Finite Group Databasebeta

← Group #257467

Character table — Group #257467

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444444444444444888888888888888824444444448888
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
χ3111111111111111111111111111111-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111111-1-1-1-1-1-11111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111
χ7111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-11111-1-1-1-1
χ911111111111-1-1-1-111111-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-111-1-111-1-1
χ1011111111111-1-1-1-111111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-111-1-111
χ1111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-111
χ1211111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1111-1-11111-1-1
χ1311111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1-111-1-1-111-1-111
χ1411111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-111-111-1-111-1-1
χ1511111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-111-1-11-1-11111-1-1
χ1611111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-111-1-1111-1-1-1-111
χ17222222222222222-2-2-2-2222-2-22222-2-200-222-2-2-2-200000000000000000000000000000000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-2-2-200-2-2-2222200000000000000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-22-2-2222222-2-2002-2-2-2-22200000000000000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-222-2-2-2-2-2-20022222-2-200000000000000000000000000000000
χ2122222222-2-2-222222222-2-2-2220000-2-222-2000000220000000000000000-20000-200000000
χ2222222222-2-2-222222222-2-2-2220000-2-2-2-2-2000000-2-2000000000000000020000200000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-200002200200000000000000000000000002-22-2000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-20000220020000000000000000000000000-22-22000000000
χ2522222222-2-2-2-2-2-2-22222-222-2-20000-2-2222000000-2-20000000000000000-20000200000000
χ2622222222-2-2-2-2-2-2-22222-222-2-20000-2-2-2-2200000022000000000000000020000-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-200000000000000000000000002-2-22000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-20000000000000000000000000-222-2000000000
χ2922-222-2-2-22-2-200002-22-2200002i2i−2i−2i2-2000002i−2i0000000022-2-200000000000000002i−2i0000
χ3022-222-2-2-22-2-200002-22-2200002i2i−2i−2i2-2000002i−2i00000000-2-2220000000000000000−2i2i0000
χ3122-222-2-2-22-2-200002-22-220000−2i−2i2i2i2-200000−2i2i0000000022-2-20000000000000000−2i2i0000
χ3222-222-2-2-22-2-200002-22-220000−2i−2i2i2i2-200000−2i2i00000000-2-22200000000000000002i−2i0000
χ3322-222-2-2-22-2-20000-22-22200002i2i−2i−2i-2200000−2i2i000022-2-20000000000000000002i−2i000000
χ3422-222-2-2-22-2-20000-22-22200002i2i−2i−2i-2200000−2i2i0000-2-222000000000000000000−2i2i000000
χ3522-222-2-2-22-2-20000-22-2220000−2i−2i2i2i-22000002i−2i000022-2-2000000000000000000−2i2i000000
χ3622-222-2-2-22-2-20000-22-2220000−2i−2i2i2i-22000002i−2i0000-2-2220000000000000000002i−2i000000
χ372-22-22-22-20002i2i−2i−2i2-2-220002i−2i0000002i−2i00000002-22−22−2i2−i2i2−i2i2i2−i2−i222−2−200000000000000
χ382-22-22-22-20002i2i−2i−2i2-2-220002i−2i0000002i−2i00000002-2−22−22−i2i2−i2i2−i2−i2i2i2−2−22200000000000000
χ392-22-22-22-20002i2i−2i−2i2-2-220002i−2i000000−2i2i0000000-222−22−2i2−i2i2−i2−i2−i2i2i2−2−22200000000000000
χ402-22-22-22-20002i2i−2i−2i2-2-220002i−2i000000−2i2i0000000-22−22−22−i2i2−i2i2i2i2−i2−i222−2−200000000000000
χ412-22-22-22-2000−2i−2i2i2i2-2-22000−2i2i0000002i−2i0000000-222−22−2−i2i2−i2i2i2i2−i2−i2−2−22200000000000000
χ422-22-22-22-2000−2i−2i2i2i2-2-22000−2i2i0000002i−2i0000000-22−22−22i2−i2i2−i2−i2−i2i2i222−2−200000000000000
χ432-22-22-22-2000−2i−2i2i2i2-2-22000−2i2i000000−2i2i00000002-22−22−2−i2i2−i2i2−i2−i2i2i222−2−200000000000000
χ442-22-22-22-2000−2i−2i2i2i2-2-22000−2i2i000000−2i2i00000002-2−22−22i2−i2i2−i2i2i2−i2−i2−2−22200000000000000
χ452-2-22-2-22222-22-22-20000-22-2002i−2i2i−2i000002i−2i00000000000000i2−i2i2−i2i2−i2i2−i200000000002−22−2
χ462-2-22-2-22222-22-22-20000-22-2002i−2i2i−2i000002i−2i00000000000000−i2i2−i2i2−i2i2−i2i20000000000−22−22
χ472-2-22-2-22222-22-22-20000-22-200−2i2i−2i2i00000−2i2i00000000000000i2−i2i2−i2i2−i2i2−i20000000000−22−22
χ482-2-22-2-22222-22-22-20000-22-200−2i2i−2i2i00000−2i2i00000000000000−i2i2−i2i2−i2i2−i2i200000000002−22−2
χ492-2-22-2-22222-2-22-220000-2-22002i−2i2i−2i00000−2i2i00000000000000i2−i2i2−i2−i2i2−i2i200000000002−2−22
χ502-2-22-2-22222-2-22-220000-2-22002i−2i2i−2i00000−2i2i00000000000000−i2i2−i2i2i2−i2i2−i20000000000−222−2
χ512-2-22-2-22222-2-22-220000-2-2200−2i2i−2i2i000002i−2i00000000000000i2−i2i2−i2−i2i2−i2i20000000000−222−2
χ522-2-22-2-22222-2-22-220000-2-2200−2i2i−2i2i000002i−2i00000000000000−i2i2−i2i2i2−i2i2−i200000000002−2−22
χ5344-444-4-4-4-44400004-44-4-400000000-4400000000000000000000000000000000000000000
χ5444-444-4-4-4-4440000-44-44-4000000004-400000000000000000000000000000000000000000
χ5544-4-4-444-40004i−4i−4i4i00000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ5644-4-4-444-40004i−4i−4i4i0000000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ5744-4-4-444-4000−4i4i4i−4i00000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ5844-4-4-444-4000−4i4i4i−4i0000000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ594-444-44-4-44-4400000000-400004-4-440000000000000000000000000000000000000000000
χ604-444-44-4-44-4400000000-40000-444-40000000000000000000000000000000000000000000
χ614-444-44-4-4-44-4000000004000000000000000004i−4i00000000000000000000000000000000
χ624-444-44-4-4-44-400000000400000000000000000−4i4i00000000000000000000000000000000
χ634-44-44-44-40004i4i−4i−4i-444-4000−4i4i00000000000000000000000000000000000000000000000
χ644-44-44-44-4000−4i−4i4i4i-444-40004i−4i00000000000000000000000000000000000000000000000
χ654-4-44-4-444-4-444-44-400004-440000000000000000000000000000000000000000000000000
χ664-4-44-4-444-4-44-44-44000044-40000000000000000000000000000000000000000000000000
χ674-4-4-444-44000000044-4-4000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ684-4-4-444-44000000044-4-400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ694-4-4-444-440000000-4-444000000000000000000000022−22−222200000000000000000000000000
χ704-4-4-444-440000000-4-4440000000000000000000000−222222−2200000000000000000000000000
χ71888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000

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