Finite Group Databasebeta

← Group #99839

Character table — Group #99839

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444442244444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2122222222-2-2-2-22222-2-2-2-222-2-222-2-20000000000000000000000000000000000002i−2i2i−2i
χ2222222222-2-2-2-22222-2-2-2-222-2-222-2-2000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000000000000000002i−2i2i−2i0000
χ2422222222-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000−2i2i−2i2i0000
χ2522222222-2-2-2-2-2-2-2-2222222-2-2-2-2220000000000000000000000000000000000002-2-22
χ2622222222-2-2-2-2-2-2-2-2222222-2-2-2-222000000000000000000000000000000000000-222-2
χ2722222222-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000000000-222-20000
χ29222-2-22-2-2-2-22222-2-222-2-200000000002i−2i002i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ30222-2-22-2-2-2-22222-2-222-2-200000000002i−2i002i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ31222-2-22-2-2-2-22222-2-222-2-20000000000−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ32222-2-22-2-2-2-22222-2-222-2-20000000000−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ33222-2-22-2-2-2-222-2-222-2-22200000000002i−2i00−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ34222-2-22-2-2-2-222-2-222-2-22200000000002i−2i00−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ35222-2-22-2-2-2-222-2-222-2-2220000000000−2i2i002i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ36222-2-22-2-2-2-222-2-222-2-2220000000000−2i2i002i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ3722-22-2-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-2002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ3822-22-2-22-22-22-22i−2i2i−2i2i−2i2i−2i000000002-2002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ3922-22-2-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000-2200−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4022-22-2-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000-2200−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4122-22-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-200−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4222-22-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000002-200−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4322-22-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-22002i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4422-22-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000-22002i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4522-2-22-2-222-2-222i−2i−2i2i−2i2i2i−2i2-22-22i−2i2i−2i0000000000000000000000002i−2i2-2000000000000
χ4622-2-22-2-222-2-222i−2i−2i2i−2i2i2i−2i2-22-22i−2i2i−2i000000000000000000000000−2i2i-22000000000000
χ4722-2-22-2-222-2-222i−2i−2i2i−2i2i2i−2i-22-22−2i2i−2i2i00000000000000000000000000002i−2i2-200000000
χ4822-2-22-2-222-2-222i−2i−2i2i−2i2i2i−2i-22-22−2i2i−2i2i0000000000000000000000000000−2i2i-2200000000
χ4922-2-22-2-222-2-22−2i2i2i−2i2i−2i−2i2i2-22-2−2i2i−2i2i0000000000000000000000002i−2i-22000000000000
χ5022-2-22-2-222-2-22−2i2i2i−2i2i−2i−2i2i2-22-2−2i2i−2i2i000000000000000000000000−2i2i2-2000000000000
χ5122-2-22-2-222-2-22−2i2i2i−2i2i−2i−2i2i-22-222i−2i2i−2i00000000000000000000000000002i−2i-2200000000
χ5222-2-22-2-222-2-22−2i2i2i−2i2i−2i−2i2i-22-222i−2i2i−2i0000000000000000000000000000−2i2i2-200000000
χ5322-2-22-2-22-222-22i−2i−2i2i2i−2i−2i2i2-2-222i−2i−2i2i00000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ5422-2-22-2-22-222-22i−2i−2i2i2i−2i−2i2i2-2-222i−2i−2i2i0000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ5522-2-22-2-22-222-22i−2i−2i2i2i−2i−2i2i-222-2−2i2i2i−2i000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ5622-2-22-2-22-222-22i−2i−2i2i2i−2i−2i2i-222-2−2i2i2i−2i00000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ5722-2-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i2-2-22−2i2i2i−2i00000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ5822-2-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i2-2-22−2i2i2i−2i0000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ5922-2-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i-222-22i−2i−2i2i000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ6022-2-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i-222-22i−2i−2i2i00000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ61444-4-44-4-444-4-444-4-4-4-444000000000000000000000000000000000000000000000000
χ62444-4-44-4-444-4-4-4-44444-4-4000000000000000000000000000000000000000000000000
χ6344-44-4-44-4-44-444i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000
χ6444-44-4-44-4-44-44−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000
χ658-8888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ668-88-8-8-888000000000000000000000000000000000000000000000000000000000000
χ678-8-88-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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