Finite Group Databasebeta

← Group #101697

Character table — Group #101697

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888822444444488888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
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−i11-1-1-111-1-1ii−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−i11-1-1-111-1-1ii−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-1-1-111-1-111ii−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-1-1-111-1-111ii−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-1-1-111-1-111−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-1-1-111-1-111−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−iiiii11-1-1-111-1-1−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−iiiii11-1-1-111-1-1−i−iii−i−iii-1-1-1-11111ii−i−iii−i−i-11
χ17222222222222-2-22222-2-2-2-2-2-222000000000000000022-222-2-2-2-200000000000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-2220000000000000000-2-2-2-2-2222200000000000000000000000000
χ192222222222-2-22222-2-22222-2-2-2-2000000002222222200-20000000000-2-2-2-2000000000000000000
χ202222222222-2-22222-2-22222-2-2-2-200000000-2-2-2-2-2-2-2-200-200000000002222000000000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-222-2-22i2i2i2i−2i−2i−2i−2i00000000002000000−2i−2i2i2i0000000000000000000000
χ222222222222-2-2-2-222-2-2-2-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i000000000020000002i2i−2i−2i0000000000000000000000
χ2322222222-2-22222-2-22222-2-222-2-2222222220000000000-2000000-2-2-2-20000000000000000000000
χ2422222222-2-22222-2-22222-2-222-2-2-2-2-2-2-2-2-2-20000000000-200000022220000000000000000000000
χ2522222222-2-222-2-2-2-222-2-222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i0020000000000−2i−2i2i2i000000000000000000
χ2622222222-2-222-2-2-2-222-2-222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i00200000000002i2i−2i−2i000000000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-2-2-2220000000000000000222-2-2-2-22200000000000000000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-2-2-2220000000000000000-2-222222-2-200000000000000000000000000
χ29222-2-2-22-22i−2i002i−2i2i−2i002i−2i2-20000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000i2i2−i2−i222−2−200001−i−1+i1+i−1−i00
χ30222-2-2-22-22i−2i002i−2i2i−2i002i−2i2-20000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000000−i2−i2i2i2−2−2220000−1+i1−i−1−i1+i00
χ31222-2-2-22-22i−2i002i−2i2i−2i002i−2i2-2000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000i2i2−i2−i222−2−20000−1+i1−i−1−i1+i00
χ32222-2-2-22-22i−2i002i−2i2i−2i002i−2i2-2000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000000000000−i2−i2i2i2−2−22200001−i−1+i1+i−1−i00
χ33222-2-2-22-2−2i2i00−2i2i−2i2i00−2i2i2-20000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000i2i2−i2−i2−2−22200001+i−1−i1−i−1+i00
χ34222-2-2-22-2−2i2i00−2i2i−2i2i00−2i2i2-20000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000000−i2−i2i2i222−2−20000−1−i1+i−1+i1−i00
χ35222-2-2-22-2−2i2i00−2i2i−2i2i00−2i2i2-2000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000i2i2−i2−i2−2−2220000−1−i1+i−1+i1−i00
χ36222-2-2-22-2−2i2i00−2i2i−2i2i00−2i2i2-2000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000−i2−i2i2i222−2−200001+i−1−i1−i−1+i00
χ3722-22-2-2-222i−2i2i−2i00−2i2i2i−2i0000002-21+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i2-202i−2i00001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000000000
χ3822-22-2-2-222i−2i2i−2i00−2i2i2i−2i0000002-21+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i-220−2i2i00001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000000000
χ3922-22-2-2-222i−2i2i−2i00−2i2i2i−2i0000002-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i-220−2i2i0000−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000000000
χ4022-22-2-2-222i−2i2i−2i00−2i2i2i−2i0000002-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-202i−2i0000−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000000000
χ4122-22-2-2-222i−2i−2i2i00−2i2i−2i2i000000-221−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000002i−2i2-2−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000000000
χ4222-22-2-2-222i−2i−2i2i00−2i2i−2i2i000000-221−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000−2i2i-22−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000000000
χ4322-22-2-2-222i−2i−2i2i00−2i2i−2i2i000000-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000−2i2i-221−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000000000
χ4422-22-2-2-222i−2i−2i2i00−2i2i−2i2i000000-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000002i−2i2-21−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000000000
χ4522-22-2-2-22−2i2i2i−2i002i−2i2i−2i000000-221+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000−2i2i2-2−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000000000
χ4622-22-2-2-22−2i2i2i−2i002i−2i2i−2i000000-221+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000002i−2i-22−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000000000
χ4722-22-2-2-22−2i2i2i−2i002i−2i2i−2i000000-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000002i−2i-221+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000000000
χ4822-22-2-2-22−2i2i2i−2i002i−2i2i−2i000000-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000−2i2i2-21+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000000000
χ4922-22-2-2-22−2i2i−2i2i002i−2i−2i2i0000002-21−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i2-20−2i2i00001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000000000
χ5022-22-2-2-22−2i2i−2i2i002i−2i−2i2i0000002-21−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i-2202i−2i00001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000000000
χ5122-22-2-2-22−2i2i−2i2i002i−2i−2i2i0000002-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i-2202i−2i0000−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000000000
χ5222-22-2-2-22−2i2i−2i2i002i−2i−2i2i0000002-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-20−2i2i0000−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000000000
χ532-2-2-2-222200222200-2-2-2-2002-2002i−2i2i−2i2i−2i2i−2i00000000000000000000000002−22−22−22−2i2−i2i2−i2000000
χ542-2-2-2-222200222200-2-2-2-2002-2002i−2i2i−2i2i−2i2i−2i0000000000000000000000000−22−22−22−22−i2i2−i2i2000000
χ552-2-2-2-222200222200-2-2-2-2002-200−2i2i−2i2i−2i2i−2i2i00000000000000000000000002−22−22−22−2−i2i2−i2i2000000
χ562-2-2-2-222200222200-2-2-2-2002-200−2i2i−2i2i−2i2i−2i2i0000000000000000000000000−22−22−22−22i2−i2i2−i2000000
χ572-2-2-2-222200-2-2-2-2002222002-2002-22-2-22-2200000000000000000000000002−22−2−22−222−2−22000000
χ582-2-2-2-222200-2-2-2-2002222002-2002-22-2-22-220000000000000000000000000−22−222−22−2−222−2000000
χ592-2-2-2-222200-2-2-2-2002222002-200-22-222-22-200000000000000000000000002−22−2−22−22−222−2000000
χ602-2-2-2-222200-2-2-2-2002222002-200-22-222-22-20000000000000000000000000−22−222−22−22−2−22000000
χ61444-4-4-44-44i−4i00−4i4i4i−4i00−4i4i-440000000000000000000000000000000000000000000000000000000
χ62444-4-4-44-4−4i4i004i−4i−4i4i004i−4i-440000000000000000000000000000000000000000000000000000000
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
χ674-44-44-4-44004i−4i0000−4i4i000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000000
χ684-44-44-4-44004i−4i0000−4i4i00000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000000
χ694-44-44-4-4400−4i4i00004i−4i000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000000
χ704-44-44-4-4400−4i4i00004i−4i00000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000000
χ714-4-444-44-400004i−4i0000−4i4i0000000000000000000000000000000000000002i−2i−2i2i2-2-220000000000
χ724-4-444-44-400004i−4i0000−4i4i000000000000000000000000000000000000000−2i2i2i−2i-222-20000000000
χ734-4-444-44-40000−4i4i00004i−4i0000000000000000000000000000000000000002i−2i−2i2i-222-20000000000
χ744-4-444-44-40000−4i4i00004i−4i000000000000000000000000000000000000000−2i2i2i−2i2-2-220000000000
χ754-4-4-4-44440044-4-400-4-44400-4400000000000000000000000000000000000000000000000000000
χ764-4-4-4-444400-4-4440044-4-400-4400000000000000000000000000000000000000000000000000000
χ778-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000

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