Finite Group Databasebeta

← Group #101397

Character table — Group #101397

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222224444448888888888161616161616161616161616161616161616161616161616
order12222222222244444444444488888888222224444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11-1111-11-1ii−i−iii−i−i11-1-111-1-1ii−i−ii−ii−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-11-1111-11-1ii−i−iii−i−i11-1-1-1-111ii−i−i−ii−ii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-11-1111-11-1ii−i−iii−i−i-1-11111-1-1−i−iiii−ii−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-11-1111-11-1ii−i−iii−i−i-1-111-1-111−i−iii−ii−ii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-11-1111-11-1−i−iii−i−iii11-1-111-1-1−i−iii−ii−ii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-11-1111-11-1−i−iii−i−iii11-1-1-1-111−i−iiii−ii−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-11-1111-11-1−i−iii−i−iii-1-11111-1-1ii−i−i−ii−ii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-11-1111-11-1−i−iii−i−iii-1-111-1-111ii−i−ii−ii−i11-1-1−i−iii
χ172222222222222222-2-222-2-2-2-22222-2-2-2-2000000000000000000000000
χ182222222222222222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000
χ19222222222222-2-2-2-222-2-222-2-20000000000002-22-20000000000000000
χ20222222222222-2-2-2-222-2-222-2-2000000000000-22-220000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-222000000000000000000002i−2i−2i2i00000000
χ22222222222222-2-2-2-2-2-2-2-2-2-22200000000000000000000−2i2i2i−2i00000000
χ2322222222-2-2-2-222222-2-2-22-2-220000000000002-2-220000000000000000
χ2422222222-2-2-2-222222-2-2-22-2-22000000000000-222-20000000000000000
χ2522222222-2-2-2-22222-22-2-2-222-20000000000000000000022-2-200000000
χ2622222222-2-2-2-22222-22-2-2-222-200000000000000000000-2-22200000000
χ2722222222-2-2-2-2-2-2-2-2-2222-22-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2222-22-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ292-2-222-2-2222-2-222-2-2002-2000000002i−2i2i−2i00000000000000002−22−2i2−i2i2−i2
χ302-2-222-2-2222-2-222-2-2002-2000000002i−2i2i−2i0000000000000000−22−22−i2i2−i2i2
χ312-2-222-2-2222-2-222-2-2002-200000000−2i2i−2i2i00000000000000002−22−2−i2i2−i2i2
χ322-2-222-2-2222-2-222-2-2002-200000000−2i2i−2i2i0000000000000000−22−22i2−i2i2−i2
χ332-2-222-2-22-2-222-2-222002-2000000002-2-2200000000000000002−2−222−2−22
χ342-2-222-2-22-2-222-2-222002-2000000002-2-220000000000000000−222−2−222−2
χ352-2-222-2-22-2-222-2-222002-200000000-222-200000000000000002−2−22−222−2
χ362-2-222-2-22-2-222-2-222002-200000000-222-20000000000000000−222−22−2−22
χ37444-4-4-4-4400004-44-40000000000000000000000002i−2i2i−2i000000000000
χ38444-4-4-4-4400004-44-4000000000000000000000000−2i2i−2i2i000000000000
χ39444-4-4-4-440000-44-440000000000000000000000002-2-22000000000000
χ40444-4-4-4-440000-44-44000000000000000000000000-222-2000000000000
χ4144-44-44-4-44-44-40000000000002i2−2i22i2−2i20000000000000000000000000000
χ4244-44-44-4-44-44-4000000000000−2i22i2−2i22i20000000000000000000000000000
χ4344-44-44-4-4-44-4400000000000022−22−22220000000000000000000000000000
χ4444-44-44-4-4-44-44000000000000−222222−220000000000000000000000000000
χ454-444-4-44-44-4-4400004-400-440000000000000000000000000000000000
χ464-444-4-44-44-4-440000-44004-40000000000000000000000000000000000
χ474-444-4-44-4-444-400004400-4-40000000000000000000000000000000000
χ484-444-4-44-4-444-40000-4-400440000000000000000000000000000000000
χ494-4-444-4-4444-4-4-4-44400-44000000000000000000000000000000000000
χ504-4-444-4-44-4-44444-4-400-44000000000000000000000000000000000000
χ514-4-4-4-444400004-4-4400000000000000002-22-200000000000000000000
χ524-4-4-4-444400004-4-440000000000000000-22-2200000000000000000000
χ534-4-4-4-44440000-444-400000000000000002-2-2200000000000000000000
χ544-4-4-4-44440000-444-40000000000000000-222-200000000000000000000
χ5588-8-88-88-8000000000000000000000000000000000000000000000000
χ568-88-888-8-8000000000000000000000000000000000000000000000000

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