Finite Group Databasebeta

← Group #134451

Character table — Group #134451

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444488888888
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
χ51111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000
χ19222222222222-2-2-2-222222222-2-222-2-2-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000
χ21222-2-22-2-222-2-222-2-222-2-2000000002-20000000000000000002−22−22−22−2
χ22222-2-22-2-222-2-222-2-222-2-2000000002-2000000000000000000−22−22−22−22
χ23222-2-22-2-222-2-222-2-2-2-22200000000-220000000000000000002−22−2−22−22
χ24222-2-22-2-222-2-222-2-2-2-22200000000-22000000000000000000−22−222−22−2
χ25222-2-22-2-222-2-2-2-22222-2-200000000-22000000000000000000i2−i2−i2i2i2−i2−i2i2
χ26222-2-22-2-222-2-2-2-22222-2-200000000-22000000000000000000−i2i2i2−i2−i2i2i2−i2
χ27222-2-22-2-222-2-2-2-222-2-222000000002-2000000000000000000i2−i2−i2i2−i2i2i2−i2
χ28222-2-22-2-222-2-2-2-222-2-222000000002-2000000000000000000−i2i2i2−i2i2−i2−i2i2
χ29222-2-22-2-2-2-22200002-22-22i−2i2i−2i002i−2i0000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ30222-2-22-2-2-2-22200002-22-22i−2i2i−2i002i−2i000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ31222-2-22-2-2-2-22200002-22-2−2i2i−2i2i00−2i2i0000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ32222-2-22-2-2-2-22200002-22-2−2i2i−2i2i00−2i2i000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ33222-2-22-2-2-2-2220000-22-222i−2i2i−2i00−2i2i0000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ34222-2-22-2-2-2-2220000-22-222i−2i2i−2i00−2i2i000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ35222-2-22-2-2-2-2220000-22-22−2i2i−2i2i002i−2i0000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ36222-2-22-2-2-2-2220000-22-22−2i2i−2i2i002i−2i000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ3722-22-2-22-22-22-22-22-2000022-2-22-2000000002-2002-20000000000000000
χ3822-22-2-22-22-22-22-22-2000022-2-22-200000000-2200-220000000000000000
χ3922-22-2-22-22-22-22-22-20000-2-222-220000002i−2i002i−2i000000000000000000
χ4022-22-2-22-22-22-22-22-20000-2-222-22000000−2i2i00−2i2i000000000000000000
χ4122-22-2-22-22-22-2-22-22000022-2-2-220000002i−2i00−2i2i000000000000000000
χ4222-22-2-22-22-22-2-22-22000022-2-2-22000000−2i2i002i−2i000000000000000000
χ4322-22-2-22-22-22-2-22-220000-2-2222-2000000002-200-220000000000000000
χ4422-22-2-22-22-22-2-22-220000-2-2222-200000000-22002-20000000000000000
χ4544444444-4-4-4-400004-4-44000000000000000000000000000000000000
χ4644444444-4-4-4-40000-444-4000000000000000000000000000000000000
χ4744-44-4-44-4-44-440000000000000000004i−4i000000000000000000000000
χ4844-44-4-44-4-44-44000000000000000000−4i4i000000000000000000000000
χ4944-4-44-4-444-4-444-4-440000000000000000000000000000000000000000
χ5044-4-44-4-444-4-44-444-40000000000000000000000000000000000000000
χ5144-4-44-4-44-444-4000000004i−4i−4i4i00000000000000000000000000000000
χ5244-4-44-4-44-444-400000000−4i4i4i−4i00000000000000000000000000000000
χ538-8888-8-8-8000000000000000000000000000000000000000000000000
χ548-88-8-8-888000000000000000000000000000000000000000000000000
χ558-8-88-88-88000000000000000000000000000000000000000000000000
χ568-8-8-8888-8000000000000000000000000000000000000000000000000

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