Finite Group Databasebeta

← Group #352513

Character table — Group #352513

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
χ511111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111111111111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ121111111111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-111-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111-1-1111-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222-2-22-2-2222-2-22222-2-2-2-2-2-20000000022-2-22-2000000000000000000000000
χ182222222222-2-22-2-2222-2-2-2-2-2-22222-2-200000000-2-2222-2000000000000000000000000
χ192222222222-2-22-2-22-2-2-2-22222-2-2-2-22200000000-2-222-22000000000000000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-2-2-22222220000000022-2-2-22000000000000000000000000
χ2122222222-2-222-222-222-2-20000000022222222220000-2-2-2-2-2-200000000000000000000
χ2222222222-2-222-222-222-2-20000000022-2-2-2-2-2-2-2-20000-2-2222200000000000000000000
χ2322222222-2-222-222-2-2-2-2-200000000-2-22222-2-2-2-2000022-2-22200000000000000000000
χ2422222222-2-222-222-2-2-2-2-200000000-2-2-2-2-2-2222200002222-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222200000000-2-2000000000000-2200002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2222200000000-2-2000000000000-220000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22200000000220000000000002-200002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22200000000220000000000002-20000−2i−2i2i2i2i2i−2i−2i000000000000
χ29222-2-2-2-2200-2-202202-200000000002-22i2i−2i−2i2i2i−2i−2i0000000000000000002−22−2i2−i2i2−i20000
χ30222-2-2-2-2200-2-202202-200000000002-22i2i−2i−2i2i2i−2i−2i000000000000000000−22−22−i2i2−i2i20000
χ31222-2-2-2-2200-2-202202-200000000002-2−2i−2i2i2i−2i−2i2i2i0000000000000000002−22−2−i2i2−i2i20000
χ32222-2-2-2-2200-2-202202-200000000002-2−2i−2i2i2i−2i−2i2i2i000000000000000000−22−22i2−i2i2−i20000
χ33222-2-2-2-2200-2-20220-220000000000-222i2i−2i−2i−2i−2i2i2i0000000000000000002−2−22i2−i2−i2i20000
χ34222-2-2-2-2200-2-20220-220000000000-222i2i−2i−2i−2i−2i2i2i000000000000000000−222−2−i2i2i2−i20000
χ35222-2-2-2-2200-2-20220-220000000000-22−2i−2i2i2i2i2i−2i−2i0000000000000000002−2−22−i2i2i2−i20000
χ36222-2-2-2-2200-2-20220-220000000000-22−2i−2i2i2i2i2i−2i−2i000000000000000000−222−2i2−i2−i2i20000
χ3722-222-2-2-2222-2-22-2-2002-2000000000000002-22-22-22-200002-22-22-20000000000000000
χ3822-222-2-2-2222-2-22-2-2002-2000000000000002-22-2-22-2200002-2-22-220000000000000000
χ3922-222-2-2-2222-2-22-2-2002-200000000000000-22-222-22-20000-22-22-220000000000000000
χ4022-222-2-2-2222-2-22-2-2002-200000000000000-22-22-22-220000-222-22-20000000000000000
χ4122-222-2-2-222-22-2-22-200-2200000000002-22-200002-2-22002-20000002-22-2000000000000
χ4222-222-2-2-222-22-2-22-200-2200000000002-22-20000-222-2002-2000000-22-22000000000000
χ4322-222-2-2-222-22-2-22-200-220000000000-22-2200002-2-2200-22000000-22-22000000000000
χ4422-222-2-2-222-22-2-22-200-220000000000-22-220000-222-200-220000002-22-2000000000000
χ4522-222-2-2-2-2-22-222-2200-222i2i−2i−2i2i2i−2i−2i0000002-22-200000000-2200002i−2i−2i2i000000000000
χ4622-222-2-2-2-2-22-222-2200-222i2i−2i−2i2i2i−2i−2i000000-22-22000000002-20000−2i2i2i−2i000000000000
χ4722-222-2-2-2-2-22-222-2200-22−2i−2i2i2i−2i−2i2i2i0000002-22-200000000-220000−2i2i2i−2i000000000000
χ4822-222-2-2-2-2-22-222-2200-22−2i−2i2i2i−2i−2i2i2i000000-22-22000000002-200002i−2i−2i2i000000000000
χ4922-222-2-2-2-2-2-222-222002-22i2i−2i−2i−2i−2i2i2i002-22-20000000000-2200−2i2i2i−2i0000000000000000
χ5022-222-2-2-2-2-2-222-222002-22i2i−2i−2i−2i−2i2i2i00-22-2200000000002-2002i−2i−2i2i0000000000000000
χ5122-222-2-2-2-2-2-222-222002-2−2i−2i2i2i2i2i−2i−2i002-22-20000000000-22002i−2i−2i2i0000000000000000
χ5222-222-2-2-2-2-2-222-222002-2−2i−2i2i2i2i2i−2i−2i00-22-2200000000002-200−2i2i2i−2i0000000000000000
χ53444-4-4-4-4400440-4-404-40000000000-4400000000000000000000000000000000000000
χ54444-4-4-4-4400440-4-40-4400000000004-400000000000000000000000000000000000000
χ5544-4-4-444-4004-40-440000000000000004i−4i−4i4i0000000000000000000000000000000000
χ5644-4-4-444-4004-40-44000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ5744-4-4-444-400-4404-400000000000000000004i−4i−4i4i000000000000000000000000000000
χ5844-4-4-444-400-4404-40000000000000000000−4i4i4i−4i000000000000000000000000000000
χ594-444-44-4-44-400400-4000000004-44-40000000000000000000000000000000000000000
χ604-444-44-4-44-400400-400000000-44-440000000000000000000000000000000000000000
χ614-444-44-4-4-4400-400400004i−4i4i−4i00000000000000000000000000000000000000000000
χ624-444-44-4-4-4400-40040000−4i4i−4i4i00000000000000000000000000000000000000000000
χ634-4-44-4-4444-400-400400004-4-4400000000000000000000000000000000000000000000
χ644-4-44-4-4444-400-40040000-444-400000000000000000000000000000000000000000000
χ654-4-44-4-444-4400400-4000000004i−4i−4i4i0000000000000000000000000000000000000000
χ664-4-44-4-444-4400400-400000000−4i4i4i−4i0000000000000000000000000000000000000000
χ678-88-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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