Finite Group Databasebeta

← Group #9813

Character table — Group #9813

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122222222222222222244444444444444444444441616161616161616
order1222222244444488888888244444444488888888888824448888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ9111111-1-11-1-11-1-11111-1-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i11-1-11-11-1i−ii−i
χ10111111-1-11-1-11-1-11111-1-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i11-1-1-11-11−ii−ii
χ11111111-1-11-1-11-1-11111-1-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-1−ii−ii
χ12111111-1-11-1-11-1-11111-1-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii11-1-1-11-11i−ii−i
χ13111111-1-11-1-11-1-1-1-1-1-11111-11iiii−i−i−i−i−i−i−i−iiiii-1-1111-1-11i−i−ii
χ14111111-1-11-1-11-1-1-1-1-1-11111-11iiii−i−i−i−i−i−i−i−iiiii-1-111-111-1−iii−i
χ15111111-1-11-1-11-1-1-1-1-1-11111-11−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1-11−iii−i
χ16111111-1-11-1-11-1-1-1-1-1-11111-11−i−i−i−iiiiiiiii−i−i−i−i-1-111-111-1i−i−ii
χ1722222222-2-2-2-2-2-2000000002-2000000002i2i−2i−2i2i2i−2i−2i000000000000
χ1822222222-2-2-2-2-2-2000000002-200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ19222222-2-2-222-22200000000-2-20000000022-2-2-2-222000000000000
χ20222222-2-2-222-22200000000-2-200000000-2-22222-2-2000000000000
χ212222-2-2222222-2-222222222-2-20000000000000000-2-2-2-200000000
χ222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222200000000
χ232222-2-222-2-2-2-22200000000-2222-2-222-2-200000000000000000000
χ242222-2-222-2-2-2-22200000000-22-2-222-2-22200000000000000000000
χ252222-2-2-2-22-2-22222222-2-2-2-22-20000000000000000-2-22200000000
χ262222-2-2-2-22-2-2222-2-2-2-222222-2000000000000000022-2-200000000
χ272222-2-2-2-2-222-2-2-200000000222i2i−2i−2i−2i−2i2i2i00000000000000000000
χ282222-2-2-2-2-222-2-2-20000000022−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ2922-2-22-20002i−2i02i−2i22−2−2i2i2−i2−i2001+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ−2ζ2ζ3−2ζ3002−2i2−i200000000
χ3022-2-22-20002i−2i02i−2i22−2−2i2i2−i2−i200−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ2ζ−2ζ32ζ3002−2i2−i200000000
χ3122-2-22-20002i−2i02i−2i−2−222−i2−i2i2i2001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ2ζ−2ζ32ζ300−22−i2i200000000
χ3222-2-22-20002i−2i02i−2i−2−222−i2−i2i2i200−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ−2ζ2ζ3−2ζ300−22−i2i200000000
χ3322-2-22-2000−2i2i0−2i2i22−2−2−i2−i2i2i2001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ32ζ3−2ζ2ζ002−2−i2i200000000
χ3422-2-22-2000−2i2i0−2i2i22−2−2−i2−i2i2i200−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ3−2ζ32ζ−2ζ002−2−i2i200000000
χ3522-2-22-2000−2i2i0−2i2i−2−222i2i2−i2−i2001−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ3−2ζ32ζ−2ζ00−22i2−i200000000
χ3622-2-22-2000−2i2i0−2i2i−2−222i2i2−i2−i200−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ32ζ3−2ζ2ζ00−22i2−i200000000
χ3722-2-2-220002i−2i0−2i2i22−2−2i2i2−i2−i2001−i−1+i−1+i1−i1+i−1−i−1−i1+i2ζ3−2ζ300002ζ−2ζ−22−i2i200000000
χ3822-2-2-220002i−2i0−2i2i22−2−2i2i2−i2−i200−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2ζ32ζ30000−2ζ2ζ−22−i2i200000000
χ3922-2-2-220002i−2i0−2i2i−2−222−i2−i2i2i2001−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ32ζ30000−2ζ2ζ2−2i2−i200000000
χ4022-2-2-220002i−2i0−2i2i−2−222−i2−i2i2i200−1+i1−i1−i−1+i−1−i1+i1+i−1−i2ζ3−2ζ300002ζ−2ζ2−2i2−i200000000
χ4122-2-2-22000−2i2i02i−2i22−2−2−i2−i2i2i2001+i−1−i−1−i1+i1−i−1+i−1+i1−i−2ζ2ζ0000−2ζ32ζ3−22i2−i200000000
χ4222-2-2-22000−2i2i02i−2i22−2−2−i2−i2i2i200−1−i1+i1+i−1−i−1+i1−i1−i−1+i2ζ−2ζ00002ζ3−2ζ3−22i2−i200000000
χ4322-2-2-22000−2i2i02i−2i−2−222i2i2−i2−i2001+i−1−i−1−i1+i1−i−1+i−1+i1−i2ζ−2ζ00002ζ3−2ζ32−2−i2i200000000
χ4422-2-2-22000−2i2i02i−2i−2−222i2i2−i2−i200−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ2ζ0000−2ζ32ζ32−2−i2i200000000
χ454-44-4004-40000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000
χ464-44-4004-4000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000
χ474-44-400-440000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ484-44-400-44000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ494-4-440000400-4004i−4i−4i4i0000000000000000000000000000000000
χ504-4-440000400-400−4i4i4i−4i0000000000000000000000000000000000
χ514-4-440000-40040000004-4-44000000000000000000000000000000
χ524-4-440000-4004000000-444-4000000000000000000000000000000

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