Finite Group Databasebeta

← Group #148243

Character table — Group #148243

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222244444444444488888888888816161616161616161616161616161616161616161616
order12442224442222224444444444444444442444444444444444448888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911-1-11-1-111-11-1-111-1111-1-1-1iiii−i−i−i−iii−i−i1-1i−i1-111-1-1ii−i−i11-1-1i−ii−i
χ1011-1-11-1-111-11-1-111-1111-1-1-1iiii−i−i−i−iii−i−i-11i−i-1111-1-1−i−iii-1-111−ii−ii
χ1111-1-11-1-111-11-1-111-1111-1-1-1iiii−i−i−i−i−i−iii1-1−ii1-1-1-111ii−i−i-1-111−ii−ii
χ1211-1-11-1-111-11-1-111-1111-1-1-1iiii−i−i−i−i−i−iii-11−ii-11-1-111−i−iii11-1-1i−ii−i
χ1311-1-11-1-111-11-1-111-1111-1-1-1−i−i−i−iiiiiii−i−i1-1i−i1-1-1-111−i−iii-1-111i−ii−i
χ1411-1-11-1-111-11-1-111-1111-1-1-1−i−i−i−iiiiiii−i−i-11i−i-11-1-111ii−i−i11-1-1−ii−ii
χ1511-1-11-1-111-11-1-111-1111-1-1-1−i−i−i−iiiii−i−iii1-1−ii1-111-1-1−i−iii11-1-1−ii−ii
χ1611-1-11-1-111-11-1-111-1111-1-1-1−i−i−i−iiiii−i−iii-11−ii-1111-1-1ii−i−i-1-111i−ii−i
χ1722222222222-2-2-2-222-2-22-2-20000000000002200-2-20000000000000000
χ1822222222222-2-2-2-222-2-22-2-2000000000000-2-200220000000000000000
χ192222222222-22-22-2-2-22-2-22-200000000000000000000000000000022-2-2
χ202222222222-22-22-2-2-22-2-22-2000000000000000000000000000000-2-222
χ212222222222-2-22-22-2-2-22-2-2200000000222200-2-2000000000000000000
χ222222222222-2-22-22-2-2-22-2-2200000000-2-2-2-20022000000000000000000
χ2322222-2-2-2-2222-2-22-2-22-22-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ2422222-2-2-2-2222-2-22-2-22-22-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ2522222-2-2-2-222-222-2-2-2-2222-200000000000000000000002i−2i2i−2i00000000
χ2622222-2-2-2-222-222-2-2-2-2222-20000000000000000000000−2i2i−2i2i00000000
χ2722222-2-2-2-22-222-2-22222-2-2-2000000000000000000000000002i−2i2i−2i0000
χ2822222-2-2-2-22-222-2-22222-2-2-200000000000000000000000000−2i2i−2i2i0000
χ2922222-2-2-2-22-2-2-22222-2-2-2220000000000000000002-22-2000000000000
χ3022222-2-2-2-22-2-2-22222-2-2-222000000000000000000-22-22000000000000
χ3122-2-2222-2-2-222-22-22-2-22-2-2200000000000000000000002-2-2200000000
χ3222-2-2222-2-2-222-22-22-2-22-2-220000000000000000000000-222-200000000
χ3322-2-2222-2-2-22-22-222-22-2-22-222-2-2-2-22200000000000000000000000000
χ3422-2-2222-2-2-22-22-222-22-2-22-2-2-22222-2-200000000000000000000000000
χ3522-2-2222-2-2-2-22222-22-2-22-2-20000000000000000002-2-22000000000000
χ3622-2-2222-2-2-2-22222-22-2-22-2-2000000000000000000-222-2000000000000
χ3722-2-2222-2-2-2-2-2-2-2-2-2222222000000000000000000000000002i−2i−2i2i0000
χ3822-2-2222-2-2-2-2-2-2-2-2-222222200000000000000000000000000−2i2i2i−2i0000
χ3922-2-22-2-222-2222-2-2-22-2-2-2220000000000002-200-220000000000000000
χ4022-2-22-2-222-2222-2-2-22-2-2-222000000000000-22002-20000000000000000
χ4122-2-22-2-222-2-22-2-222-2-2222-2000000002i2i−2i−2i00−2i2i000000000000000000
χ4222-2-22-2-222-2-22-2-222-2-2222-200000000−2i−2i2i2i002i−2i000000000000000000
χ4322-2-22-2-222-2-2-222-22-22-22-220000000000000000000000000000002i−2i−2i2i
χ4422-2-22-2-222-2-2-222-22-22-22-22000000000000000000000000000000−2i2i2i−2i
χ454444-44-44-4-40000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ464444-44-44-4-4000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ474444-4-44-44-40000000000002-2-222-2-2200000000000000000000000000
χ484444-4-44-44-4000000000000-222-2-222-200000000000000000000000000
χ4944-4-4-44-4-4440000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5044-4-4-44-4-444000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5144-4-4-4-444-440000000000002-22-2-22-2200000000000000000000000000
χ5244-4-4-4-444-44000000000000-22-222-22-200000000000000000000000000
χ538-88i−8i000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000000000
χ548-88i−8i00000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000000000
χ558-8−8i8i000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000000000
χ568-8−8i8i00000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000000000

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