Finite Group Databasebeta

← Group #134459

Character table — Group #134459

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12224444224422444444888844888888444488888888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222-2-2-2-222222-2-222-2-2-2-2000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-2-2-22222000000000000000000000000
χ19222222222222-2-2-22222-22222-2-2-2-2-2-222000000000000000000000000
χ20222222222222-2-2-22222-2-2-2-2-2-2-22222-2-2000000000000000000000000
χ212222-2-2-2-222-2-222-222-2-2-200002-20000002-22-200000000000000000000
χ222222-2-2-2-222-2-222-222-2-2-200002-2000000-22-2200000000000000000000
χ232222-2-2-2-222-2-222-2-2-222-20000-2200000000002i−2i2i−2i0000000000000000
χ242222-2-2-2-222-2-222-2-2-222-20000-220000000000−2i2i−2i2i0000000000000000
χ252222-2-2-2-222-2-2-2-2222-2-220000-2200000000002i−2i−2i2i0000000000000000
χ262222-2-2-2-222-2-2-2-2222-2-220000-220000000000−2i2i2i−2i0000000000000000
χ272222-2-2-2-222-2-2-2-22-2-222200002-20000002-2-2200000000000000000000
χ282222-2-2-2-222-2-2-2-22-2-222200002-2000000-222-200000000000000000000
χ2922-2-222-2-22-22-22-220000-222-2-2002-20000000000002−22−22−22−200000000
χ3022-2-222-2-22-22-22-220000-222-2-2002-2000000000000−22−22−22−2200000000
χ3122-2-222-2-22-22-22-220000-2-2-22200-220000000000002−22−2−22−2200000000
χ3222-2-222-2-22-22-22-220000-2-2-22200-22000000000000−22−222−22−200000000
χ3322-2-222-2-22-22-2-22-20000222-2-200-22000000000000i2−i2−i2i2i2−i2−i2i200000000
χ3422-2-222-2-22-22-2-22-20000222-2-200-22000000000000−i2i2i2−i2−i2i2i2−i200000000
χ3522-2-222-2-22-22-2-22-200002-2-222002-2000000000000i2−i2−i2i2−i2i2i2−i200000000
χ3622-2-222-2-22-22-2-22-200002-2-222002-2000000000000−i2i2i2−i2i2−i2−i2i200000000
χ3722-2-2-2-222-222-20002i−2i2i−2i02-22-20000002i−2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ3822-2-2-2-222-222-20002i−2i2i−2i02-22-20000002i−2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ3922-2-2-2-222-222-20002i−2i2i−2i0-22-22000000−2i2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ4022-2-2-2-222-222-20002i−2i2i−2i0-22-22000000−2i2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ4122-2-2-2-222-222-2000−2i2i−2i2i02-22-2000000−2i2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ4222-2-2-2-222-222-2000−2i2i−2i2i02-22-2000000−2i2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ4322-2-2-2-222-222-2000−2i2i−2i2i0-22-220000002i−2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ4422-2-2-2-222-222-2000−2i2i−2i2i0-22-220000002i−2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ4544444444-4-4-4-400000000000000004i−4i00000000000000000000000000
χ4644444444-4-4-4-40000000000000000−4i4i00000000000000000000000000
χ474444-4-4-4-4-4-444000000004-4-4400000000000000000000000000000000
χ484444-4-4-4-4-4-44400000000-444-400000000000000000000000000000000
χ4944-4-444-4-4-44-440004i−4i−4i4i0000000000000000000000000000000000000
χ5044-4-444-4-4-44-44000−4i4i4i−4i0000000000000000000000000000000000000
χ5144-4-4-4-4444-4-444-4-400004000000000000000000000000000000000000
χ5244-4-4-4-4444-4-44-4440000-4000000000000000000000000000000000000
χ538-88-88i−8i8i−8i000000000000000000000000000000000000000000000000
χ548-88-8−8i8i−8i8i000000000000000000000000000000000000000000000000
χ558-8-888i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000

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