Finite Group Databasebeta

← Group #101696

Character table — Group #101696

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888844444444488888888888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i-11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i-11111-1-1-1-1ii−i−iii−i−i-1-1-1-11111−i−iii−i−iii-11
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-11111ii−i−i−i−iii1111-1-1-1-1ii−i−i−i−iii-11
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-11111ii−i−i−i−iii-1-1-1-11111−i−iiiii−i−i1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-11111−i−iiiii−i−i1111-1-1-1-1−i−iiiii−i−i-11
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-11111−i−iiiii−i−i-1-1-1-11111ii−i−i−i−iii1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii-11111-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii-11111-1-1-1-1−i−iii−i−iii-1-1-1-11111ii−i−iii−i−i-11
χ17222222222222-2-22222-2-2-2-2-2-2220000000000000000-222-2-222-2-200000000000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-2220000000000000000-2-2-222-2-22200000000000000000000000000
χ192222222222-2-22222-2-222-2-222-2-22222222200000000-200000000-2-2-2-20000000000000000000000
χ202222222222-2-22222-2-222-2-222-2-2-2-2-2-2-2-2-2-200000000-20000000022220000000000000000000000
χ212222222222-2-2-2-222-2-2-2-222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i2000000000000−2i−2i2i2i000000000000000000
χ222222222222-2-2-2-222-2-2-2-222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i20000000000002i2i−2i−2i000000000000000000
χ2322222222-2-22222-2-2222222-2-2-2-20000000022222222-2000000000000-2-2-2-2000000000000000000
χ2422222222-2-22222-2-2222222-2-2-2-200000000-2-2-2-2-2-2-2-2-20000000000002222000000000000000000
χ2522222222-2-222-2-2-2-222-2-2-2-222-2-22i2i2i2i−2i−2i−2i−2i00000000200000000−2i−2i2i2i0000000000000000000000
χ2622222222-2-222-2-2-2-222-2-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i000000002000000002i2i−2i−2i0000000000000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-2-2-2220000000000000000222-2-2-2-22200000000000000000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-2-2-22200000000000000002-2-22222-2-200000000000000000000000000
χ29222-2-2-2-222200-2-2-2-20022002-2002i2i−2i−2i2i2i−2i−2i0000000000000000000000000i2i2−i2−i2i2i2−i2−i22−22−2000000
χ30222-2-2-2-222200-2-2-2-20022002-2002i2i−2i−2i2i2i−2i−2i0000000000000000000000000−i2−i2i2i2−i2−i2i2i2−22−22000000
χ31222-2-2-2-222200-2-2-2-20022002-200−2i−2i2i2i−2i−2i2i2i0000000000000000000000000i2i2−i2−i2i2i2−i2−i2−22−22000000
χ32222-2-2-2-222200-2-2-2-20022002-200−2i−2i2i2i−2i−2i2i2i0000000000000000000000000−i2−i2i2i2−i2−i2i2i22−22−2000000
χ33222-2-2-2-22-2-200222200-2-2002-20022-2-2-2-2220000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ34222-2-2-2-22-2-200222200-2-2002-20022-2-2-2-2220000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ35222-2-2-2-22-2-200222200-2-2002-200-2-22222-2-20000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ36222-2-2-2-22-2-200222200-2-2002-200-2-22222-2-20000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ3722-222-2-2-2002i−2i2i−2i002i−2i2i−2i2-20000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000002−22−2i2−i2i2−i200001+i−1−i1−i−1+i00
χ3822-222-2-2-2002i−2i2i−2i002i−2i2i−2i2-20000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000−22−22−i2i2−i2i20000−1−i1+i−1+i1−i00
χ3922-222-2-2-2002i−2i2i−2i002i−2i2i−2i2-2000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000002−22−2i2−i2i2−i20000−1−i1+i−1+i1−i00
χ4022-222-2-2-2002i−2i2i−2i002i−2i2i−2i2-2000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000−22−22−i2i2−i2i200001+i−1−i1−i−1+i00
χ4122-222-2-2-200−2i2i−2i2i00−2i2i−2i2i2-20000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000002−22−2−i2i2−i2i20000−1+i1−i−1−i1+i00
χ4222-222-2-2-200−2i2i−2i2i00−2i2i−2i2i2-20000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000−22−22i2−i2i2−i200001−i−1+i1+i−1−i00
χ4322-222-2-2-200−2i2i−2i2i00−2i2i−2i2i2-2000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000002−22−2−i2i2−i2i200001−i−1+i1+i−1−i00
χ4422-222-2-2-200−2i2i−2i2i00−2i2i−2i2i2-2000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000−22−22i2−i2i2−i20000−1+i1−i−1−i1+i00
χ452-222-22-2-22i−2i2i−2i002i−2i−2i2i0000002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0002i−2i002-21+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000000000
χ462-222-22-2-22i−2i2i−2i002i−2i−2i2i0000002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000−2i2i00-221+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000000000
χ472-222-22-2-22i−2i2i−2i002i−2i−2i2i0000002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000−2i2i00-22−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000000000
χ482-222-22-2-22i−2i2i−2i002i−2i−2i2i0000002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0002i−2i002-2−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000000000
χ492-222-22-2-22i−2i−2i2i002i−2i2i−2i000000-221+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i02-2002i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000000000
χ502-222-22-2-22i−2i−2i2i002i−2i2i−2i000000-221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0-2200−2i2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000000000
χ512-222-22-2-22i−2i−2i2i002i−2i2i−2i000000-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0-2200−2i2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000000000
χ522-222-22-2-22i−2i−2i2i002i−2i2i−2i000000-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i02-2002i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000000000
χ532-222-22-2-2−2i2i2i−2i00−2i2i−2i2i000000-221−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i02-200−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000000000
χ542-222-22-2-2−2i2i2i−2i00−2i2i−2i2i000000-221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0-22002i−2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000000000
χ552-222-22-2-2−2i2i2i−2i00−2i2i−2i2i000000-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0-22002i−2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000000000
χ562-222-22-2-2−2i2i2i−2i00−2i2i−2i2i000000-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i02-200−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000000000
χ572-222-22-2-2−2i2i−2i2i00−2i2i2i−2i0000002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000−2i2i002-21−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000000000
χ582-222-22-2-2−2i2i−2i2i00−2i2i2i−2i0000002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0002i−2i00-221−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000000000
χ592-222-22-2-2−2i2i−2i2i00−2i2i2i−2i0000002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0002i−2i00-22−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000000000
χ602-222-22-2-2−2i2i−2i2i00−2i2i2i−2i0000002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000−2i2i002-2−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000000000
χ61444-4-4-4-44440044-4-400-4-400-4400000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-4-400-4-444004400-4400000000000000000000000000000000000000000000000000000
χ6344-444-4-4-4004i−4i−4i4i004i−4i−4i4i-440000000000000000000000000000000000000000000000000000000
χ6444-444-4-4-400−4i4i4i−4i00−4i4i4i−4i-440000000000000000000000000000000000000000000000000000000
χ6544-4-4-444-400004i−4i0000−4i4i0000000000000000000000000000000000000002i−2i−2i2i2-2-220000000000
χ6644-4-4-444-400004i−4i0000−4i4i000000000000000000000000000000000000000−2i2i2i−2i-222-20000000000
χ6744-4-4-444-40000−4i4i00004i−4i0000000000000000000000000000000000000002i−2i−2i2i-222-20000000000
χ6844-4-4-444-40000−4i4i00004i−4i000000000000000000000000000000000000000−2i2i2i−2i2-2-220000000000
χ694-44-44-44-44i−4i0000−4i4i00000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000000
χ704-44-44-44-44i−4i0000−4i4i0000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000000
χ714-44-44-44-4−4i4i00004i−4i00000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000000
χ724-44-44-44-4−4i4i00004i−4i0000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000000
χ734-4-44-4-44400440000-4-400000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ744-4-44-4-44400440000-4-40000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ754-4-44-4-44400-4-4000044000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ764-4-44-4-44400-4-40000440000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ778-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000

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