Finite Group Databasebeta

← Group #9681

Character table — Group #9681

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222222222224444444444444444448888888888888888444444442444
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222-2-2-2-2-2-2-2-2-2-222-2-20000000000000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-222-2-2-2-20000000000000000000000000000
χ1922222222-2-2-2-2222222222222-2-2-2-2-2-20000000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-20000000000000000000000000000
χ2122-222-2-2-2000022-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ2222-222-2-2-2000022-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ2322-222-2-2-2000022-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ2422-222-2-2-2000022-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ2522-222-2-2-20000-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ2622-222-2-2-20000-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ2722-222-2-2-20000-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ2822-222-2-2-20000-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ2922-2-2-222-22-22-22i−2i2i−2i00000000002i−2i00i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ3022-2-2-222-22-22-22i−2i2i−2i00000000002i−2i00−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ3122-2-2-222-22-22-2−2i2i−2i2i0000000000−2i2i00i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ3222-2-2-222-22-22-2−2i2i−2i2i0000000000−2i2i00−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ3322-2-2-222-2-22-222i−2i2i−2i0000000000−2i2i0022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ3422-2-2-222-2-22-222i−2i2i−2i0000000000−2i2i00−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ3522-2-2-222-2-22-22−2i2i−2i2i00000000002i−2i0022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ3622-2-2-222-2-22-22−2i2i−2i2i00000000002i−2i00−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ372-222-22-2-22-2-2200002i−2i2i−2i00002i−2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-222-22-2-22-2-2200002i−2i2i−2i00002i−2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ392-222-22-2-22-2-220000−2i2i−2i2i0000−2i2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ402-222-22-2-22-2-220000−2i2i−2i2i0000−2i2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ412-222-22-2-2-222-200002i−2i2i−2i0000−2i2i0000i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ422-222-22-2-2-222-200002i−2i2i−2i0000−2i2i0000−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ432-222-22-2-2-222-20000−2i2i−2i2i00002i−2i0000i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ442-222-22-2-2-222-20000−2i2i−2i2i00002i−2i0000−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ452-2-2-222-2222-2-2000000002-22-200002-2000000002i−2i−2i2i2i−2i−2i2i000000000000
χ462-2-2-222-2222-2-2000000002-22-200002-200000000−2i2i2i−2i−2i2i2i−2i000000000000
χ472-2-2-222-2222-2-200000000-22-220000-222i−2i−2i2i2i−2i−2i2i00000000000000000000
χ482-2-2-222-2222-2-200000000-22-220000-22−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ492-2-2-222-22-2-222000000002-22-20000-222-2-22-222-200000000000000000000
χ502-2-2-222-22-2-222000000002-22-20000-22-222-22-2-2200000000000000000000
χ512-2-2-222-22-2-22200000000-22-2200002-2000000002-2-22-222-2000000000000
χ522-2-2-222-22-2-22200000000-22-2200002-200000000-222-22-2-22000000000000
χ53444-4-4-4-4400004i−4i−4i4i000000000000000000000000000000000000000000
χ54444-4-4-4-440000−4i4i4i−4i000000000000000000000000000000000000000000
χ554-44-44-44-40000000000004i−4i−4i4i0000000000000000000000000000000000
χ564-44-44-44-4000000000000−4i4i4i−4i0000000000000000000000000000000000
χ574-4-44-4-444000000004-4-4400000000000000000000000000000000000000
χ584-4-44-4-44400000000-444-400000000000000000000000000000000000000

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