Finite Group Databasebeta

← Group #140312

Character table — Group #140312

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order1222444444444424888888888888444488888888888888888816161616161616162488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111-1-1-1-111-1-1-11iiii−i−i−i−i11-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ10111111-1-1-1-111-1-1-11iiii−i−i−i−i11-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-11−ii
χ11111111-1-1-1-111-1-1-11iiii−i−i−i−i11-1-1ii−i−i1-1-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ12111111-1-1-1-111-1-1-11iiii−i−i−i−i11-1-1ii−i−i1-1-1-1-1-11111−i−i−i−iiiii-1-111−i−iii1-1i−i
χ13111111-1-1-1-111-1-1-11−i−i−i−iiiii11-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ14111111-1-1-1-111-1-1-11−i−i−i−iiiii11-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-11i−i
χ15111111-1-1-1-111-1-1-11−i−i−i−iiiii11-1-1−i−iii1-1-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-11i−i
χ16111111-1-1-1-111-1-1-11−i−i−i−iiiii11-1-1−i−iii1-1-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i1-1−ii
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000
χ1922222222-2-2-2-2-2-22-20000000022-2-20000-22000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2022222222-2-2-2-2-2-22-20000000022-2-20000-2200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2122222222-2-2-2-2-2-22-200000000-2-22200002-22i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2222222222-2-2-2-2-2-22-200000000-2-22200002-2−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ23222222-2-222-2-222-2-20000000022220000-2-20000000022-2-2-2-222000000000000
χ24222222-2-222-2-222-2-20000000022220000-2-200000000-2-22222-2-2000000000000
χ25222222-2-222-2-222-2-200000000-2-2-2-20000222i2i−2i−2i−2i−2i2i2i00000000000000000000
χ26222222-2-222-2-222-2-200000000-2-2-2-2000022−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ27222222-2-2-2-222-2-2-222i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i-220000000000000000000000000000
χ28222222-2-2-2-222-2-2-22−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i-220000000000000000000000000000
χ292222-2-222-2-2-2-222-2222-2-222-2-200000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ302222-2-222-2-2-2-222-2222-2-222-2-200000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ312222-2-222-2-2-2-222-22-2-222-2-22200000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ322222-2-222-2-2-2-222-22-2-222-2-22200000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ332222-2-2-2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000i2−i2−i2i2−222−20000
χ342222-2-2-2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000−i2i2i2−i22−2−220000
χ352222-2-2-2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000i2−i2−i2i22−2−220000
χ362222-2-2-2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000−i2i2i2−i2−222−20000
χ3722-2-22-2002i−2i002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22i−2i1+i−1−i1−i−1+i00i2−i2i2−i22−22−2002ζ3−2ζ32ζ−2ζ00000000000000
χ3822-2-22-2002i−2i002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22i−2i1+i−1−i1−i−1+i00−i2i2−i2i2−22−2200−2ζ32ζ3−2ζ2ζ00000000000000
χ3922-2-22-2002i−2i002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i−1−i1+i−1+i1−i002−2−22i2−i2−i2i22ζ−2ζ00002ζ3−2ζ3000000000000
χ4022-2-22-2002i−2i002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i−1−i1+i−1+i1−i00−222−2−i2i2i2−i2−2ζ2ζ0000−2ζ32ζ3000000000000
χ4122-2-22-2002i−2i002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22i−2i−1−i1+i−1+i1−i00i2−i2i2−i22−22−200−2ζ32ζ3−2ζ2ζ00000000000000
χ4222-2-22-2002i−2i002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22i−2i−1−i1+i−1+i1−i00−i2i2−i2i2−22−22002ζ3−2ζ32ζ−2ζ00000000000000
χ4322-2-22-2002i−2i002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i1+i−1−i1−i−1+i002−2−22i2−i2−i2i2−2ζ2ζ0000−2ζ32ζ3000000000000
χ4422-2-22-2002i−2i002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i1+i−1−i1−i−1+i00−222−2−i2i2i2−i22ζ−2ζ00002ζ3−2ζ3000000000000
χ4522-2-22-200−2i2i00−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2−2i2i1−i−1+i1+i−1−i00i2−i2i2−i2−22−22002ζ−2ζ2ζ3−2ζ300000000000000
χ4622-2-22-200−2i2i00−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2−2i2i1−i−1+i1+i−1−i00−i2i2−i2i22−22−200−2ζ2ζ−2ζ32ζ300000000000000
χ4722-2-22-200−2i2i00−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i−1+i1−i−1−i1+i002−2−22−i2i2i2−i2−2ζ32ζ30000−2ζ2ζ000000000000
χ4822-2-22-200−2i2i00−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i−1+i1−i−1−i1+i00−222−2i2−i2−i2i22ζ3−2ζ300002ζ−2ζ000000000000
χ4922-2-22-200−2i2i00−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2−2i2i−1+i1−i−1−i1+i00i2−i2i2−i2−22−2200−2ζ2ζ−2ζ32ζ300000000000000
χ5022-2-22-200−2i2i00−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2−2i2i−1+i1−i−1−i1+i00−i2i2−i2i22−22−2002ζ−2ζ2ζ3−2ζ300000000000000
χ5122-2-22-200−2i2i00−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i1−i−1+i1+i−1−i002−2−22−i2i2i2−i22ζ3−2ζ300002ζ−2ζ000000000000
χ5222-2-22-200−2i2i00−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i1−i−1+i1+i−1−i00−222−2i2−i2−i2i2−2ζ32ζ30000−2ζ2ζ000000000000
χ534444-4-4444444-4-4-4-40000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-444444-40000000000000000000000000000000000000000000000
χ5544-4-4-44004i−4i00−4i4i002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000
χ5644-4-4-44004i−4i00−4i4i00−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000
χ5744-4-4-4400−4i4i004i−4i002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000
χ5844-4-4-4400−4i4i004i−4i00−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000
χ598-88-8008i−8i000000000000000000000000000000000000000000000000000000
χ608-88-800−8i8i000000000000000000000000000000000000000000000000000000
χ618-8-880000008-800000000000000000000000000000000000000000000000000
χ628-8-88000000-8800000000000000000000000000000000000000000000000000

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