Finite Group Databasebeta

← Group #351021

Character table — Group #351021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444444444444444444488888888444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11-11-1
χ611111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-11-11
χ711111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-11
χ811111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-111-1
χ91111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ101111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1111-11-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222-2-222-2-22222222-2-2-2-2-2-2-2-2000000002-222-2-2000000000000000000000000
χ18222222222-2-222-2-222222-2-222-2-2-2-2-2-200000000-22-2-222000000000000000000000000
χ19222222222-2-222-2-22-2-2-2-222-2-2-2-22222000000002-2-2-222000000000000000000000000
χ20222222222-2-222-2-22-2-2-2-2-2-222-2-2222200000000-2222-2-2000000000000000000000000
χ2122222222-222-2-222-200002222-2-2000022222222-2-20000-2-20000-2-20000000000000000
χ2222222222-222-2-222-200002222-2-20000-2-2-2-2-2-2-2-2-2-20000220000220000000000000000
χ2322222222-222-2-222-20000-2-2-2-2-2-200002222-2-2-2-2220000-2-20000220000000000000000
χ2422222222-222-2-222-20000-2-2-2-2-2-20000-2-2-2-22222220000220000-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-2000022-2-222000000000000-220000002i2i−2i−2i002i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2000022-2-222000000000000-22000000−2i−2i2i2i00−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-222220000000000002-20000002i2i−2i−2i00−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-222220000000000002-2000000−2i−2i2i2i002i2i−2i−2i000000000000
χ29222-2-2-2-2222-2-2-22-2222-2-200002-222-2-200002i2i−2i−2i0000000000002i−2i2i−2i2i−2i000000000000
χ30222-2-2-2-2222-2-2-22-2222-2-200002-222-2-20000−2i−2i2i2i000000000000−2i2i−2i2i−2i2i000000000000
χ31222-2-2-2-2222-2-2-22-22-2-22200002-2-2-22200002i2i−2i−2i0000000000002i−2i−2i2i−2i2i000000000000
χ32222-2-2-2-2222-2-2-22-22-2-22200002-2-2-2220000−2i−2i2i2i000000000000−2i2i2i−2i2i−2i000000000000
χ33222-2-2-2-222-22-2-2-22222-2-20000-22-2-2222i2i−2i−2i00000000002i−2i2i−2i2i−2i000000000000000000
χ34222-2-2-2-222-22-2-2-22222-2-20000-22-2-222−2i−2i2i2i0000000000−2i2i−2i2i−2i2i000000000000000000
χ35222-2-2-2-222-22-2-2-222-2-2220000-2222-2-22i2i−2i−2i00000000002i−2i−2i2i−2i2i000000000000000000
χ36222-2-2-2-222-22-2-2-222-2-2220000-2222-2-2−2i−2i2i2i0000000000−2i2i2i−2i2i−2i000000000000000000
χ37222-2-2-2-22-22-2222-2-200000000-22000000002i2i−2i−2i002i−2i2i−2i002-2-22−2i2i0000000000000000
χ38222-2-2-2-22-22-2222-2-200000000-22000000002i2i−2i−2i00−2i2i−2i2i00-222-2−2i2i0000000000000000
χ39222-2-2-2-22-22-2222-2-200000000-2200000000−2i−2i2i2i002i−2i2i−2i00-222-22i−2i0000000000000000
χ40222-2-2-2-22-22-2222-2-200000000-2200000000−2i−2i2i2i00−2i2i−2i2i002-2-222i−2i0000000000000000
χ41222-2-2-2-22-2-2222-22-2000000002-200002i2i−2i−2i0000002i−2i−2i2i−2i2i000000-222-2000000000000
χ42222-2-2-2-22-2-2222-22-2000000002-200002i2i−2i−2i000000−2i2i2i−2i−2i2i0000002-2-22000000000000
χ43222-2-2-2-22-2-2222-22-2000000002-20000−2i−2i2i2i0000002i−2i−2i2i2i−2i0000002-2-22000000000000
χ44222-2-2-2-22-2-2222-22-2000000002-20000−2i−2i2i2i000000−2i2i2i−2i2i−2i000000-222-2000000000000
χ4522-2-2-222-20-2-20022000002-22-20000002i−2i2i−2i2i−2i2i−2i000000000000000000i2−i2i2−i22−22−20000
χ4622-2-2-222-20-2-20022000002-22-20000002i−2i2i−2i2i−2i2i−2i000000000000000000−i2i2−i2i2−22−220000
χ4722-2-2-222-20-2-20022000002-22-2000000−2i2i−2i2i−2i2i−2i2i000000000000000000i2−i2i2−i2−22−220000
χ4822-2-2-222-20-2-20022000002-22-2000000−2i2i−2i2i−2i2i−2i2i000000000000000000−i2i2−i2i22−22−20000
χ4922-2-2-222-20-2-2002200000-22-220000002i−2i2i−2i−2i2i−2i2i000000000000000000i2−i2−i2i22−2−220000
χ5022-2-2-222-20-2-2002200000-22-220000002i−2i2i−2i−2i2i−2i2i000000000000000000−i2i2i2−i2−222−20000
χ5122-2-2-222-20-2-2002200000-22-22000000−2i2i−2i2i2i−2i2i−2i000000000000000000i2−i2−i2i2−222−20000
χ5222-2-2-222-20-2-2002200000-22-22000000−2i2i−2i2i2i−2i2i−2i000000000000000000−i2i2i2−i22−2−220000
χ5344-444-4-4-404-400-440000000000000004-4-440000000000000000000000000000000000
χ5444-444-4-4-404-400-44000000000000000-444-40000000000000000000000000000000000
χ5544-444-4-4-40-44004-400000000000000000004-4-44000000000000000000000000000000
χ5644-444-4-4-40-44004-40000000000000000000-444-4000000000000000000000000000000
χ5744-4-4-444-404400-4-4000004-4-4400000000000000000000000000000000000000000000
χ5844-4-4-444-404400-4-400000-444-400000000000000000000000000000000000000000000
χ594-444-44-4-44004-400-44-44-4000000000000000000000000000000000000000000000000
χ604-444-44-4-44004-400-4-44-44000000000000000000000000000000000000000000000000
χ614-444-44-4-4-400-4400400000000004i−4i4i−4i00000000000000000000000000000000000000
χ624-444-44-4-4-400-440040000000000−4i4i−4i4i00000000000000000000000000000000000000
χ634-44-44-44-4400-4400-44-4-44000000000000000000000000000000000000000000000000
χ644-44-44-44-4400-4400-4-444-4000000000000000000000000000000000000000000000000
χ654-44-44-44-4-4004-400400000000004i−4i−4i4i00000000000000000000000000000000000000
χ664-44-44-44-4-4004-40040000000000−4i4i4i−4i00000000000000000000000000000000000000
χ678-8-88-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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