Finite Group Databasebeta

← Group #500581

Character table — Group #500581

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order1222224444444444444488882488888822224444444444441616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ911111111-1-1-1-111-1-111111111-1-1-1-111-1-11-1111-11-11-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-111111111-1-1-1-111-1-11-1-1-11-11-11-111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-111111111-1-1-1-111-1-1-1111-11-11-11-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-111-1-111111111-1-1-1-111-1-1-11-1-1-11-11-1111-1-11111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111-1111-1-11-11-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111-1-1-11-1-11-111111-1-1-1-11111-1-1
χ1511111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1111-111-11-1-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-11-1-1-111-11-11111-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ1922222222-2-2-2-222-2-22222-2-2-2-2-2-222-2-222000000000000000000000000
χ2022222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000
χ21222222-2-22222-2-2-2-222-2-20000-2200000000000000000000002−22−22−22−2
χ22222222-2-22222-2-2-2-222-2-20000-220000000000000000000000−22−22−22−22
χ23222222-2-22222-2-2-2-2-2-22200002-200000000000000000000002−22−2−22−22
χ24222222-2-22222-2-2-2-2-2-22200002-20000000000000000000000−22−222−22−2
χ25222222-2-2-2-2-2-2-2-22222-2-200002-200000000000000000000002−2−222−2−22
χ26222222-2-2-2-2-2-2-2-22222-2-200002-20000000000000000000000−222−2−222−2
χ27222222-2-2-2-2-2-2-2-222-2-2220000-2200000000000000000000002−2−22−222−2
χ28222222-2-2-2-2-2-2-2-222-2-2220000-220000000000000000000000−222−22−2−22
χ292222-2-2-2-222-2-2222-200002-22-2002-2000000000022-2-200000000000000
χ302222-2-2-2-222-2-2222-200002-22-2002-20000000000-2-22200000000000000
χ312222-2-2-2-222-2-2222-20000-22-2200-2200002200-2-2000000000000000000
χ322222-2-2-2-222-2-2222-20000-22-2200-220000-2-20022000000000000000000
χ332222-2-2-2-2-2-22222-2200002-22-200-2200000000002-2-2200000000000000
χ342222-2-2-2-2-2-22222-2200002-22-200-220000000000-222-200000000000000
χ352222-2-2-2-2-2-22222-220000-22-22002-200002-200-22000000000000000000
χ362222-2-2-2-2-2-22222-220000-22-22002-20000-22002-2000000000000000000
χ3722-2-22-22-200002-2002i−2i2i−2i2-2-2200002i−2i00002-2000000002i−2i0000000000
χ3822-2-22-22-200002-2002i−2i2i−2i2-2-2200002i−2i0000-2200000000−2i2i0000000000
χ3922-2-22-22-200002-2002i−2i2i−2i-222-20000−2i2i0000000000002i−2i002-200000000
χ4022-2-22-22-200002-2002i−2i2i−2i-222-20000−2i2i000000000000−2i2i00-2200000000
χ4122-2-22-22-200002-200−2i2i−2i2i2-2-220000−2i2i00002-200000000−2i2i0000000000
χ4222-2-22-22-200002-200−2i2i−2i2i2-2-220000−2i2i0000-22000000002i−2i0000000000
χ4322-2-22-22-200002-200−2i2i−2i2i-222-200002i−2i0000000000002i−2i00-2200000000
χ4422-2-22-22-200002-200−2i2i−2i2i-222-200002i−2i000000000000−2i2i002-200000000
χ454444-4-44444-4-4-4-4-440000000000000000000000000000000000000000
χ464444-4-444-4-444-4-44-40000000000000000000000000000000000000000
χ4744-4-44-4-440000-44004i−4i−4i4i000000000000000000000000000000000000
χ4844-4-44-4-440000-4400−4i4i4i−4i000000000000000000000000000000000000
χ4944-4-4-444-40000-4400000000000000004i−4i000000000000000000000000
χ5044-4-4-444-40000-440000000000000000−4i4i000000000000000000000000
χ5144-4-4-44-4400004-400000044-4-400000000000000000000000000000000
χ5244-4-4-44-4400004-4000000-4-44400000000000000000000000000000000
χ538-88-80000008i−8i00000000000000000000000000000000000000000000
χ548-88-8000000−8i8i00000000000000000000000000000000000000000000
χ558-8-8800008-80000000000000000000000000000000000000000000000
χ568-8-880000-880000000000000000000000000000000000000000000000

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