Finite Group Databasebeta

← Group #97282

Character table — Group #97282

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444444444888888882244444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1111111111-11-11-1-1-11-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-11-11-11-1-1-11-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-11-11111-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-1-1-11111-1-1iiii−i−i−i−i111-1-1-11-1-11ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1-11111-11-1ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−iiiii111-1-1-11-1-11−i−iii−i−iii−i−iii
χ1211111111-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1-11111-11-1−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−i1-111-11-11-1-1−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−i-11-1-11-1-1111−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii1-111-11-11-1-1ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii-11-1-11-1-1111ii−i−iii−i−i−i−iii
χ1722222222222222-2-222-2-2-2-2222200000000000000-2-200000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2000000000000002200000000000000
χ19222222222222-2-22-2-2-22-22-2000000000000020-202000-2000000000000
χ20222222222222-2-22-2-2-22-22-20000000000000-2020-20002000000000000
χ21222222222222-2-2-22-2-2-22-2200000000000020-202000-20000000000000
χ22222222222222-2-2-22-2-2-22-22000000000000-2020-200020000000000000
χ2322222222-2-2-2-22222-2-222-2-222-2-200000000000000-2200000000000000
χ2422222222-2-2-2-22222-2-222-2-2-2-222000000000000002-200000000000000
χ2522222222-2-2-2-2-2-22-2222-2-2200000000000020-20-200020000000000000
χ2622222222-2-2-2-2-2-22-2222-2-22000000000000-20202000-20000000000000
χ2722222222-2-2-2-2-2-2-2222-222-200000000000002020-2000-2000000000000
χ2822222222-2-2-2-2-2-2-2222-222-20000000000000-20-2020002000000000000
χ2922-22-2-22-22i−2i2i−2i2-2002i−2i00002-22i−2i00000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ3022-22-2-22-22i−2i2i−2i2-2002i−2i00002-22i−2i0000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ3122-22-2-22-22i−2i2i−2i2-2002i−2i0000-22−2i2i00000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ3222-22-2-22-22i−2i2i−2i2-2002i−2i0000-22−2i2i0000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ3322-22-2-22-2−2i2i−2i2i2-200−2i2i00002-2−2i2i00000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ3422-22-2-22-2−2i2i−2i2i2-200−2i2i00002-2−2i2i0000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ3522-22-2-22-2−2i2i−2i2i2-200−2i2i0000-222i−2i00000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ3622-22-2-22-2−2i2i−2i2i2-200−2i2i0000-222i−2i0000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ37444-4-44-4-444-4-40000000000000022-2-222-2-20000000000000000000000
χ38444-4-44-4-444-4-400000000000000-2-222-2-2220000000000000000000000
χ39444-4-44-4-4-4-444000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ40444-4-44-4-4-4-44400000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ4144-44-4-44-44i−4i4i−4i-4400−4i4i00000000000000000000000000000000000000
χ4244-44-4-44-4−4i4i−4i4i-44004i−4i00000000000000000000000000000000000000
χ4344-4-44-4-444i−4i−4i4i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ4444-4-44-4-444i−4i−4i4i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4544-4-44-4-44−4i4i4i−4i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ4644-4-44-4-44−4i4i4i−4i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ474-4-44-44-440000004000-400000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ484-4-44-44-440000004000-40000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ494-4-44-44-44000000-4000400000002-22-2-22-220000000000000000000000
χ504-4-44-44-44000000-400040000000-22-222-22-20000000000000000000000
χ514-4-4-4444-400000004000-40000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ524-4-4-4444-400000004000-4000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ534-4-4-4444-40000000-400040000002-2-22-222-20000000000000000000000
χ544-4-4-4444-40000000-40004000000-222-22-2-220000000000000000000000
χ558-8888-8-8-8000000000000000000000000000000000000000000000000
χ568-88-8-8-888000000000000000000000000000000000000000000000000

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