2-2-22-222-22-200-2-20022000002-20i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−2i2i−2i2i000000000000000000−22−22
χ3922-2-2-22-222-22-200-2-20022000002-20−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002i−2i2i−2i000000000000000000−22−22
χ4022-2-2-22-222-22-200-2-20022000002-20−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−2i2i−2i2i0000000000000000002−22−2
χ4122-2-2-22-22-22-22002200-2-2000002-2022−2−222−2−2−2−222−2−22200002i−2i−2i2i000000000000000000−i2i2i2−i2
χ4222-2-2-22-22-22-22002200-2-2000002-2022−2−222−2−2−2−222−2−2220000−2i2i2i−2i000000000000000000i2−i2−i2i2
χ4322-2-2-22-22-22-22002200-2-2000002-20−2−222−2−22222−2−222−2−200002i−2i−2i2i000000000000000000i2−i2−i2i2
χ4422-2-2-22-22-22-22002200-2-2000002-20−2−222−2−22222−2−222−2−20000−2i2i2i−2i000000000000000000−i2i2i2−i2
χ452-22-2-222-200002i−2i2i−2i2i−2i2i−2i002-200001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i000000002-22i−2i0000001−i−1+i1+i−1−i00000000
χ462-22-2-222-200002i−2i2i−2i2i−2i2i−2i002-200001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i00000000-22−2i2i000000−1+i1−i−1−i1+i00000000
χ472-22-2-222-200002i−2i2i−2i2i−2i2i−2i002-20000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i000000002-22i−2i000000−1+i1−i−1−i1+i00000000
χ482-22-2-222-200002i−2i2i−2i2i−2i2i−2i002-20000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i00000000-22−2i2i0000001−i−1+i1+i−1−i00000000
χ492-22-2-222-20000−2i2i−2i2i−2i2i−2i2i002-200001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i000000002-2−2i2i0000001+i−1−i1−i−1+i00000000
χ502-22-2-222-20000−2i2i−2i2i−2i2i−2i2i002-200001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i00000000-222i−2i000000−1−i1+i−1+i1−i00000000
χ512-22-2-222-20000−2i2i−2i2i−2i2i−2i2i002-20000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i000000002-2−2i2i000000−1−i1+i−1+i1−i00000000
χ522-22-2-222-20000−2i2i−2i2i−2i2i−2i2i002-20000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i00000000-222i−2i0000001+i−1−i1−i−1+i00000000
χ534444-4-4-4-444-4-4-4-4004400-440000000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4444400-4-400-440000000000000000000000000000000000000000000000000000
χ5544-4-44-44-44-4-4400000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ5644-4-44-44-44-4-440000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ5744-4-44-44-4-444-4000000000000000022-2-2-2-222-2-22222-2-2000000000000000000000000000000
χ5844-4-44-44-4-444-40000000000000000-2-22222-2-222-2-2-2-222000000000000000000000000000000
χ5944-4-4-44-444-44-4004400-4-400000-4400000000000000000000000000000000000000000000000
χ6044-4-4-44-44-44-4400-4-4004400000-4400000000000000000000000000000000000000000000000
χ614-44-44-4-4400004i−4i00−4i4i00000000002ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3000000000000000000000000000000
χ624-44-44-4-4400004i−4i00−4i4i0000000000−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ3000000000000000000000000000000
χ634-44-44-4-440000−4i4i004i−4i00000000002ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ000000000000000000000000000000
χ644-44-44-4-440000−4i4i004i−4i0000000000−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ000000000000000000000000000000
χ654-44-4-444-400004i−4i−4i4i4i−4i−4i4i00-4400000000000000000000000000000000000000000000000000
χ664-44-4-444-40000−4i4i4i−4i−4i4i4i−4i00-4400000000000000000000000000000000000000000000000000
χ674-4-4444-4-40000004i−4i00−4i4i000000002ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ3000000000000000000000000000000
χ684-4-4444-4-40000004i−4i00−4i4i00000000−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3000000000000000000000000000000
χ694-4-4444-4-4000000−4i4i004i−4i000000002ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ000000000000000000000000000000
χ704-4-4444-4-4000000−4i4i004i−4i00000000−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ000000000000000000000000000000
χ714-4-44-4-4440000000000000000400-42i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ724-4-44-4-4440000000000000000400-4−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ734-4-44-4-4440000000000000000-40042-2-22-222-2-222-22-2-22000000000000000000000000000000
χ744-4-44-4-4440000000000000000-4004-222-22-2-222-2-22-222-2000000000000000000000000000000

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