Finite Group Databasebeta

← Group #148477

Character table — Group #148477

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222244444444444488888888888816161616161616161616161616161616161616161616
order12442224442222224444444444888888882444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ911-1-11-1-11-11111-1-1-111-1-1-11ii−i−i1111-1-1-1-11-1i−i1-1ii−i−iii−i−ii−ii−i11-1-1
χ1011-1-11-1-11-11111-1-1-111-1-1-11ii−i−i1111-1-1-1-1-11i−i-11ii−i−i−i−iii−ii−ii-1-111
χ1111-1-11-1-11-11111-1-1-111-1-1-11ii−i−i-1-1-1-111111-1i−i1-1−i−iii−i−iiii−ii−i-1-111
χ1211-1-11-1-11-11111-1-1-111-1-1-11ii−i−i-1-1-1-11111-11i−i-11−i−iiiii−i−i−ii−ii11-1-1
χ1311-1-11-1-11-11111-1-1-111-1-1-11−i−iii1111-1-1-1-11-1−ii1-1−i−iii−i−iii−ii−ii11-1-1
χ1411-1-11-1-11-11111-1-1-111-1-1-11−i−iii1111-1-1-1-1-11−ii-11−i−iiiii−i−ii−ii−i-1-111
χ1511-1-11-1-11-11111-1-1-111-1-1-11−i−iii-1-1-1-111111-1−ii1-1ii−i−iii−i−i−ii−ii-1-111
χ1611-1-11-1-11-11111-1-1-111-1-1-11−i−iii-1-1-1-11111-11−ii-11ii−i−i−i−iiii−ii−i11-1-1
χ1722222222222-2-22-2-2-2-22-2-220000000000002200-2-20000000000000000
χ1822222222222-2-22-2-2-2-22-2-22000000000000-2-200220000000000000000
χ192222222222-22-2-22-22-2-22-2-20000000000000000000000000022-2-20000
χ202222222222-22-2-22-22-2-22-2-200000000000000000000000000-2-2220000
χ212222222222-2-22-2-22-22-2-22-222220000000000-2-2000000000000000000
χ222222222222-2-22-2-22-22-2-22-2-2-2-2-2000000000022000000000000000000
χ2322222-2-2-22-222-2-2-22-2222-2-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ2422222-2-2-22-222-2-2-22-2222-2-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ2522222-2-2-22-22-22-22-22-22-22-20000000000000000000000000000002i−2i2i−2i
χ2622222-2-2-22-22-22-22-22-22-22-2000000000000000000000000000000−2i2i−2i2i
χ2722222-2-2-22-2-2222-2-2-2-2-222200000000000000000000002i−2i2i−2i00000000
χ2822222-2-2-22-2-2222-2-2-2-2-22220000000000000000000000−2i2i−2i2i00000000
χ2922222-2-2-22-2-2-2-222222-2-2-220000000000000000002-22-2000000000000
χ3022222-2-2-22-2-2-2-222222-2-2-22000000000000000000-22-22000000000000
χ3122-2-2222-2-2-222-222-2-22-2-22-200002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ3222-2-2222-2-2-222-222-2-22-2-22-20000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ3322-2-2222-2-2-22-222-222-2-22-2-20000000000000000000000000000002i−2i−2i2i
χ3422-2-2222-2-2-22-222-222-2-22-2-2000000000000000000000000000000−2i2i2i−2i
χ3522-2-2222-2-2-2-222-222-2-22-2-2200000000000000000000002-2-2200000000
χ3622-2-2222-2-2-2-222-222-2-22-2-220000000000000000000000-222-200000000
χ3722-2-2222-2-2-2-2-2-2-2-2-22222220000000000000000002i−2i−2i2i000000000000
χ3822-2-2222-2-2-2-2-2-2-2-2-2222222000000000000000000−2i2i2i−2i000000000000
χ3922-2-22-2-22-222-2-2-222-2-2-22220000000000002-200-220000000000000000
χ4022-2-22-2-22-222-2-2-222-2-2-2222000000000000-22002-20000000000000000
χ4122-2-22-2-22-22-22-22-222-22-22-2000000000000000000000000002i−2i−2i2i0000
χ4222-2-22-2-22-22-22-22-222-22-22-200000000000000000000000000−2i2i2i−2i0000
χ4322-2-22-2-22-22-2-2222-2-2222-2-22i2i−2i−2i0000000000−2i2i000000000000000000
χ4422-2-22-2-22-22-2-2222-2-2222-2-2−2i−2i2i2i00000000002i−2i000000000000000000
χ454444-44-44-4-400000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ464444-44-44-4-40000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ474444-4-44-4-4400000000000000002-2-222-2-220000000000000000000000
χ484444-4-44-4-440000000000000000-222-2-222-20000000000000000000000
χ4944-4-4-44-4-44400000000000000002-2-22-222-20000000000000000000000
χ5044-4-4-44-4-4440000000000000000-222-22-2-220000000000000000000000
χ5144-4-4-4-4444-400000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ5244-4-4-4-4444-40000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ538-88i−8i0000000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000000000
χ548-88i−8i000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000000000
χ558-8−8i8i0000000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000000000
χ568-8−8i8i000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000000000

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