Finite Group Databasebeta

← Group #141585

Character table — Group #141585

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222444444444444444888888888888888888888816161616323232323232
order12222244888822224444488888844444444448888888888882222448888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-11-1-1-1-111-1-1-1-1-11iiii−i−i−i−i-1-111iiii−i−i−i−i1111-1-1ii−i−i
χ611111111111111-1-11-1-1-1-111-1-1-1-1-11iiii−i−i−i−i-1-111iiii−i−i−i−i-1-1-1-111−i−iii
χ711111111111111-1-11-1-1-1-111-1-1-1-1-11−i−i−i−iiiii-1-111−i−i−i−iiiii1111-1-1−i−iii
χ811111111111111-1-11-1-1-1-111-1-1-1-1-11−i−i−i−iiiii-1-111−i−i−i−iiiii-1-1-1-111ii−i−i
χ911111111-1-1-1-1111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-11-1
χ1011111111-1-1-1-1111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-11
χ1111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-11-11
χ1211111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-11-1
χ1311111111-1-1-1-111-1-11-1-1-1-1-1-11111-11iiii−i−i−i−i11-1-1−i−i−i−iiiii11-1-1-11i−i−ii
χ1411111111-1-1-1-111-1-11-1-1-1-1-1-11111-11iiii−i−i−i−i11-1-1−i−i−i−iiiii-1-1111-1−iii−i
χ1511111111-1-1-1-111-1-11-1-1-1-1-1-11111-11−i−i−i−iiiii11-1-1iiii−i−i−i−i11-1-1-11−iii−i
χ1611111111-1-1-1-111-1-11-1-1-1-1-1-11111-11−i−i−i−iiiii11-1-1iiii−i−i−i−i-1-1111-1i−i−ii
χ17222222222222-2-222222-2-2222222-2-200000000-2-2-2-2000000000000000000
χ18222222222222-2-2-2-22-2-22222-2-2-2-22-20000000022-2-2000000000000000000
χ1922222222-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000
χ2022222222-2-2-2-2-2-2-2-22-2-222-2-222222-200000000-2-222000000000000000000
χ21222222-2-200002222-2-2-2-2-20000002-20000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ22222222-2-200002222-2-2-2-2-20000002-2000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ23222222-2-2000022-2-2-22222000000-2-200000000000022-2-2-2-2220000000000
χ24222222-2-2000022-2-2-22222000000-2-2000000000000-2-22222-2-20000000000
χ25222222-2-20000-2-222-2-2-222000000-2222-2-222-2-20000000000000000000000
χ26222222-2-20000-2-222-2-2-222000000-22-2-222-2-2220000000000000000000000
χ27222222-2-20000-2-2-2-2-222-2-2000000222i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ28222222-2-20000-2-2-2-2-222-2-200000022−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ2922-2-22-20022−2−22-20002i−2i2i−2i2−2i2i2−i2−i2001+i−1−i1+i−1−i1−i−1+i1−i−1+ii2−i22−2002ζ−2ζ2ζ3−2ζ3000000000000
χ3022-2-22-20022−2−22-20002i−2i2i−2i2−2i2i2−i2−i200−1−i1+i−1−i1+i−1+i1−i−1+i1−ii2−i22−200−2ζ2ζ−2ζ32ζ3000000000000
χ3122-2-22-20022−2−22-2000−2i2i−2i2i2−2−i2−i2i2i2001−i−1+i1−i−1+i1+i−1−i1+i−1−i−i2i22−200−2ζ32ζ3−2ζ2ζ000000000000
χ3222-2-22-20022−2−22-2000−2i2i−2i2i2−2−i2−i2i2i200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−i2i22−2002ζ3−2ζ32ζ−2ζ000000000000
χ3322-2-22-20022−2−2-220002i−2i−2i2i2−2i2i2−i2−i2001−i−1+i−1+i1−i1+i−1−i−1−i1+i−i2i2−222ζ3−2ζ300002ζ−2ζ0000000000
χ3422-2-22-20022−2−2-220002i−2i−2i2i2−2i2i2−i2−i200−1+i1−i1−i−1+i−1−i1+i1+i−1−i−i2i2−22−2ζ32ζ30000−2ζ2ζ0000000000
χ3522-2-22-20022−2−2-22000−2i2i2i−2i2−2−i2−i2i2i2001+i−1−i−1−i1+i1−i−1+i−1+i1−ii2−i2−22−2ζ2ζ0000−2ζ32ζ30000000000
χ3622-2-22-20022−2−2-22000−2i2i2i−2i2−2−i2−i2i2i200−1−i1+i1+i−1−i−1+i1−i1−i−1+ii2−i2−222ζ−2ζ00002ζ3−2ζ30000000000
χ3722-2-22-200−2−2222-20002i−2i2i−2i−22−i2−i2i2i2001+i−1−i1+i−1−i1−i−1+i1−i−1+i−i2i2−2200−2ζ2ζ−2ζ32ζ3000000000000
χ3822-2-22-200−2−2222-20002i−2i2i−2i−22−i2−i2i2i200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−i2i2−22002ζ−2ζ2ζ3−2ζ3000000000000
χ3922-2-22-200−2−2222-2000−2i2i−2i2i−22i2i2−i2−i2001−i−1+i1−i−1+i1+i−1−i1+i−1−ii2−i2−22002ζ3−2ζ32ζ−2ζ000000000000
χ4022-2-22-200−2−2222-2000−2i2i−2i2i−22i2i2−i2−i200−1+i1−i−1+i1−i−1−i1+i−1−i1+ii2−i2−2200−2ζ32ζ3−2ζ2ζ000000000000
χ4122-2-22-200−2−222-220002i−2i−2i2i−22−i2−i2i2i2001−i−1+i−1+i1−i1+i−1−i−1−i1+ii2−i22−2−2ζ32ζ30000−2ζ2ζ0000000000
χ4222-2-22-200−2−222-220002i−2i−2i2i−22−i2−i2i2i200−1+i1−i1−i−1+i−1−i1+i1+i−1−ii2−i22−22ζ3−2ζ300002ζ−2ζ0000000000
χ4322-2-22-200−2−222-22000−2i2i2i−2i−22i2i2−i2−i2001+i−1−i−1−i1+i1−i−1+i−1+i1−i−i2i22−22ζ−2ζ00002ζ3−2ζ30000000000
χ4422-2-22-200−2−222-22000−2i2i2i−2i−22i2i2−i2−i200−1−i1+i1+i−1−i−1+i1−i1−i−1+i−i2i22−2−2ζ2ζ0000−2ζ32ζ30000000000
χ454444-4-44444440000-40000-4-4000000000000000000000000000000000000
χ464444-4-444-4-4-4-40000-4000044000000000000000000000000000000000000
χ474444-4-4-4-40000000040000004i−4i4i−4i00000000000000000000000000000000
χ484444-4-4-4-4000000004000000−4i4i−4i4i00000000000000000000000000000000
χ4944-4-4-44002222−22−22004-400000−222222−22−222200000000000000000000000000000000
χ5044-4-4-44002222−22−2200-4400000−2222−222222−2200000000000000000000000000000000
χ5144-4-4-4400−22−222222004-40000022−22−222222−2200000000000000000000000000000000
χ5244-4-4-4400−22−22222200-440000022−2222−22−222200000000000000000000000000000000
χ534-4-4400-444-44-400000000000000000000000000000000000002-22-2000000
χ544-4-4400-444-44-40000000000000000000000000000000000000-22-22000000
χ554-4-4400-44-44-4400000000000000000000000000000000000002-2-22000000
χ564-4-4400-44-44-440000000000000000000000000000000000000-222-2000000
χ578-88-8000042−42−424200000000000000000000000000000000000000000000000
χ588-88-80000−424242−4200000000000000000000000000000000000000000000000
χ598-8-88008-8000000000000000000000000000000000000000000000000000

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