Finite Group Databasebeta

← Group #97274

Character table — Group #97274

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444422444444444444444444442244444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-111-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-111-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111
χ811111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−i1-11-11-11-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−i-111-1-11-11-11ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii1-11-11-11-11-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii-111-1-11-11-11−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i1-1-11-111-1-11−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i-11-111-1-111-1−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiii1-1-11-111-1-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiii-11-111-1-111-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-222-2-222-2-2220000000000-2-2000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2000000000022000000000000000000
χ19222222222222-2-22-2-2-22-2002-2000000000000002200-2-2000000000000
χ20222222222222-2-22-2-2-22-2002-200000000000000-2-20022000000000000
χ21222222222222-2-2-22-2-2-2200-220000000000220000-2-200000000000000
χ22222222222222-2-2-22-2-2-2200-220000000000-2-200002200000000000000
χ2322222222-2-2-2-2222-2-2-22-200-2200000000002-20000-2200000000000000
χ2422222222-2-2-2-2222-2-2-22-200-220000000000-2200002-200000000000000
χ2522222222-2-2-2-222-22-2-2-22002-2000000000000002-200-22000000000000
χ2622222222-2-2-2-222-22-2-2-22002-200000000000000-22002-2000000000000
χ2722222222-2-2-2-2-2-222222222-2-2-2-20000000000-22000000000000000000
χ2822222222-2-2-2-2-2-2222222-2-2-2-22200000000002-2000000000000000000
χ292-2-22-2-22222-2-22-2002-2002-2002-20000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ302-2-22-2-22222-2-22-2002-2002-2002-20000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ312-2-22-2-22222-2-22-2002-200-2200-220000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ322-2-22-2-22222-2-22-2002-200-2200-220000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ332-2-22-2-222-2-222-22002-2002-200-2200000000000000000000002−2−222−2−22
χ342-2-22-2-222-2-222-22002-2002-200-220000000000000000000000−222−2−222−2
χ352-2-22-2-222-2-222-22002-200-22002-200000000000000000000002−2−22−222−2
χ362-2-22-2-222-2-222-22002-200-22002-20000000000000000000000−222−22−2−22
χ37444-4-4-44-44-44-40000000000000022-2-222-2-20000000000000000000000
χ38444-4-4-44-44-44-400000000000000-2-222-2-2220000000000000000000000
χ39444-4-4-44-4-44-44000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ40444-4-4-44-4-44-4400000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ4144-444-4-4-400000004000-40000002-22-22-22-20000000000000000000000
χ4244-444-4-4-400000004000-4000000-22-22-22-220000000000000000000000
χ4344-444-4-4-40000000-400040000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ4444-444-4-4-40000000-40004000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ4544-4-4-44-440000004000-400000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ4644-4-4-44-440000004000-40000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ4744-4-4-44-44000000-4000400000002-2-222-2-220000000000000000000000
χ4844-4-4-44-44000000-400040000000-222-2-222-20000000000000000000000
χ494-4-44-4-44444-4-4-4400-4400000000000000000000000000000000000000
χ504-4-44-4-444-4-4444-400-4400000000000000000000000000000000000000
χ514-4-4-4444-44-4-44000000000000000000000000000000002-22-200000000
χ524-4-4-4444-44-4-4400000000000000000000000000000000-22-2200000000
χ534-4-4-4444-4-444-4000000000000000000000000000000002i−2i−2i2i00000000
χ544-4-4-4444-4-444-400000000000000000000000000000000−2i2i2i−2i00000000
χ558-888-88-8-8000000000000000000000000000000000000000000000000
χ568-88-88-8-88000000000000000000000000000000000000000000000000

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