Finite Group Databasebeta

← Group #137331

Character table — Group #137331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1
χ911-1-1-1-1111-11-111-1-1iiii−i−i−i−iii−i−i-1111-1-111-1-1ii−i−i1-11-11-1i−iii−i−iii−i−i11-1-1
χ1011-1-1-1-1111-11-111-1-1iiii−i−i−i−iii−i−i-1111-1-111-1-1ii−i−i1-1-11-11i−i−i−iii−i−iii-1-111
χ1111-1-1-1-1111-11-111-1-1iiii−i−i−i−i−i−iii-11-1-111-1-111−i−iii1-11-11-1i−iii−i−i−i−iii-1-111
χ1211-1-1-1-1111-11-111-1-1iiii−i−i−i−i−i−iii-11-1-111-1-111−i−iii1-1-11-11i−i−i−iiiii−i−i11-1-1
χ1311-1-1-1-1111-11-111-1-1−i−i−i−iiiiiii−i−i-11-1-111-1-111ii−i−i1-11-11-1−ii−i−iiiii−i−i-1-111
χ1411-1-1-1-1111-11-111-1-1−i−i−i−iiiiiii−i−i-11-1-111-1-111ii−i−i1-1-11-11−iiii−i−i−i−iii11-1-1
χ1511-1-1-1-1111-11-111-1-1−i−i−i−iiiii−i−iii-1111-1-111-1-1−i−iii1-11-11-1−ii−i−iii−i−iii11-1-1
χ1611-1-1-1-1111-11-111-1-1−i−i−i−iiiii−i−iii-1111-1-111-1-1−i−iii1-1-11-11−iiii−i−iii−i−i-1-111
χ172222222222222222222222220000-2-2000000000000-2-20000-2-2000000000000
χ182222222222222222-2-2-2-2-2-2-2-20000-2-2000000000000-2-2000022000000000000
χ19222222222222-2-2-2-20000000000002-22222-2-2-2-200002-2000000000000000000
χ20222222222222-2-2-2-20000000000002-2-2-2-2-2222200002-2000000000000000000
χ21222222222222-2-2-2-2000000002222-2200000000-2-2-2-2-22000000000000000000
χ22222222222222-2-2-2-200000000-2-2-2-2-22000000002222-22000000000000000000
χ23222-22-2-2-222-2-22-22-222-2-222-2-20000000000000000000000000000002−22−22−22−2
χ24222-22-2-2-222-2-22-22-222-2-222-2-2000000000000000000000000000000−22−22−22−22
χ25222-22-2-2-222-2-22-22-2-2-222-2-2220000000000000000000000000000002−22−2−22−22
χ26222-22-2-2-222-2-22-22-2-2-222-2-222000000000000000000000000000000−22−222−22−2
χ2722-22-22-2-22-2-222-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000i2−i2−i2i22−2−22
χ2822-22-22-2-22-2-222-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000−i2i2i2−i2−222−2
χ2922-22-22-2-22-2-222-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000i2−i2−i2i2−222−2
χ3022-22-22-2-22-2-222-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000−i2i2i2−i22−2−22
χ3122-2-2-2-2222-22-222-2-22i2i2i2i−2i−2i−2i−2i00002-2000000000000-220000−2i2i000000000000
χ3222-2-2-2-2222-22-222-2-2−2i−2i−2i−2i2i2i2i2i00002-2000000000000-2200002i−2i000000000000
χ3322-2-2-2-2222-22-2-2-222000000000000-2-222-2-2-2-222000022000000000000000000
χ3422-2-2-2-2222-22-2-2-222000000000000-2-2-2-22222-2-2000022000000000000000000
χ3522-2-2-2-2222-22-2-2-222000000002i2i−2i−2i2200000000−2i−2i2i2i-2-2000000000000000000
χ3622-2-2-2-2222-22-2-2-22200000000−2i−2i2i2i22000000002i2i−2i−2i-2-2000000000000000000
χ3744444444-4-4-4-40000000000000000000000000000000022-2-200000000000000
χ3844444444-4-4-4-400000000000000000000000000000000-2-22200000000000000
χ39444-44-4-4-444-4-4-44-440000000000000000000000000000000000000000000000
χ40444-44-4-4-4-4-444000000000000000000000000000000000000002i−2i2i−2i00000000
χ41444-44-4-4-4-4-44400000000000000000000000000000000000000−2i2i−2i2i00000000
χ4244-44-44-4-44-4-44-444-40000000000000000000000000000000000000000000000
χ4344-44-44-4-4-444-4000000000000000000000000000000000000002-2-2200000000
χ4444-44-44-4-4-444-400000000000000000000000000000000000000-222-200000000
χ4544-4-4-4-444-44-44000000000000000000000000000000002-2-2200000000000000
χ4644-4-4-4-444-44-4400000000000000000000000000000000-222-200000000000000
χ474-444-4-4-44000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000002-22-2000000000000000000000000
χ484-444-4-4-44000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000-22-22000000000000000000000000
χ494-444-4-4-4400000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000-22-22000000000000000000000000
χ504-444-4-4-4400000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000002-22-2000000000000000000000000
χ514-44-4-444-4000000002i−2i−2i2i2i−2i−2i2i0000002i−2i2i−2i00002-22-200000000000000000000
χ524-44-4-444-4000000002i−2i−2i2i2i−2i−2i2i000000−2i2i−2i2i0000-22-2200000000000000000000
χ534-44-4-444-400000000−2i2i2i−2i−2i2i2i−2i0000002i−2i2i−2i0000-22-2200000000000000000000
χ544-44-4-444-400000000−2i2i2i−2i−2i2i2i−2i000000−2i2i−2i2i00002-22-200000000000000000000
χ554-4-444-44-4000000002-2-22-222-20000002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ564-4-444-44-4000000002-2-22-222-2000000−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ574-4-444-44-400000000-222-22-2-220000002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ584-4-444-44-400000000-222-22-2-22000000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ594-4-4-444-44000000002-22-2-22-222-2-220000002-2-22000000000000000000000000
χ604-4-4-444-44000000002-22-2-22-22-222-2000000-222-2000000000000000000000000
χ614-4-4-444-4400000000-22-222-22-22-2-22000000-222-2000000000000000000000000
χ624-4-4-444-4400000000-22-222-22-2-222-20000002-2-22000000000000000000000000

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