Finite Group Databasebeta

← Group #100494

Character table — Group #100494

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888844444888888888888888888888888888844
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
χ511111111111111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1111-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1iiii−i−i−i−i11-1-11ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ1011111111-1-1111-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1iiii−i−i−i−i11-1-11ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ1111111111-1-1111-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1−i−i−i−iiiii11-1-11−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ1211111111-1-1111-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1−i−i−i−iiiii11-1-11−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ1311111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1iiii−i−i−i−i-1-1111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ1411111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1iiii−i−i−i−i-1-1111ii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ1511111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1−i−i−i−iiiii-1-1111−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ1611111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1−i−i−i−iiiii-1-1111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ17222222222222222-2-2-2-222-2-22222-2-2-2-2-2-2200000000-2-222-2000000000000000000000000000000
χ18222222222222222-2-2-2-222-2-2-2-2-2-2-2-2222220000000022-2-2-2000000000000000000000000000000
χ192222222222-2-2-2222222-2-2-2-20000220000-2222222220000-2-2-2-2-200000000000000000000000000
χ202222222222-2-2-2222222-2-2-2-20000220000-2-2-2-2-2-2-2-2-20000-2222200000000000000000000000000
χ212222222222-2-2-222-2-2-2-2-2-2220000-2-20000-2000000000000200002i2i−2i−2i2i2i−2i−2i000000000000000000
χ222222222222-2-2-222-2-2-2-2-2-2220000-2-20000-200000000000020000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2322222222-2-2222-2-222222-2222222-2-22222-200000000-2-2-2-2-2000000000000000000000000000000
χ2422222222-2-2222-2-222222-222-2-2-2-2-2-2-2-2-2-2-2000000002222-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-22-2-20000-2-2000020000000000002000022-2-2-2-222000000000000000000
χ2622222222-2-2-2-2-2-2-22222-22-2-20000-2-20000200000000000020000-2-22222-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222000022000022i2i2i2i−2i−2i−2i−2i0000-2−2i−2i2i2i00000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222200002200002−2i−2i−2i−2i2i2i2i2i0000-22i2i−2i−2i00000000000000000000000000
χ2922-222-2-2-2002-2-20022-2-2202-22i2i−2i−2i002i2i−2i−2i0000000000000000000000000022−2−222−2−2i2−i2i2−i2000000
χ3022-222-2-2-2002-2-20022-2-2202-22i2i−2i−2i002i2i−2i−2i00000000000000000000000000−2−222−2−222−i2i2−i2i2000000
χ3122-222-2-2-2002-2-20022-2-2202-2−2i−2i2i2i00−2i−2i2i2i0000000000000000000000000022−2−222−2−2−i2i2−i2i2000000
χ3222-222-2-2-2002-2-20022-2-2202-2−2i−2i2i2i00−2i−2i2i2i00000000000000000000000000−2−222−2−222i2−i2i2−i2000000
χ3322-222-2-2-2002-2-200-2-22220-222i2i−2i−2i00−2i−2i2i2i00000000000000000000000000i2i2−i2−i2−i2−i2i2i2−222−2000000
χ3422-222-2-2-2002-2-200-2-22220-222i2i−2i−2i00−2i−2i2i2i00000000000000000000000000−i2−i2i2i2i2i2−i2−i22−2−22000000
χ3522-222-2-2-2002-2-200-2-22220-22−2i−2i2i2i002i2i−2i−2i00000000000000000000000000i2i2−i2−i2−i2−i2i2i22−2−22000000
χ3622-222-2-2-2002-2-200-2-22220-22−2i−2i2i2i002i2i−2i−2i00000000000000000000000000−i2−i2i2i2i2i2−i2−i2−222−2000000
χ372-222-22-2-22222-2-2-20000-22002-22-2000000-222−2−222−2−2002-202−22−22−22−22−22−2000000000000000000
χ382-222-22-2-22222-2-2-20000-22002-22-2000000-2−2−222−2−222002-20−22−22−22−22−22−22000000000000000000
χ392-222-22-2-22222-2-2-20000-2200-22-22000000-222−2−222−2−200-2202−22−2−22−22−22−22000000000000000000
χ402-222-22-2-22222-2-2-20000-2200-22-22000000-2−2−222−2−22200-220−22−222−22−22−22−2000000000000000000
χ412-222-22-2-222-2-22-2-200002-2000000002i−2i2i−2i222−2−222−2−22i−2i000−22−22i2−i2−i2i2i2−i2−i2i2000000000000000000
χ422-222-22-2-222-2-22-2-200002-2000000002i−2i2i−2i2−2−222−2−2222i−2i0002−22−2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ432-222-22-2-222-2-22-2-200002-200000000−2i2i−2i2i222−2−222−2−2−2i2i000−22−22−i2i2i2−i2−i2i2i2−i2000000000000000000
χ442-222-22-2-222-2-22-2-200002-200000000−2i2i−2i2i2−2−222−2−222−2i2i0002−22−2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ452-222-22-2-2-2-222-2220000-2-2002-22-20000002i2i2−i2−i2−i2−i2i2i200-220i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ462-222-22-2-2-2-222-2220000-2-2002-22-20000002−i2−i2i2i2i2i2−i2−i200-220−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ472-222-22-2-2-2-222-2220000-2-200-22-220000002i2i2−i2−i2−i2−i2i2i2002-20i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ482-222-22-2-2-2-222-2220000-2-200-22-220000002−i2−i2i2i2i2i2−i2−i2002-20−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ492-222-22-2-2-2-2-2-2222000022000000002i−2i2i−2i-2i2i2−i2−i2−i2−i2i2i2−2i2i000−i2i2i2−i22−2−22−222−2000000000000000000
χ502-222-22-2-2-2-2-2-2222000022000000002i−2i2i−2i-2−i2−i2i2i2i2i2−i2−i2−2i2i000i2−i2−i2i2−222−22−2−22000000000000000000
χ512-222-22-2-2-2-2-2-222200002200000000−2i2i−2i2i-2i2i2−i2−i2−i2−i2i2i22i−2i000−i2i2i2−i2−222−22−2−22000000000000000000
χ522-222-22-2-2-2-2-2-222200002200000000−2i2i−2i2i-2−i2−i2i2i2i2i2−i2−i22i−2i000i2−i2−i2i22−2−22−222−2000000000000000000
χ532-2-2-2222-22i−2i0002i−2i2i−2i2i−2i000000002-2000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002−2i2−i200
χ542-2-2-2222-22i−2i0002i−2i2i−2i2i−2i000000002-2000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−22−i2i200
χ552-2-2-2222-22i−2i0002i−2i2i−2i2i−2i000000002-200000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−22−i2i200
χ562-2-2-2222-22i−2i0002i−2i2i−2i2i−2i000000002-200000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002−2i2−i200
χ572-2-2-2222-2−2i2i000−2i2i−2i2i−2i2i000000002-2000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−22i2−i200
χ582-2-2-2222-2−2i2i000−2i2i−2i2i−2i2i000000002-2000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002−2−i2i200
χ592-2-2-2222-2−2i2i000−2i2i−2i2i−2i2i000000002-200000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002−2−i2i200
χ602-2-2-2222-2−2i2i000−2i2i−2i2i−2i2i000000002-200000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−22i2−i200
χ6144-444-4-4-400-4440044-4-4-40-44000000000000000000000000000000000000000000000000000000
χ6244-444-4-4-400-44400-4-444-404-4000000000000000000000000000000000000000000000000000000
χ6344-4-4-44-444i−4i000−4i4i00000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000
χ6444-4-4-44-444i−4i000−4i4i0000000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000
χ6544-4-4-44-44−4i4i0004i−4i00000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000
χ6644-4-4-44-44−4i4i0004i−4i0000000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000
χ674-44-44-4-4400000004i−4i−4i4i00000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000
χ684-44-44-4-4400000004i−4i−4i4i0000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000
χ694-44-44-4-440000000−4i4i4i−4i00000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000
χ704-44-44-4-440000000−4i4i4i−4i0000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000
χ714-4-44-4-444004-44000000-40004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ724-4-44-4-444004-44000000-4000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ734-4-44-4-44400-44-400000040000000004-4-4400000000000000000000000000000000000000000000
χ744-4-44-4-44400-44-40000004000000000-444-400000000000000000000000000000000000000000000
χ754-4-4-4444-44i−4i0004i−4i−4i4i−4i4i00000000-44000000000000000000000000000000000000000000000000
χ764-4-4-4444-4−4i4i000−4i4i4i−4i4i−4i00000000-44000000000000000000000000000000000000000000000000
χ77888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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