Finite Group Databasebeta

← Group #100271

Character table — Group #100271

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222244444444448888888844444888888888888888888888888888844
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
χ511111111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ101111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ121111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ131111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ141111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ151111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ161111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ17222222222222-2-22222-2-22222-2-2-2-2-2-2-2-22200000000-2-2-222000000000000000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-2-2-2-2-222222200000000-222-2-2000000000000000000000000000000
χ192222222222-2-22222-2-222222222-2-22222-2-200000000-2-2-2-2-2000000000000000000000000000000
χ202222222222-2-22222-2-222-2-2-2-222-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000
χ2122222222-2-22222-2-222220000-2-2220000-2-222222222-20000-2-2-2-200000000000000000000000000
χ2222222222-2-22222-2-222220000-2-2220000-2-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ2322222222-2-222-2-2-2-222-2-2000022-2-20000-2-2000000002000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ2422222222-2-222-2-2-2-222-2-2000022-2-20000-2-200000000200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2522222222-2-2-2-222-2-2-2-2220000-2-2-2-20000220000000020000000022-2-2-2-222000000000000000000
χ2622222222-2-2-2-222-2-2-2-2220000-2-2-2-200002200000000200000000-2-22222-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000022220000222i2i2i2i−2i−2i−2i−2i-20000−2i−2i2i2i00000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200002222000022−2i−2i−2i−2i2i2i2i2i-200002i2i−2i−2i00000000000000000000000000
χ29222-2-2-2-222-22i−2i002-22i−2i000000000022-2-22i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i02i−2i001+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ30222-2-2-2-222-22i−2i002-22i−2i000000000022-2-22i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i02i−2i00−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ31222-2-2-2-222-22i−2i002-22i−2i0000000000-2-2222i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0−2i2i001+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ32222-2-2-2-222-22i−2i002-22i−2i0000000000-2-2222i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0−2i2i00−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ33222-2-2-2-222-2−2i2i002-2−2i2i000000000022-2-2−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0−2i2i001−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ34222-2-2-2-222-2−2i2i002-2−2i2i000000000022-2-2−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0−2i2i00−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ35222-2-2-2-222-2−2i2i002-2−2i2i0000000000-2-222−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i02i−2i001−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ36222-2-2-2-222-2−2i2i002-2−2i2i0000000000-2-222−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i02i−2i00−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ37222-2-2-2-22-222i−2i00-222i−2i0022-2-200000000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0002i−2i−1−i1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000
χ38222-2-2-2-22-222i−2i00-222i−2i0022-2-200000000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0002i−2i1+i−1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000
χ39222-2-2-2-22-222i−2i00-222i−2i00-2-22200000000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000−2i2i−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000
χ40222-2-2-2-22-222i−2i00-222i−2i00-2-22200000000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000−2i2i1+i−1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000
χ41222-2-2-2-22-22−2i2i00-22−2i2i0022-2-2000000002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000−2i2i−1+i1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000
χ42222-2-2-2-22-22−2i2i00-22−2i2i0022-2-2000000002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000−2i2i1−i−1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000
χ43222-2-2-2-22-22−2i2i00-22−2i2i00-2-222000000002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0002i−2i−1+i1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000
χ44222-2-2-2-22-22−2i2i00-22−2i2i00-2-222000000002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0002i−2i1−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000
χ4522-2-22-22-2002i−2i2i−2i00−2i2i2i−2i0000002-20000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00002−2i2−i200
χ4622-2-22-22-2002i−2i2i−2i00−2i2i2i−2i0000002-20000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000−22−i2i200
χ4722-2-22-22-2002i−2i2i−2i00−2i2i2i−2i0000002-2000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000−22−i2i200
χ4822-2-22-22-2002i−2i2i−2i00−2i2i2i−2i0000002-2000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002−2i2−i200
χ4922-2-22-22-200−2i2i−2i2i002i−2i−2i2i0000002-20000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−22i2−i200
χ5022-2-22-22-200−2i2i−2i2i002i−2i−2i2i0000002-20000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00002−2−i2i200
χ5122-2-22-22-200−2i2i−2i2i002i−2i−2i2i0000002-2000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00002−2−i2i200
χ5222-2-22-22-200−2i2i−2i2i002i−2i−2i2i0000002-2000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000−22i2−i200
χ532-22-2-222-2-22002i−2i2-200−2i2i2-22-22i−2i002i−2i2i−2i0000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1+i−1−i000000
χ542-22-2-222-2-22002i−2i2-200−2i2i2-22-22i−2i002i−2i2i−2i000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1−i1+i000000
χ552-22-2-222-2-22002i−2i2-200−2i2i-22-222i−2i00−2i2i−2i2i0000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1−i1+i000000
χ562-22-2-222-2-22002i−2i2-200−2i2i-22-222i−2i00−2i2i−2i2i000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1+i−1−i000000
χ572-22-2-222-2-2200−2i2i2-2002i−2i2-22-2−2i2i00−2i2i−2i2i0000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1−i−1+i000000
χ582-22-2-222-2-2200−2i2i2-2002i−2i2-22-2−2i2i00−2i2i−2i2i000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1+i1−i000000
χ592-22-2-222-2-2200−2i2i2-2002i−2i-22-22−2i2i002i−2i2i−2i0000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1+i1−i000000
χ602-22-2-222-2-2200−2i2i2-2002i−2i-22-22−2i2i002i−2i2i−2i000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1−i−1+i000000
χ6144-44-44-4-400440000-4-4000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ6244-44-44-4-400440000-4-40000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ6344-44-44-4-400-4-400004400000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ6444-44-44-4-400-4-40000440000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ6544-4-44-44-4004i−4i−4i4i00−4i4i−4i4i000000-440000000000000000000000000000000000000000000000000
χ6644-4-44-44-400−4i4i4i−4i004i−4i4i−4i000000-440000000000000000000000000000000000000000000000000
χ674-4444-4-4-4440000-4-400004-4-4400000000000000000000000000000000000000000000000000000
χ684-4444-4-4-4440000-4-40000-444-400000000000000000000000000000000000000000000000000000
χ694-4444-4-4-4-4-40000440000000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ704-4444-4-4-4-4-4000044000000000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ714-44-4-444-44-4004i−4i-4400−4i4i0000−4i4i000000000000000000000000000000000000000000000000000
χ724-44-4-444-44-400−4i4i-44004i−4i00004i−4i000000000000000000000000000000000000000000000000000
χ734-4-44-4-4440000440000-4-40000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ744-4-44-4-4440000440000-4-4000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ754-4-44-4-4440000-4-40000440000000000000000000000000000000000000002-2-222-2-220000000000
χ764-4-44-4-4440000-4-4000044000000000000000000000000000000000000000-222-2-222-20000000000
χ778-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000

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