Finite Group Databasebeta

← Group #134142

Character table — Group #134142

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444444444444444444488881616161616163232323232323232
order12222222224444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ91111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11-11-11-11-1
χ101111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-11-11-11-11
χ111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111i−ii−i−ii−ii
χ121111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−ii−iii−ii−i
χ131111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-111-1-11
χ141111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-111-1-111-1
χ151111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1i−i−ii−iii−i
χ161111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1−iii−ii−i−ii
χ1722222222222222-2-2-2-2-2-2-2-2000000000000000022-2-22-2000000000000
χ1822222222222222-2-2-2-2-2-2-2-20000000000000000-2-222-22000000000000
χ192222222222-2-2-2-2-2-2-2-22222000000000000000022-2-2-22000000000000
χ202222222222-2-2-2-2-2-2-2-222220000000000000000-2-2222-2000000000000
χ212222-2-2-2-222000022-2-20000000000002222-2-2-2-22-22-200002-200000000
χ222222-2-2-2-222000022-2-20000000000002222-2-2-2-2-22-220000-2200000000
χ232222-2-2-2-222000022-2-2000000000000-2-2-2-222222-22-20000-2200000000
χ242222-2-2-2-222000022-2-2000000000000-2-2-2-22222-22-2200002-200000000
χ252222-2-2-2-2220000-2-22200002222-2-2-2-2000000002-2-22002-20000000000
χ262222-2-2-2-2220000-2-22200002222-2-2-2-200000000-222-200-220000000000
χ272222-2-2-2-2220000-2-2220000-2-2-2-22222000000002-2-2200-220000000000
χ282222-2-2-2-2220000-2-2220000-2-2-2-2222200000000-222-2002-20000000000
χ29444444-4-4-4-40000000044-4-40000000000000000000000000000000000
χ30444444-4-4-4-400000000-4-4440000000000000000000000000000000000
χ314444-4-444-4-444-4-4000000000000000000000000000000000000000000
χ324444-4-444-4-4-4-444000000000000000000000000000000000000000000
χ3344-4-4004-400004-40000000022-2-222-2-222-2-222-2-2000000000000000000
χ3444-4-4004-400004-400000000-2-222-2-222-2-222-2-222000000000000000000
χ3544-4-4004-40000-440000000022-2-222-2-2-2-222-2-222000000000000000000
χ3644-4-4004-40000-4400000000-2-222-2-22222-2-222-2-2000000000000000000
χ3744-4-400-44004-4000000000022-2-2-2-22222-2-2-2-222000000000000000000
χ3844-4-400-44004-40000000000-2-22222-2-2-2-22222-2-2000000000000000000
χ3944-4-400-4400-44000000000022-2-2-2-222-2-22222-2-2000000000000000000
χ4044-4-400-4400-440000000000-2-22222-2-222-2-2-2-222000000000000000000
χ414-44-400004-40000004-4000000004i−4i4i−4i00000000000000000000000000
χ424-44-400004-40000004-400000000−4i4i−4i4i00000000000000000000000000
χ434-44-400004-4000000-4400004i−4i4i−4i000000000000000000000000000000
χ444-44-400004-4000000-440000−4i4i−4i4i000000000000000000000000000000
χ454-44-40000-4400004-40000000000000000004i−4i4i−4i000000000000000000
χ464-44-40000-4400004-4000000000000000000−4i4i−4i4i000000000000000000
χ474-44-40000-440000-44000000000000004i−4i4i−4i0000000000000000000000
χ484-44-40000-440000-4400000000000000−4i4i−4i4i0000000000000000000000
χ494-4-444-4000000000000004-42i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000
χ504-4-444-4000000000000004-4−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000
χ514-4-444-400000000000000-442i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000
χ524-4-444-400000000000000-44−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000
χ534-4-44-440000000000004-4002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000
χ544-4-44-440000000000004-400−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000
χ554-4-44-44000000000000-44002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000
χ564-4-44-44000000000000-4400−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000

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