Finite Group Databasebeta

← Group #94261

Character table — Group #94261

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888888888881616161616161616161616161632323232
order12222244444444444224444448888888828888888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1iiii−i−i−i−iii−i−i
χ61111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1−i−i−i−iiiii−i−iii
χ71111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ81111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ9111111-1-111-1-1-11111-1-111-1-1-1-1iiii−i−i−i−i1ii−i−i11-1-111-1-1i−ii−i
χ10111111-1-111-1-1-11111-1-111-1-1-1-1iiii−i−i−i−i1ii−i−i-1-111-1-111−ii−ii
χ11111111-1-111-1-1-11111-1-111-1-1-1-1−i−i−i−iiiii1−i−iii11-1-111-1-1−ii−ii
χ12111111-1-111-1-1-11111-1-111-1-1-1-1−i−i−i−iiiii1−i−iii-1-111-1-111i−ii−i
χ13111111-1-111-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i-1−i−iiiii−i−i−i−iii-111-1
χ14111111-1-111-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i-1−i−iii−i−iiiii−i−i1-1-11
χ15111111-1-111-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii-1ii−i−iii−i−i−i−iii1-1-11
χ16111111-1-111-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii-1ii−i−i−i−iiiii−i−i-111-1
χ1722222222222222222-2-2-2-222-2-200000000-20000000000000000
χ182222222222222-2-2-2-2-2-2-2-2-2-2220000000020000000000000000
χ19222222-2-222-2-2-2222222-2-2-2-22200000000-20000000000000000
χ20222222-2-222-2-2-2-2-2-2-222-2-222-2-20000000020000000000000000
χ2122-2-22-2002-20002i2i−2i−2i2-200002i−2ii2i2−i2−i2i2i2−i2−i202−22−2000000000000
χ2222-2-22-2002-20002i2i−2i−2i2-200002i−2i−i2−i2i2i2−i2−i2i2i20−22−22000000000000
χ2322-2-22-2002-20002i2i−2i−2i-220000−2i2i22−2−2−2−2220−i2i2i2−i2000000000000
χ2422-2-22-2002-20002i2i−2i−2i-220000−2i2i−2−22222−2−20i2−i2−i2i2000000000000
χ2522-2-22-2002-2000−2i−2i2i2i2-20000−2i2ii2i2−i2−i2i2i2−i2−i20−22−22000000000000
χ2622-2-22-2002-2000−2i−2i2i2i2-20000−2i2i−i2−i2i2i2−i2−i2i2i202−22−2000000000000
χ2722-2-22-2002-2000−2i−2i2i2i-2200002i−2i22−2−2−2−2220i2−i2−i2i2000000000000
χ2822-2-22-2002-2000−2i−2i2i2i-2200002i−2i−2−22222−2−20−i2i2i2−i2000000000000
χ2944444444-4-44-4-40000000000000000000000000000000000000
χ30444444-4-4-4-4-4440000000000000000000000000000000000000
χ314444-4-44400-4000000000000002-22-22-22-200000000000000000
χ324444-4-44400-400000000000000-22-22-22-2200000000000000000
χ334444-4-4-4-4004000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000
χ344444-4-4-4-400400000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000
χ3544-4-44-400-440000000004i−4i00000000000000000000000000000
χ3644-4-44-400-44000000000−4i4i00000000000000000000000000000
χ3744-4-4-44000004i−4i0000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000
χ3844-4-4-44000004i−4i000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000
χ3944-4-4-4400000−4i4i0000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000
χ4044-4-4-4400000−4i4i000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000
χ414-44-4004i−4i000002i−2i2i−2i00002-20000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ424-44-4004i−4i000002i−2i2i−2i00002-2000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ434-44-4004i−4i00000−2i2i−2i2i0000-220000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ444-44-4004i−4i00000−2i2i−2i2i0000-22000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ454-44-400−4i4i000002i−2i2i−2i0000-220000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ464-44-400−4i4i000002i−2i2i−2i0000-22000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ474-44-400−4i4i00000−2i2i−2i2i00002-20000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ484-44-400−4i4i00000−2i2i−2i2i00002-2000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ498-8-880000000004-4-44000000000000000000000000000000000
χ508-8-88000000000-444-4000000000000000000000000000000000

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