Finite Group Databasebeta

← Group #255448

Character table — Group #255448

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444422444444444888888888888888822444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-1-1-11-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ7111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1
χ911111111111-1-1-1-111111-1-1-1-1111111-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-1
χ1011111111111-1-1-1-111111-1-1-1-1111111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-1-111-1-111
χ1111111111111-1-1-1-111111-1-1-1-1111111-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1111-1-1-1-111
χ1211111111111-1-1-1-111111-1-1-1-1111111-1-111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-11-1-11111-1-1
χ1311111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-111-1-111
χ1411111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111-111-1-111-1-1
χ1511111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11-1-11111-1-1
χ1611111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1111-1-1-1-111
χ17222222222222222-2-2-2-2222-2-22222-2-2-2-2-2-2-2220000000000000000000000000000000000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-2-2-22222-2-2-20000000000000000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-22-2-2222222-2-222-2-22-2-20000000000000000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-222-2-2-2-2-2-2-2-2222220000000000000000000000000000000000
χ2122222222-2-2-222222222-2-2-2220000-2-20000-200222200000000000000000000-2-200000000
χ2222222222-2-2-222222222-2-2-2220000-2-20000-200-2-2-2-2000000000000000000002200000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-20000220000200000000000000000000002-22-20000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-2000022000020000000000000000000000-22-220000000000
χ2522222222-2-2-2-2-2-2-22222-222-2-20000-2-2000020022-2-200000000000000000000-2200000000
χ2622222222-2-2-2-2-2-2-22222-222-2-20000-2-20000200-2-222000000000000000000002-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-200000000000000000000002-2-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-20000000000000000000000-222-20000000000
χ292222-2-2-2-22-2-222-2-2000022-2002i2i−2i−2i00000002i−2i000000000000i2i2−i2−i2i2i2−i2−i200000000002−22−2
χ302222-2-2-2-22-2-222-2-2000022-2002i2i−2i−2i00000002i−2i000000000000−i2−i2i2i2−i2−i2i2i20000000000−22−22
χ312222-2-2-2-22-2-222-2-2000022-200−2i−2i2i2i0000000−2i2i000000000000i2i2−i2−i2i2i2−i2−i20000000000−22−22
χ322222-2-2-2-22-2-222-2-2000022-200−2i−2i2i2i0000000−2i2i000000000000−i2−i2i2i2−i2−i2i2i200000000002−22−2
χ332222-2-2-2-22-2-2-2-22200002-22002i2i−2i−2i0000000−2i2i000000000000i2i2−i2−i2−i2−i2i2i200000000002−2−22
χ342222-2-2-2-22-2-2-2-22200002-22002i2i−2i−2i0000000−2i2i000000000000−i2−i2i2i2i2i2−i2−i20000000000−222−2
χ352222-2-2-2-22-2-2-2-22200002-2200−2i−2i2i2i00000002i−2i000000000000i2i2−i2−i2−i2−i2i2i20000000000−222−2
χ362222-2-2-2-22-2-2-2-22200002-2200−2i−2i2i2i00000002i−2i000000000000−i2−i2i2i2i2i2−i2−i200000000002−2−22
χ3722-2-222-2-20002i−2i2i−2i2-22-20002i−2i00000000000002i−2i2-2i2i2−i2−i222−2−22−22−2i2−i2i2−i200000000000000
χ3822-2-222-2-20002i−2i2i−2i2-22-20002i−2i00000000000002i−2i2-2−i2−i2i2i2−2−222−22−22−i2i2−i2i200000000000000
χ3922-2-222-2-20002i−2i2i−2i2-22-20002i−2i0000000000000−2i2i-22i2i2−i2−i222−2−2−22−22−i2i2−i2i200000000000000
χ4022-2-222-2-20002i−2i2i−2i2-22-20002i−2i0000000000000−2i2i-22−i2−i2i2i2−2−2222−22−2i2−i2i2−i200000000000000
χ4122-2-222-2-2000−2i2i−2i2i2-22-2000−2i2i00000000000002i−2i-22i2i2−i2−i2−2−2222−22−2−i2i2−i2i200000000000000
χ4222-2-222-2-2000−2i2i−2i2i2-22-2000−2i2i00000000000002i−2i-22−i2−i2i2i222−2−2−22−22i2−i2i2−i200000000000000
χ4322-2-222-2-2000−2i2i−2i2i2-22-2000−2i2i0000000000000−2i2i2-2i2i2−i2−i2−2−222−22−22i2−i2i2−i200000000000000
χ4422-2-222-2-2000−2i2i−2i2i2-22-2000−2i2i0000000000000−2i2i2-2−i2−i2i2i222−2−22−22−2−i2i2−i2i200000000000000
χ452-22-22-22-222-200002-2-22-200002-22-22-2002-2000000000002i−2i2i−2i00000000000000002i−2i0000
χ462-22-22-22-222-200002-2-22-200002-22-22-2002-200000000000−2i2i−2i2i0000000000000000−2i2i0000
χ472-22-22-22-222-200002-2-22-20000-22-222-200-22000000000002i−2i2i−2i0000000000000000−2i2i0000
χ482-22-22-22-222-200002-2-22-20000-22-222-200-2200000000000−2i2i−2i2i00000000000000002i−2i0000
χ492-22-22-22-222-20000-222-2-200002-22-2-2200-2200000002i−2i2i−2i0000000000000000002i−2i000000
χ502-22-22-22-222-20000-222-2-200002-22-2-2200-220000000−2i2i−2i2i000000000000000000−2i2i000000
χ512-22-22-22-222-20000-222-2-20000-22-22-22002-200000002i−2i2i−2i000000000000000000−2i2i000000
χ522-22-22-22-222-20000-222-2-20000-22-22-22002-20000000−2i2i−2i2i0000000000000000002i−2i000000
χ534444-4-4-4-4-44444-4-40000-4-440000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-444-4-4440000-44-40000000000000000000000000000000000000000000000000
χ5544-4-444-4-40004i−4i4i−4i-44-44000−4i4i00000000000000000000000000000000000000000000000
χ5644-4-444-4-4000−4i4i−4i4i-44-440004i−4i00000000000000000000000000000000000000000000000
χ5744-4-4-4-4440004i−4i−4i4i00000000000000000000000000000000002i−2i−2i2i-222-200000000000000
χ5844-4-4-4-4440004i−4i−4i4i0000000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ5944-4-4-4-444000−4i4i4i−4i00000000000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ6044-4-4-4-444000−4i4i4i−4i0000000000000000000000000000000000−2i2i2i−2i-222-200000000000000
χ614-44-44-44-4-4-4400004-4-44400000000-4400000000000000000000000000000000000000000
χ624-44-44-44-4-4-440000-444-44000000004-400000000000000000000000000000000000000000
χ634-44-4-44-444-4400000000-400004i−4i−4i4i0000000000000000000000000000000000000000000
χ644-44-4-44-444-4400000000-40000−4i4i4i−4i0000000000000000000000000000000000000000000
χ654-44-4-44-44-44-400000000400000000004-4000000000000000000000000000000000000000
χ664-44-4-44-44-44-40000000040000000000-44000000000000000000000000000000000000000
χ674-4-444-4-44000000044-4-4000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ684-4-444-4-44000000044-4-400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ694-4-444-4-440000000-4-444000000000000000000000022−22−222200000000000000000000000000
χ704-4-444-4-440000000-4-4440000000000000000000000−222222−2200000000000000000000000000
χ718-8-88-888-8000000000000000000000000000000000000000000000000000000000000000

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