Finite Group Databasebeta

← Group #134158

Character table — Group #134158

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444444444444444444488881616161616163232323232323232
order12222244442222224444444444444444444444444424444488888888
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
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i
χ9111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11-11-11-1
χ10111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-11-11-11
χ11111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ12111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ13111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-111-1-11
χ14111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-111-1-111-1
χ15111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1i−i−ii−iii−i
χ16111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1−iii−ii−i−ii
χ172222222222-2-20000-2-20000000000002222-2-2-2-222-2-200002-200000000
χ182222222222-2-20000-2-20000000000002222-2-2-2-2-2-2220000-2200000000
χ192222222222-2-20000-2-2000000000000-2-2-2-2222222-2-20000-2200000000
χ202222222222-2-20000-2-2000000000000-2-2-2-22222-2-22200002-200000000
χ21222222-2-2-2-2222222-2-2-2-2-2-200000000000000002-22-2002-20000000000
χ22222222-2-2-2-2222222-2-2-2-2-2-20000000000000000-22-2200-220000000000
χ23222222-2-2-2-222-2-2-2-2-2-2222200000000000000002-22-200-220000000000
χ24222222-2-2-2-222-2-2-2-2-2-222220000000000000000-22-22002-20000000000
χ25222222-2-2-2-2-2-200002200002222-2-2-2-2000000002-2-222-2000000000000
χ26222222-2-2-2-2-2-200002200002222-2-2-2-200000000-222-2-22000000000000
χ27222222-2-2-2-2-2-20000220000-2-2-2-22222000000002-2-22-22000000000000
χ28222222-2-2-2-2-2-20000220000-2-2-2-2222200000000-222-22-2000000000000
χ294444-4-444-4-40000000000000000000000004i4i−4i−4i000000000000000000
χ304444-4-444-4-4000000000000000000000000−4i−4i4i4i000000000000000000
χ314444-4-4-4-444000000000000000000004i4i−4i−4i0000000000000000000000
χ324444-4-4-4-44400000000000000000000−4i−4i4i4i0000000000000000000000
χ3344-4-400004i−4i0022-2-2002i2i−2i−2i22-2-22i2i−2i−2i00002+2i−2−2i2−2i−2+2i000000000000000000
χ3444-4-400004i−4i0022-2-2002i2i−2i−2i-2-222−2i−2i2i2i0000−2−2i2+2i−2+2i2−2i000000000000000000
χ3544-4-400004i−4i00-2-22200−2i−2i2i2i22-2-22i2i−2i−2i0000−2−2i2+2i−2+2i2−2i000000000000000000
χ3644-4-400004i−4i00-2-22200−2i−2i2i2i-2-222−2i−2i2i2i00002+2i−2−2i2−2i−2+2i000000000000000000
χ3744-4-40000−4i4i0022-2-200−2i−2i2i2i22-2-2−2i−2i2i2i00002−2i−2+2i2+2i−2−2i000000000000000000
χ3844-4-40000−4i4i0022-2-200−2i−2i2i2i-2-2222i2i−2i−2i0000−2+2i2−2i−2−2i2+2i000000000000000000
χ3944-4-40000−4i4i00-2-222002i2i−2i−2i22-2-2−2i−2i2i2i0000−2+2i2−2i−2−2i2+2i000000000000000000
χ4044-4-40000−4i4i00-2-222002i2i−2i−2i-2-2222i2i−2i−2i00002−2i−2+2i2+2i−2−2i000000000000000000
χ414-44-4004i−4i00002-22-2002i−2i2i−2i2i−2i2i−2i2-22-22+2i−2−2i2−2i−2+2i0000000000000000000000
χ424-44-4004i−4i00002-22-2002i−2i2i−2i−2i2i−2i2i-22-22−2−2i2+2i−2+2i2−2i0000000000000000000000
χ434-44-4004i−4i0000-22-2200−2i2i−2i2i2i−2i2i−2i2-22-2−2−2i2+2i−2+2i2−2i0000000000000000000000
χ444-44-4004i−4i0000-22-2200−2i2i−2i2i−2i2i−2i2i-22-222+2i−2−2i2−2i−2+2i0000000000000000000000
χ454-44-400−4i4i00002-22-200−2i2i−2i2i2i−2i2i−2i-22-22−2+2i2−2i−2−2i2+2i0000000000000000000000
χ464-44-400−4i4i00002-22-200−2i2i−2i2i−2i2i−2i2i2-22-22−2i−2+2i2+2i−2−2i0000000000000000000000
χ474-44-400−4i4i0000-22-22002i−2i2i−2i2i−2i2i−2i-22-222−2i−2+2i2+2i−2−2i0000000000000000000000
χ484-44-400−4i4i0000-22-22002i−2i2i−2i−2i2i−2i2i2-22-2−2+2i2−2i−2−2i2+2i0000000000000000000000
χ494-4-444-400000000004-4000000004i−4i−4i4i00000000000000000000000000
χ504-4-444-400000000004-400000000−4i4i4i−4i00000000000000000000000000
χ514-4-444-40000000000-4400004i−4i−4i4i000000000000000000000000000000
χ524-4-444-40000000000-440000−4i4i4i−4i000000000000000000000000000000
χ534-4-44-4400004-40000004-4-440000000000000000000000000000000000
χ544-4-44-4400004-4000000-444-40000000000000000000000000000000000
χ554-4-44-440000-444-4-440000000000000000000000000000000000000000
χ564-4-44-440000-44-444-40000000000000000000000000000000000000000

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