Finite Group Databasebeta

← Group #100722

Character table — Group #100722

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444448888888888888888888888888881616161616161616161616163232
order12222222444422444444444444444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-11-11-1111-1-11-111-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-1-1-11-11-1111-1-11-111-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-11
χ1111111111-1-1-1-1-1-11-11-1111-1-11-111-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−iii−i−i-1-111-11
χ1211111111-1-1-1-1-1-11-11-1111-1-11-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii−i−iii11-1-11-1
χ1311111111-1-1-1-1-1-11-11-11-1-1111-1-1-111ii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-11
χ1411111111-1-1-1-1-1-11-11-11-1-1111-1-1-111ii−i−iii−i−i−i−i−i−iiiii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1-1-1-1-11-11-11-1-1111-1-1-111−i−iii−i−iiiiiii−i−i−i−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-1-1-11-11-11-1-1111-1-1-111−i−iii−i−iiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-11
χ1722222222222222-2-2-2-220000-2-200000000000022-2-222-2-200000000000000
χ1822222222222222-2-2-2-220000-2-2000000000000-2-222-2-22200000000000000
χ19222222222222-2-22-22-2-22222-22-2-2-2-2000000000000000000000000000000
χ20222222222222-2-22-22-2-2-2-2-2-2-222222000000000000000000000000000000
χ21222222222222-2-2-22-22-200002-200002222-2-2-2-20000000000000000000000
χ22222222222222-2-2-22-22-200002-20000-2-2-2-222220000000000000000000000
χ2322222222-2-2-2-2222222-222-2-2-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2-2222222-2-2-222-2-222-2-2000000000000000000000000000000
χ2522222222-2-2-2-222-2-2-2-2-200002200002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2622222222-2-2-2-222-2-2-2-2-20000220000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ2722222222-2-2-2-2-2-2-22-2220000-220000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-22-2220000-22000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ292-22-2-22-2200002-22-2-220002i−2i002i−2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000000000
χ302-22-2-22-2200002-22-2-220002i−2i002i−2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000000000
χ312-22-2-22-2200002-22-2-22000−2i2i00−2i2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000000000
χ322-22-2-22-2200002-22-2-22000−2i2i00−2i2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000000000
χ332-22-2-22-2200002-2-222-202-20000002-2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000000000
χ342-22-2-22-2200002-2-222-202-20000002-2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000000000
χ352-22-2-22-2200002-2-222-20-22000000-22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000
χ362-22-2-22-2200002-2-222-20-22000000-22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000
χ372-22-2-22-220000-2222-2-20002i−2i00−2i2i00i2−i2−i2i2i2−i2−i2i22−22−2−22−2200000000000000
χ382-22-2-22-220000-2222-2-20002i−2i00−2i2i00−i2i2i2−i2−i2i2i2−i2−22−222−22−200000000000000
χ392-22-2-22-220000-2222-2-2000−2i2i002i−2i00i2−i2−i2i2i2−i2−i2i2−22−222−22−200000000000000
χ402-22-2-22-220000-2222-2-2000−2i2i002i−2i00−i2i2i2−i2−i2i2i2−i22−22−2−22−2200000000000000
χ412-22-2-22-220000-22-2-22202-2000000-222−22−2−22−222−2−22−222−200000000000000
χ422-22-2-22-220000-22-2-22202-2000000-22−22−222−22−2−222−22−2−2200000000000000
χ432-22-2-22-220000-22-2-2220-220000002-22−22−2−22−22−222−22−2−2200000000000000
χ442-22-2-22-220000-22-2-2220-220000002-2−22−222−22−22−2−22−222−200000000000000
χ4544-44-4-4-444i−4i4i−4i000000000000000000000000000000000000000002-22i−2i00
χ4644-44-4-4-444i−4i4i−4i00000000000000000000000000000000000000000-22−2i2i00
χ4744-44-4-4-44−4i4i−4i4i000000000000000000000000000000000000000002-2−2i2i00
χ4844-44-4-4-44−4i4i−4i4i00000000000000000000000000000000000000000-222i−2i00
χ494-4444-4-4-444-4-40000000000000000000000000000000002-22-20000000000
χ504-4444-4-4-444-4-4000000000000000000000000000000000-22-220000000000
χ514-4444-4-4-4-4-4440000000000000000000000000000000002i−2i−2i2i0000000000
χ524-4444-4-4-4-4-444000000000000000000000000000000000−2i2i2i−2i0000000000
χ534-4-44-444-44i−4i−4i4i00000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3000000
χ544-4-44-444-44i−4i−4i4i0000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3000000
χ554-4-44-444-4−4i4i4i−4i00000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ000000
χ564-4-44-444-4−4i4i4i−4i0000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ000000
χ57888-8-8-88-8000000000000000000000000000000000000000000000000000
χ5888-8-888-8-8000000000000000000000000000000000000000000000000000
χ598-8-8-88-888000000000000000000000000000000000000000000000000000

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