Finite Group Databasebeta

← Group #116361

Character table — Group #116361

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444222244442222444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ9111-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111ii−i−i−i−iii
χ11111-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111−i−iiiii−i−i
χ12111-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ13111-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111−i−iii−i−iii
χ14111-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ16111-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111ii−i−iii−i−i
χ1722222222222222-2-222-2-2-2-2-2-22-22-2000000000000000022-2-222-2-20000000000000000
χ1822222222222222-2-222-2-2-2-2-2-22-22-20000000000000000-2-222-2-2220000000000000000
χ19222222222222-2-222-2-222-2-2-2-2-22-220000000022-2-222-2-2000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-22-2200000000-2-222-2-222000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000002-22-2000000000000
χ22222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000-22-22000000000000
χ2322222222-2-2-2-22222222222-2-2-2-2-2-200000000000000000000000000002i−2i2i−2i00000000
χ2422222222-2-2-2-22222222222-2-2-2-2-2-20000000000000000000000000000−2i2i−2i2i00000000
χ2522222222-2-2-2-222-2-222-2-2-2-222-22-22000000000000000000000000000000002i−2i2i−2i0000
χ2622222222-2-2-2-222-2-222-2-2-2-222-22-2200000000000000000000000000000000−2i2i−2i2i0000
χ2722222222-2-2-2-2-2-222-2-222-2-2222-22-20000000000000000000000000000000000002i−2i2i−2i
χ2822222222-2-2-2-2-2-222-2-222-2-2222-22-2000000000000000000000000000000000000−2i2i−2i2i
χ2922222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222222222-2-2-2-200000000000000000000000000000000
χ3022222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ31222-2-2-2-2222-2-222-2-2-2-222-222-22-2-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ32222-2-2-2-2222-2-222-2-2-2-222-222-22-2-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ33222-2-2-2-2222-2-2-2-22222-2-2-222-2-222-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ34222-2-2-2-2222-2-2-2-22222-2-2-222-2-222-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ35222-2-2-2-2222-2-2-2-2-2-222222-2-22-2-2220000000000000000000000002-2-22000000000000
χ36222-2-2-2-2222-2-2-2-2-2-222222-2-22-2-222000000000000000000000000-222-2000000000000
χ37222-2-2-2-22-2-2222222-2-2-2-22-22-2-2-22200000000000000000000000000002i−2i−2i2i00000000
χ38222-2-2-2-22-2-2222222-2-2-2-22-22-2-2-2220000000000000000000000000000−2i2i2i−2i00000000
χ39222-2-2-2-22-2-22222-2-2-2-222-22-22-222-2000000000000000000000000000000002-2-220000
χ40222-2-2-2-22-2-22222-2-2-2-222-22-22-222-200000000000000000000000000000000-222-20000
χ41222-2-2-2-22-2-222-2-22222-2-2-22-222-2-220000000000000000000000000000000000002-2-22
χ42222-2-2-2-22-2-222-2-22222-2-2-22-222-2-22000000000000000000000000000000000000-222-2
χ43222-2-2-2-22-2-222-2-2-2-222222-22-222-2-222-2-2-2-22200000000000000000000000000000000
χ44222-2-2-2-22-2-222-2-2-2-222222-22-222-2-2-2-22222-2-200000000000000000000000000000000
χ4544-444-4-4-40000004i−4i004i−4i0000000000000000000000002-22i−2i2-22i−2i0000000000000000
χ4644-444-4-4-40000004i−4i004i−4i000000000000000000000000-22−2i2i-22−2i2i0000000000000000
χ4744-444-4-4-4000000−4i4i00−4i4i0000000000000000000000002-2−2i2i2-2−2i2i0000000000000000
χ4844-444-4-4-4000000−4i4i00−4i4i000000000000000000000000-222i−2i-222i−2i0000000000000000
χ4944-4-4-444-40000004i−4i00−4i4i0000000000000000000000002i−2i-22−2i2i2-20000000000000000
χ5044-4-4-444-40000004i−4i00−4i4i000000000000000000000000−2i2i2-22i−2i-220000000000000000
χ5144-4-4-444-4000000−4i4i004i−4i0000000000000000000000002i−2i2-2−2i2i-220000000000000000
χ5244-4-4-444-4000000−4i4i004i−4i000000000000000000000000−2i2i-222i−2i2-20000000000000000
χ534-444-44-4-400004i−4i004i−4i0000000000000000002-22i−2i2-22i−2i000000000000000000000000
χ544-444-44-4-400004i−4i004i−4i000000000000000000-22−2i2i-22−2i2i000000000000000000000000
χ554-444-44-4-40000−4i4i00−4i4i0000000000000000002-2−2i2i2-2−2i2i000000000000000000000000
χ564-444-44-4-40000−4i4i00−4i4i000000000000000000-222i−2i-222i−2i000000000000000000000000
χ574-44-44-44-400004i−4i00−4i4i0000000000000000002i−2i-22−2i2i2-2000000000000000000000000
χ584-44-44-44-400004i−4i00−4i4i000000000000000000−2i2i2-22i−2i-22000000000000000000000000
χ594-44-44-44-40000−4i4i004i−4i0000000000000000002i−2i2-2−2i2i-22000000000000000000000000
χ604-44-44-44-40000−4i4i004i−4i000000000000000000−2i2i-222i−2i2-2000000000000000000000000
χ614-4-44-4-4444-44-400000000000000002-22-22-22-200000000000000000000000000000000
χ624-4-44-4-4444-44-40000000000000000-22-22-22-2200000000000000000000000000000000
χ634-4-44-4-444-44-4400000000000000002-22-2-22-2200000000000000000000000000000000
χ644-4-44-4-444-44-440000000000000000-22-222-22-200000000000000000000000000000000
χ654-4-4-444-444-4-4400000000000000002-2-222-2-2200000000000000000000000000000000
χ664-4-4-444-444-4-440000000000000000-222-2-222-200000000000000000000000000000000
χ674-4-4-444-44-444-400000000000000002-2-22-222-200000000000000000000000000000000
χ684-4-4-444-44-444-40000000000000000-222-22-2-2200000000000000000000000000000000

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