Finite Group Databasebeta

← Group #100433

Character table — Group #100433

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444444444444444448888888844444888888888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-1iiii−i−i−i−i1-1-111ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-1iiii−i−i−i−i1-1-111ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ1111111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-1−i−i−i−iiiii1-1-111−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ1211111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-1−i−i−i−iiiii1-1-111−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ1311111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-11111-1iiii−i−i−i−i111-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ1411111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-11111-1iiii−i−i−i−i111-1-1ii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ1511111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-11111-1−i−i−i−iiiii111-1-1−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-11111-1−i−i−i−iiiii111-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ1722222222222222-2-222-2-2-2-2-2-222222-2-2-2-2200000000-222-2-2000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2-2-222222200000000-2-2-222000000000000000000000000000000
χ19222222222222-2-222-2-22222-2-20000-20000-222222222-20000-2-2-2-200000000000000000000000000
χ20222222222222-2-222-2-22222-2-20000-20000-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2220000-20000-2000000002000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2220000-20000-200000000200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2322222222-2-2-2-222222222-2-2222222-22222-200000000-2-2-2-2-2000000000000000000000000000000
χ2422222222-2-2-2-222222222-2-222-2-2-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-222-2-2-2-200002000020000000020000000022-2-2-2-222000000000000000000
χ2622222222-2-2-2-2-2-222-2-222-2-2-2-2000020000200000000200000000-2-22222-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002000022i2i2i2i−2i−2i−2i−2i-20000−2i−2i2i2i00000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000200002−2i−2i−2i−2i2i2i2i2i-200002i2i−2i−2i00000000000000000000000000
χ292222-2-2-2-222-2-2002200-2-22-200000000000022-2-222-2-20000000000000000022−2−222−2−200002−22−200
χ302222-2-2-2-222-2-2002200-2-22-200000000000022-2-222-2-200000000000000000−2−222−2−2220000−22−2200
χ312222-2-2-2-222-2-2002200-2-22-2000000000000-2-222-2-2220000000000000000022−2−222−2−20000−22−2200
χ322222-2-2-2-222-2-2002200-2-22-2000000000000-2-222-2-22200000000000000000−2−222−2−22200002−22−200
χ332222-2-2-2-2-2-22200-2-200222-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000000i2i2−i2−i2−i2−i2i2i200002−2−2200
χ342222-2-2-2-2-2-22200-2-200222-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000000−i2−i2i2i2i2i2−i2−i20000−222−200
χ352222-2-2-2-2-2-22200-2-200222-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000i2i2−i2−i2−i2−i2i2i20000−222−200
χ362222-2-2-2-2-2-22200-2-200222-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000−i2−i2i2i2i2i2−i2−i200002−2−2200
χ3722-2-2-222-200002-22i−2i2-22i−2i002i−2i22-2-202i2i−2i−2i000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1−i−1+i000000
χ3822-2-2-222-200002-22i−2i2-22i−2i002i−2i22-2-202i2i−2i−2i00000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1+i1−i000000
χ3922-2-2-222-200002-22i−2i2-22i−2i002i−2i-2-2220−2i−2i2i2i000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1+i1−i000000
χ4022-2-2-222-200002-22i−2i2-22i−2i002i−2i-2-2220−2i−2i2i2i00000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1−i−1+i000000
χ4122-2-2-222-200002-2−2i2i2-2−2i2i00−2i2i22-2-20−2i−2i2i2i000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1+i−1−i000000
χ4222-2-2-222-200002-2−2i2i2-2−2i2i00−2i2i22-2-20−2i−2i2i2i00000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1−i1+i000000
χ4322-2-2-222-200002-2−2i2i2-2−2i2i00−2i2i-2-22202i2i−2i−2i000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1−i1+i000000
χ4422-2-2-222-200002-2−2i2i2-2−2i2i00−2i2i-2-22202i2i−2i−2i00000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1+i−1−i000000
χ452-22-2-2-2222-22-22200-2-20000002i−2i2i−2i-200002i2−i2i2−i2i2−i2i2−i202i−2i00i2−i2i2−i22−22−22−22−2000000000000000000
χ462-22-2-2-2222-22-22200-2-20000002i−2i2i−2i-200002−i2i2−i2i2−i2i2−i2i202i−2i00−i2i2−i2i2−22−22−22−22000000000000000000
χ472-22-2-2-2222-22-22200-2-2000000−2i2i−2i2i-200002i2−i2i2−i2i2−i2i2−i20−2i2i00i2−i2i2−i2−22−22−22−22000000000000000000
χ482-22-2-2-2222-22-22200-2-2000000−2i2i−2i2i-200002−i2i2−i2i2−i2i2−i2i20−2i2i00−i2i2−i2i22−22−22−22−2000000000000000000
χ492-22-2-2-2222-22-2-2-20022000000000022-22-2-2i2−i2i2−i2i2−i2i2−i20002-2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ502-22-2-2-2222-22-2-2-20022000000000022-22-2-2−i2i2−i2i2−i2i2−i2i20002-2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ512-22-2-2-2222-22-2-2-2002200000000002-22-22-2i2−i2i2−i2i2−i2i2−i2000-22−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ522-22-2-2-2222-22-2-2-2002200000000002-22-22-2−i2i2−i2i2−i2i2−i2i2000-22i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ532-22-2-2-222-22-222200-2-20000002i−2i2i−2i20000-22−22−2−22−220−2i2i002−2−22−i2i2−i2i2i2−i2i2−i2000000000000000000
χ542-22-2-2-222-22-222200-2-20000002i−2i2i−2i20000-2−22−222−22−20−2i2i00−222−2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ552-22-2-2-222-22-222200-2-2000000−2i2i−2i2i20000-22−22−2−22−2202i−2i002−2−22i2−i2i2−i2−i2i2−i2i2000000000000000000
χ562-22-2-2-222-22-222200-2-2000000−2i2i−2i2i20000-2−22−222−22−202i−2i00−222−2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ572-22-2-2-222-22-22-2-200220000000000-22-22-222−22−2−22−22000-22−222−2−222−22−2−22000000000000000000
χ582-22-2-2-222-22-22-2-200220000000000-22-22-22−22−222−22−2000-222−2−222−2−22−222−2000000000000000000
χ592-22-2-2-222-22-22-2-200220000000000-2-22-2222−22−2−22−220002-2−222−22−2−22−222−2000000000000000000
χ602-22-2-2-222-22-22-2-200220000000000-2-22-222−22−222−22−20002-22−2−22−222−22−2−22000000000000000000
χ614444-4-4-4-444-4-400-4-40044-440000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-444004400-4-4-440000000000000000000000000000000000000000000000000000000
χ6344-4-44-4-440000004i−4i00−4i4i0000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000
χ6444-4-44-4-440000004i−4i00−4i4i000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000
χ6544-4-44-4-44000000−4i4i004i−4i0000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000
χ6644-4-44-4-44000000−4i4i004i−4i000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000
χ6744-4-4-444-40000-444i−4i-444i−4i00−4i4i00000000000000000000000000000000000000000000000000000
χ6844-4-4-444-40000-44−4i4i-44−4i4i004i−4i00000000000000000000000000000000000000000000000000000
χ694-44-444-4-44-4-4400000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ704-44-444-4-44-4-440000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ714-44-444-4-4-444-4000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ724-44-444-4-4-444-40000000000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ734-4-444-44-400004-400-440000004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ744-4-444-44-400004-400-44000000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ754-4-444-44-40000-44004-4000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ764-4-444-44-40000-44004-400000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ778-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000000

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