Finite Group Databasebeta

← Group #125201

Character table — Group #125201

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888444444444488888888888816161616161616161616161616161616888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ19222222222222-2-2-2-222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ20222222222222-2-2-2-222222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2122222222-2-2-2-2222200000000-2-22222-2-2-2-200000000000022−2−222−2−222−2−222−2−2000000000000
χ2222222222-2-2-2-2222200000000-2-22222-2-2-2-2000000000000−2−222−2−222−2−222−2−222000000000000
χ2322222222-2-2-2-2222200000000-2-2-2-2-2-2222200000000000022−2−222−2−2−2−222−2−222000000000000
χ2422222222-2-2-2-2222200000000-2-2-2-2-2-22222000000000000−2−222−2−22222−2−222−2−2000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-2-2-222000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-2-2-222000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022-2-22222-2-2000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022-2-22222-2-2000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ29222-2-22-2-222-2-200002222-2-2-2-200002i−2i002i−2i00002i2i−2i−2i000000000000000000002−22−2i2−i2i2−i20000
χ30222-2-22-2-222-2-200002222-2-2-2-200002i−2i002i−2i00002i2i−2i−2i00000000000000000000−22−22−i2i2−i2i20000
χ31222-2-22-2-222-2-200002222-2-2-2-20000−2i2i00−2i2i0000−2i−2i2i2i000000000000000000002−22−2−i2i2−i2i20000
χ32222-2-22-2-222-2-200002222-2-2-2-20000−2i2i00−2i2i0000−2i−2i2i2i00000000000000000000−22−22i2−i2i2−i20000
χ33222-2-22-2-222-2-20000-2-2-2-2222200002i−2i002i−2i0000−2i−2i2i2i00000000000000000000i2−i2−i2i22−2−220000
χ34222-2-22-2-222-2-20000-2-2-2-2222200002i−2i002i−2i0000−2i−2i2i2i00000000000000000000−i2i2i2−i2−222−20000
χ35222-2-22-2-222-2-20000-2-2-2-222220000−2i2i00−2i2i00002i2i−2i−2i00000000000000000000i2−i2−i2i2−222−20000
χ36222-2-22-2-222-2-20000-2-2-2-222220000−2i2i00−2i2i00002i2i−2i−2i00000000000000000000−i2i2i2−i22−2−220000
χ3722-22-2-22-22-22-22i2i−2i−2i000000002i−2i0000000000002-22-22i2i−2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3822-22-2-22-22-22-22i2i−2i−2i000000002i−2i0000000000002-22-22i2i−2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3922-22-2-22-22-22-22i2i−2i−2i000000002i−2i000000000000-22-22−2i−2i2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ4022-22-2-22-22-22-22i2i−2i−2i000000002i−2i000000000000-22-22−2i−2i2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ4122-22-2-22-22-22-2−2i−2i2i2i00000000−2i2i0000000000002-22-2−2i−2i2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4222-22-2-22-22-22-2−2i−2i2i2i00000000−2i2i0000000000002-22-2−2i−2i2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4322-22-2-22-22-22-2−2i−2i2i2i00000000−2i2i000000000000-22-222i2i−2i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4422-22-2-22-22-22-2−2i−2i2i2i00000000−2i2i000000000000-22-222i2i−2i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4522-22-2-22-2-22-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i−2i2i0000000022-2-200000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000
χ4622-22-2-22-2-22-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i−2i2i0000000022-2-20000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000
χ4722-22-2-22-2-22-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i−2i2i00000000-2-222000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000
χ4822-22-2-22-2-22-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i−2i2i00000000-2-22200000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000
χ4922-22-2-22-2-22-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2i−2i00000000-2-222000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000000000
χ5022-22-2-22-2-22-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2i−2i00000000-2-22200000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000000000
χ5122-22-2-22-2-22-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2i−2i0000000022-2-200000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000
χ5222-22-2-22-2-22-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2i−2i0000000022-2-20000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000
χ53444-4-44-4-4-4-44400000000000000004i−4i00−4i4i0000000000000000000000000000000000000000
χ54444-4-44-4-4-4-4440000000000000000−4i4i004i−4i0000000000000000000000000000000000000000
χ5544-4-44-4-444-4-44000000000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ5644-4-44-4-444-4-4400000000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ5744-4-44-4-44-444-400004i4i−4i−4i−4i−4i4i4i00000000000000000000000000000000000000000000000000
χ5844-4-44-4-44-444-40000−4i−4i4i4i4i4i−4i−4i00000000000000000000000000000000000000000000000000
χ594-444-4-4-44000000002i2−2i22i2−2i22i2−2i22i2−2i20000004i−4i000000000022−2222−220000000000000000000000000000
χ604-444-4-4-44000000002i2−2i22i2−2i22i2−2i22i2−2i2000000−4i4i0000000000−2222−22220000000000000000000000000000
χ614-444-4-4-4400000000−2i22i2−2i22i2−2i22i2−2i22i20000004i−4i0000000000−2222−22220000000000000000000000000000
χ624-444-4-4-4400000000−2i22i2−2i22i2−2i22i2−2i22i2000000−4i4i000000000022−2222−220000000000000000000000000000
χ634-44-44-44-400004i−4i4i−4i2i2−2i22i2−2i2−2i22i2−2i22i2000000000022−2222−22000000000000000000000000000000000000
χ644-44-44-44-400004i−4i4i−4i−2i22i2−2i22i22i2−2i22i2−2i20000000000−2222−2222000000000000000000000000000000000000
χ654-44-44-44-40000−4i4i−4i4i2i2−2i22i2−2i2−2i22i2−2i22i20000000000−2222−2222000000000000000000000000000000000000
χ664-44-44-44-40000−4i4i−4i4i−2i22i2−2i22i22i2−2i22i2−2i2000000000022−2222−22000000000000000000000000000000000000
χ674-4-4444-4-40000000022−22−222222−22−2222004i−4i000000000000002i2−2i2−2i22i20000000000000000000000000000
χ684-4-4444-4-40000000022−22−222222−22−222200−4i4i00000000000000−2i22i22i2−2i20000000000000000000000000000
χ694-4-4444-4-400000000−222222−22−222222−22004i−4i00000000000000−2i22i22i2−2i20000000000000000000000000000
χ704-4-4444-4-400000000−222222−22−222222−2200−4i4i000000000000002i2−2i2−2i22i20000000000000000000000000000
χ714-4-4-4-444400004-4-4422−22−2222−222222−22000000000022−22−2222000000000000000000000000000000000000
χ724-4-4-4-444400004-4-44−222222−2222−22−22220000000000−222222−22000000000000000000000000000000000000
χ734-4-4-4-44440000-444-422−22−2222−222222−220000000000−222222−22000000000000000000000000000000000000
χ744-4-4-4-44440000-444-4−222222−2222−22−2222000000000022−22−2222000000000000000000000000000000000000

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