Finite Group Databasebeta

← Group #9712

Character table — Group #9712

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222222222224444444444444444444444444444444444888888882244
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
χ511111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ611111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ911111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ1011111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ1111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ1211111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ1411111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ1511111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ1611111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ17222222222222-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1922222222-2-2-2-2222222-2-2-2-222-2-2-2-2220000000000000000000000000000
χ2022222222-2-2-2-222-2-2-2-2222222-2-222-2-20000000000000000000000000000
χ21222-22-2-2-200002i−2i00002i2i−2i−2i2i−2i002-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ22222-22-2-2-200002i−2i00002i2i−2i−2i2i−2i002-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ23222-22-2-2-200002i−2i0000−2i−2i2i2i2i−2i00-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ24222-22-2-2-200002i−2i0000−2i−2i2i2i2i−2i00-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ25222-22-2-2-20000−2i2i00002i2i−2i−2i−2i2i00-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ26222-22-2-2-20000−2i2i00002i2i−2i−2i−2i2i00-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ27222-22-2-2-20000−2i2i0000−2i−2i2i2i−2i2i002-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ28222-22-2-2-20000−2i2i0000−2i−2i2i2i−2i2i002-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ2922-22-22-2-200002i−2i22-2-20000−2i2i00002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ3022-22-22-2-200002i−2i22-2-20000−2i2i00002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ3122-22-22-2-200002i−2i-2-2220000−2i2i0000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ3222-22-22-2-200002i−2i-2-2220000−2i2i0000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ3322-22-22-2-20000−2i2i22-2-200002i−2i0000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3422-22-22-2-20000−2i2i22-2-200002i−2i0000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3522-22-22-2-20000−2i2i-2-22200002i−2i00002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3622-22-22-2-20000−2i2i-2-22200002i−2i00002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3722-2-2-2-2222-22-22200000000-2-22-20000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ3822-2-2-2-2222-22-22200000000-2-22-2000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ3922-2-2-2-2222-22-2-2-20000000022-2200002-2-222-2-2200000000000000000000
χ4022-2-2-2-2222-22-2-2-20000000022-220000-222-2-222-200000000000000000000
χ4122-2-2-2-222-22-222200000000-2-2-2200002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ4222-2-2-2-222-22-222200000000-2-2-220000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ4322-2-2-2-222-22-22-2-200000000222-20000000000002-2-222-2-22000000000000
χ4422-2-2-2-222-22-22-2-200000000222-2000000000000-222-2-222-2000000000000
χ452-22-2-22-2222-2-2002-22-22-22-2000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ462-22-2-22-2222-2-2002-22-22-22-2000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ472-22-2-22-2222-2-200-22-22-22-22000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ482-22-2-22-2222-2-200-22-22-22-22000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ492-22-2-22-22-2-222002-22-2-22-220000000000000000000000002−2−222−2−220000
χ502-22-2-22-22-2-222002-22-2-22-22000000000000000000000000−222−2−222−20000
χ512-22-2-22-22-2-22200-22-222-22-20000000000000000000000002−2−22−222−20000
χ522-22-2-22-22-2-22200-22-222-22-2000000000000000000000000−222−22−2−220000
χ534-444-4-44-400000000004i−4i−4i4i000000000000000000000000000000000000
χ544-444-4-44-40000000000−4i4i4i−4i000000000000000000000000000000000000
χ554-4-444-4-444-4-440000000000000000000000000000000000000000000000
χ564-4-444-4-44-444-40000000000000000000000000000000000000000000000
χ574-4-4-4444-40000004-4-440000000000000000000000000000000000000000
χ584-4-4-4444-4000000-444-40000000000000000000000000000000000000000

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