Finite Group Databasebeta

← Group #111413

Character table — Group #111413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888888888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222222-2-222-2-2-2-2222222-2-2-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ18222222222222-2-222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ19222222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ20222222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2122222222-2-2-2-22222222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2222222222-2-2-2-22222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2322222222-2-2-2-222-2-2-2-222-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-222-2-22222-2-2-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-2-2-222-2-2-2-2-2-2222200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-2-2-222-2-2-2-2-2-222220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2000000000000000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-20000000000000000-2-22222-2-2000000000000000000000000
χ29222-2-22-2-222-2-2002i−2i00002i−2i2i2i−2i−2i000000i2i2−i2−i2i2i2−i2−i222−2−222−2−21+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ3−2ζ3002ζ−2ζ0000000000000000
χ30222-2-22-2-222-2-2002i−2i00002i−2i2i2i−2i−2i000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ2ζ0000000000000000
χ31222-2-22-2-222-2-2002i−2i00002i−2i2i2i−2i−2i000000−i2−i2i2i2−i2−i2i2i2−2−222−2−2221+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ32ζ300−2ζ2ζ0000000000000000
χ32222-2-22-2-222-2-2002i−2i00002i−2i2i2i−2i−2i000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ3−2ζ3002ζ−2ζ0000000000000000
χ33222-2-22-2-222-2-200−2i2i0000−2i2i−2i−2i2i2i000000i2i2−i2−i2i2i2−i2−i2−2−222−2−2221−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ−2ζ002ζ3−2ζ30000000000000000
χ34222-2-22-2-222-2-200−2i2i0000−2i2i−2i−2i2i2i000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ2ζ00−2ζ32ζ30000000000000000
χ35222-2-22-2-222-2-200−2i2i0000−2i2i−2i−2i2i2i000000−i2−i2i2i2−i2−i2i2i222−2−222−2−21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ2ζ00−2ζ32ζ30000000000000000
χ36222-2-22-2-222-2-200−2i2i0000−2i2i−2i−2i2i2i000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ−2ζ002ζ3−2ζ30000000000000000
χ37222-2-22-2-2-2-222002i−2i00002i−2i−2i−2i2i2i000000i2i2−i2−i2−i2−i2i2i222−2−2−2−2221−i−1+i−1+i1−i−1−i1+i1+i−1−i2ζ−2ζ002ζ3−2ζ3000000000000000000
χ38222-2-22-2-2-2-222002i−2i00002i−2i−2i−2i2i2i000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222−1+i1−i1−i−1+i1+i−1−i−1−i1+i−2ζ2ζ00−2ζ32ζ3000000000000000000
χ39222-2-22-2-2-2-222002i−2i00002i−2i−2i−2i2i2i000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−21−i−1+i−1+i1−i−1−i1+i1+i−1−i−2ζ2ζ00−2ζ32ζ3000000000000000000
χ40222-2-22-2-2-2-222002i−2i00002i−2i−2i−2i2i2i000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2−1+i1−i1−i−1+i1+i−1−i−1−i1+i2ζ−2ζ002ζ3−2ζ3000000000000000000
χ41222-2-22-2-2-2-22200−2i2i0000−2i2i2i2i−2i−2i000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−21+i−1−i−1−i1+i−1+i1−i1−i−1+i2ζ3−2ζ3002ζ−2ζ000000000000000000
χ42222-2-22-2-2-2-22200−2i2i0000−2i2i2i2i−2i−2i000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2−1−i1+i1+i−1−i1−i−1+i−1+i1−i−2ζ32ζ300−2ζ2ζ000000000000000000
χ43222-2-22-2-2-2-22200−2i2i0000−2i2i2i2i−2i−2i000000−i2−i2i2i2i2i2−i2−i222−2−2−2−2221+i−1−i−1−i1+i−1+i1−i1−i−1+i−2ζ32ζ300−2ζ2ζ000000000000000000
χ44222-2-22-2-2-2-22200−2i2i0000−2i2i2i2i−2i−2i000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222−1−i1+i1+i−1−i1−i−1+i−1+i1−i2ζ3−2ζ3002ζ−2ζ000000000000000000
χ452-2-2-2-22222-22-2222222-2-2-2-22-22-2-2-22-22-2000000000000000000000000000000000000000000002i−2i2i−2i
χ462-2-2-2-22222-22-2222222-2-2-2-22-22-2-2-22-22-200000000000000000000000000000000000000000000−2i2i−2i2i
χ472-2-2-2-22222-22-222-2-2-2-2-2-222-22-22222-2-22000000000000000000000000000000000000000000002-2-22
χ482-2-2-2-22222-22-222-2-2-2-2-2-222-22-22222-2-2200000000000000000000000000000000000000000000-222-2
χ492-2-2-2-22222-22-2-2-222-2-222-2-22-22-222-22-22000000000000000000000000000000002-22-2000000000000
χ502-2-2-2-22222-22-2-2-222-2-222-2-22-22-222-22-2200000000000000000000000000000000-22-22000000000000
χ512-2-2-2-22222-22-2-2-2-2-2222222-22-22-2-2-222-2000000000000000000000000000000002-2-22000000000000
χ522-2-2-2-22222-22-2-2-2-2-2222222-22-22-2-2-222-200000000000000000000000000000000-222-2000000000000
χ532-2-2-2-2222-22-22222222-2-2-2-2-22-22-2-2-22-2200000000000000000000000000000000000000002i−2i2i−2i0000
χ542-2-2-2-2222-22-22222222-2-2-2-2-22-22-2-2-22-220000000000000000000000000000000000000000−2i2i−2i2i0000
χ552-2-2-2-2222-22-2222-2-2-2-2-2-2222-22-222-222-200000000000000000000000000000000000000002-2-220000
χ562-2-2-2-2222-22-2222-2-2-2-2-2-2222-22-222-222-20000000000000000000000000000000000000000-222-20000
χ572-2-2-2-2222-22-22-2-222-2-222-2-2-22-22222-22-20000000000000000000000000000000000002-22-200000000
χ582-2-2-2-2222-22-22-2-222-2-222-2-2-22-22222-22-2000000000000000000000000000000000000-22-2200000000
χ592-2-2-2-2222-22-22-2-2-2-22222222-22-2-2-22-2-220000000000000000000000000000000000002-2-2200000000
χ602-2-2-2-2222-22-22-2-2-2-22222222-22-2-2-22-2-22000000000000000000000000000000000000-222-200000000
χ6144-44-4-44-4000000004i−4i000000004i−4i0000000022−2222−2200002i2−2i22i2−2i200000000000000000000000000000000
χ6244-44-4-44-4000000004i−4i000000004i−4i00000000−2222−22220000−2i22i2−2i22i200000000000000000000000000000000
χ6344-44-4-44-400000000−4i4i00000000−4i4i0000000022−2222−220000−2i22i2−2i22i200000000000000000000000000000000
χ6444-44-4-44-400000000−4i4i00000000−4i4i00000000−2222−222200002i2−2i22i2−2i200000000000000000000000000000000
χ6544-4-44-4-4400004-400004-40000000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ6644-4-44-4-4400004-400004-4000000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ6744-4-44-4-440000-440000-4400000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ6844-4-44-4-440000-440000-440000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ694-444-4-4-4400004-40000-440000000000004i−4i4i−4i00000000000000000000000000000000000000000000
χ704-444-4-4-4400004-40000-44000000000000−4i4i−4i4i00000000000000000000000000000000000000000000
χ714-444-4-4-440000-4400004-4000000000000000000004i−4i4i−4i000000000000000000000000000000000000
χ724-444-4-4-440000-4400004-400000000000000000000−4i4i−4i4i000000000000000000000000000000000000
χ734-44-44-44-4000000004i−4i00000000−4i4i000022−22−222200002i2−2i2−2i22i2000000000000000000000000000000000000
χ744-44-44-44-4000000004i−4i00000000−4i4i0000−222222−220000−2i22i22i2−2i2000000000000000000000000000000000000
χ754-44-44-44-400000000−4i4i000000004i−4i000022−22−22220000−2i22i22i2−2i2000000000000000000000000000000000000
χ764-44-44-44-400000000−4i4i000000004i−4i0000−222222−2200002i2−2i2−2i22i2000000000000000000000000000000000000
χ774-4-4444-4-44-4-44004i−4i0000−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ784-4-4444-4-44-4-4400−4i4i00004i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ794-4-4444-4-4-444-4004i−4i0000−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ804-4-4444-4-4-444-400−4i4i00004i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000

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