Finite Group Databasebeta

← Group #139586

Character table — Group #139586

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222222244444444488888888888888888888888816161616323232323232
order122222222244888844488888824448888161616161616161616161616161616164444444444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ911111-1-11-1-111-1-1-1-11-1-11111-1-11-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-1i−ii−i
χ1011111-1-11-1-111-1-1-1-11-1-11111-1-11-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-11−ii−ii
χ1111111-1-11-1-111-1-1-1-11-1-11111-1-11-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-1−ii−ii
χ1211111-1-11-1-111-1-1-1-11-1-11111-1-11-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-11i−ii−i
χ1311111-1-11-1-111-1-1-1-11-1-11111-1-1-11-11-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-11i−i−ii
χ1411111-1-11-1-111-1-1-1-11-1-11111-1-1-11-11-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1111-1−iii−i
χ1511111-1-11-1-111-1-1-1-11-1-11111-1-1-11-11-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11−iii−i
χ1611111-1-11-1-111-1-1-1-11-1-11111-1-1-11-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1i−i−ii
χ17222222222222-2-2-2-2222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000
χ192222222222-2-20000-2-2-200000022-2-2000022−2−222−2−222−2−222−2−20000000000
χ202222222222-2-20000-2-2-200000022-2-20000−2−222−2−222−2−222−2−2220000000000
χ212222222222-2-20000-2-2-2000000-2-222000022−2−222−2−2−2−222−2−2220000000000
χ222222222222-2-20000-2-2-2000000-2-2220000−2−222−2−22222−2−222−2−20000000000
χ2322222-2-22-2-22222222-2-2-2-2-2-2222-22-2-2-22200000000000000000000000000
χ2422222-2-22-2-22222222-2-2-2-2-2-222-22-2222-2-200000000000000000000000000
χ2522222-2-22-2-2-2-20000-2220000002-2-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000
χ2622222-2-22-2-2-2-20000-2220000002-2-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000
χ2722222-2-22-2-2-2-20000-222000000-222-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000
χ2822222-2-22-2-2-2-20000-222000000-222-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000
χ292222-22-2-22-2222222-22-222-2-2-2-200000000000000002-22-22-22-20000000000
χ302222-22-2-22-2222222-22-222-2-2-2-20000000000000000-22-22-22-220000000000
χ312222-22-2-22-222-2-2-2-2-22-2-2-22222000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ322222-22-2-22-222-2-2-2-2-22-2-2-2222200000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ332222-22-2-22-2-2-200002-2200000000002i−2i2i−2ii2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000
χ342222-22-2-22-2-2-200002-2200000000002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000
χ352222-22-2-22-2-2-200002-220000000000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000
χ362222-22-2-22-2-2-200002-220000000000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000
χ372222-2-22-2-22222222-2-22-2-222-2-2000000002-22-2-22-22000000000000000000
χ382222-2-22-2-22222222-2-22-2-222-2-200000000-22-222-22-2000000000000000000
χ392222-2-22-2-2222-2-2-2-2-2-2222-2-22200000000000000002i−2i2i−2i−2i2i−2i2i0000000000
χ402222-2-22-2-2222-2-2-2-2-2-2222-2-2220000000000000000−2i2i−2i2i2i−2i2i−2i0000000000
χ412222-2-22-2-22-2-2000022-200000000002i−2i−2i2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000
χ422222-2-22-2-22-2-2000022-200000000002i−2i−2i2i−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000
χ432222-2-22-2-22-2-2000022-20000000000−2i2i2i−2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000
χ442222-2-22-2-22-2-2000022-20000000000−2i2i2i−2i−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000
χ4544-4-444-4-4-44002222−22−2200022−2222−2222−220000000000000000000000000000000000
χ4644-4-444-4-4-4400−22−222222000−2222−2222−22220000000000000000000000000000000000
χ4744-4-44-44-44-4002222−22−22000−2222−222222−220000000000000000000000000000000000
χ4844-4-44-44-44-400−22−22222200022−2222−22−22220000000000000000000000000000000000
χ4944-4-4-4444-4-4002222−22−2200022−22−2222−22220000000000000000000000000000000000
χ5044-4-4-4444-4-400−22−222222000−222222−2222−220000000000000000000000000000000000
χ5144-4-4-4-4-4444002222−22−22000−222222−22−22220000000000000000000000000000000000
χ5244-4-4-4-4-444400−22−22222200022−22−222222−220000000000000000000000000000000000
χ534-44-4000000-444-44-40000000000000000000000000000000002i−2i2i−2i000000
χ544-44-4000000-444-44-4000000000000000000000000000000000−2i2i−2i2i000000
χ554-44-4000000-44-44-440000000000000000000000000000000002i−2i−2i2i000000
χ564-44-4000000-44-44-44000000000000000000000000000000000−2i2i2i−2i000000
χ578-88-80000008-800000000000000000000000000000000000000000000000
χ588-8-880000000042−42−42420000000000000000000000000000000000000000000
χ598-8-8800000000−424242−420000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).