Finite Group Databasebeta

← Group #100277

Character table — Group #100277

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
χ51111111111111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ1011111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ1111111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ1211111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ1311111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ1411111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ1511111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ1611111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ17222222222222-2-22222-2-2-2-22222-2-2-2-2-2-22200000000-2-2-222000000000000000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-2-2-2-2-222222200000000-222-2-2000000000000000000000000000000
χ192222222222-2-22222-2-222-2-20000220000-2-222222222-20000-2-2-2-200000000000000000000000000
χ202222222222-2-22222-2-222-2-20000220000-2-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ212222222222-2-2-2-222-2-2-2-2220000-2-20000-2-2000000002000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ222222222222-2-2-2-222-2-2-2-2220000-2-20000-2-200000000200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2322222222-2-22222-2-22222222222-2-22222-2-200000000-2-2-2-2-2000000000000000000000000000000
χ2422222222-2-22222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-20000-2-20000220000000020000000022-2-2-2-222000000000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-20000-2-200002200000000200000000-2-22222-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2220000220000222i2i2i2i−2i−2i−2i−2i-20000−2i−2i2i2i00000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222000022000022−2i−2i−2i−2i2i2i2i2i-200002i2i−2i−2i00000000000000000000000000
χ2922-22-2-2-22002-22i−2i002-22i−2i2i−2i2i2i−2i−2i0022-2-20000000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i−1+i1+i−1−i000000
χ3022-22-2-2-22002-22i−2i002-22i−2i2i−2i2i2i−2i−2i0022-2-2000000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i1−i−1−i1+i000000
χ3122-22-2-2-22002-22i−2i002-22i−2i2i−2i−2i−2i2i2i00-2-2220000000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i1−i−1−i1+i000000
χ3222-22-2-2-22002-22i−2i002-22i−2i2i−2i−2i−2i2i2i00-2-222000000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i−1+i1+i−1−i000000
χ3322-22-2-2-22002-2−2i2i002-2−2i2i−2i2i2i2i−2i−2i00-2-2220000000000000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i1+i−1+i1−i000000
χ3422-22-2-2-22002-2−2i2i002-2−2i2i−2i2i2i2i−2i−2i00-2-222000000000000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i−1−i1−i−1+i000000
χ3522-22-2-2-22002-2−2i2i002-2−2i2i−2i2i−2i−2i2i2i0022-2-20000000000000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i−1−i1−i−1+i000000
χ3622-22-2-2-22002-2−2i2i002-2−2i2i−2i2i−2i−2i2i2i0022-2-2000000000000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i1+i−1+i1−i000000
χ372-22-22-2-222i−2i2-2002i−2i-2200002-22-20000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0002i−2i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ382-22-22-2-222i−2i2-2002i−2i-2200002-22-20000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0002i−2i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ392-22-22-2-222i−2i2-2002i−2i-220000-22-220000002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000−2i2i1+i−1−i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ402-22-22-2-222i−2i2-2002i−2i-220000-22-220000002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000−2i2i−1−i1+i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ412-22-22-2-222i−2i-22002i−2i2-200000000002-22-2−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i02i−2i00−1−i1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000
χ422-22-22-2-222i−2i-22002i−2i2-200000000002-22-2−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i02i−2i001+i−1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000
χ432-22-22-2-222i−2i-22002i−2i2-20000000000-22-22−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0−2i2i00−1−i1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000
χ442-22-22-2-222i−2i-22002i−2i2-20000000000-22-22−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0−2i2i001+i−1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000
χ452-22-22-2-22−2i2i2-200−2i2i-2200002-22-2000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000−2i2i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ462-22-22-2-22−2i2i2-200−2i2i-2200002-22-2000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000−2i2i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ472-22-22-2-22−2i2i2-200−2i2i-220000-22-22000000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0002i−2i1−i−1+i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ482-22-22-2-22−2i2i2-200−2i2i-220000-22-22000000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0002i−2i−1+i1−i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ492-22-22-2-22−2i2i-2200−2i2i2-200000000002-22-22i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0−2i2i00−1+i1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000
χ502-22-22-2-22−2i2i-2200−2i2i2-200000000002-22-22i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0−2i2i001−i−1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000
χ512-22-22-2-22−2i2i-2200−2i2i2-20000000000-22-222i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i02i−2i00−1+i1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000
χ522-22-22-2-22−2i2i-2200−2i2i2-20000000000-22-222i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i02i−2i001−i−1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000
χ532-2-222-22-22i−2i002i−2i−2i2i00−2i2i0000002-20000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002−2i2−i200
χ542-2-222-22-22i−2i002i−2i−2i2i00−2i2i0000002-20000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−22−i2i200
χ552-2-222-22-22i−2i002i−2i−2i2i00−2i2i0000002-2000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−22−i2i200
χ562-2-222-22-22i−2i002i−2i−2i2i00−2i2i0000002-2000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002−2i2−i200
χ572-2-222-22-2−2i2i00−2i2i2i−2i002i−2i0000002-20000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−22i2−i200
χ582-2-222-22-2−2i2i00−2i2i2i−2i002i−2i0000002-20000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002−2−i2i200
χ592-2-222-22-2−2i2i00−2i2i2i−2i002i−2i0000002-2000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002−2−i2i200
χ602-2-222-22-2−2i2i00−2i2i2i−2i002i−2i0000002-2000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−22i2−i200
χ6144-44-4-4-4400-444i−4i00-444i−4i−4i4i0000000000000000000000000000000000000000000000000000000
χ6244-44-4-4-4400-44−4i4i00-44−4i4i4i−4i0000000000000000000000000000000000000000000000000000000
χ6344-4-444-4-4440000-4-400000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ6444-4-444-4-4440000-4-4000000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ6544-4-444-4-4-4-40000440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ6644-4-444-4-4-4-4000044000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ674-444-44-4-40000440000-4-40000000000000000000000000000000000000002-2-222-2-220000000000
χ684-444-44-4-40000440000-4-4000000000000000000000000000000000000000-222-2-222-20000000000
χ694-444-44-4-40000-4-40000440000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ704-444-44-4-40000-4-4000044000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ714-4-444-44-44i−4i00−4i4i−4i4i004i−4i000000-440000000000000000000000000000000000000000000000000
χ724-4-444-44-4−4i4i004i−4i4i−4i00−4i4i000000-440000000000000000000000000000000000000000000000000
χ734-4-4-4-444400440000-4-400004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ744-4-4-4-444400440000-4-40000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ754-4-4-4-444400-4-400004400000000004-4-44000000000000000000000000000000000000000000000
χ764-4-4-4-444400-4-40000440000000000-444-4000000000000000000000000000000000000000000000
χ77888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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