Finite Group Databasebeta

← Group #172110

Character table — Group #172110

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444422444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-11111-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-111-11111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111-11-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1111111-11-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-11-1-111-1-11111-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-11-1-11111-1-1-1-11111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-11-11-11-1-1-111-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111111-11-11-111-1-111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1111-1-1-1-111-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-11111-1-111-11-1-11111-1-111-1-1
χ1722222222222222-2-2-2-222-2-2-2-200222200000000000000-20000-2000000000000
χ1822222222222222-2-2-2-222-2-2-2-200-2-2-2-200000000000000200002000000000000
χ19222222222222-2-222-2-2-2-222-2-2220000000022000000000-2-2000000000000000
χ20222222222222-2-222-2-2-2-222-2-2-2-200000000-2-200000000022000000000000000
χ21222222222222-2-2-2-222-2-2-2-22200000022-2-20000000000000-220000000000000
χ22222222222222-2-2-2-222-2-2-2-222000000-2-22200000000000002-20000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-22200000022220000000000000-2-20000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-222000000-2-2-2-20000000000000220000000000000
χ2522222222-2-2-2-222-2-222-2-222-2-22200000000-2-2000000000-22000000000000000
χ2622222222-2-2-2-222-2-222-2-222-2-2-2-200000000220000000002-2000000000000000
χ2722222222-2-2-2-2-2-2222222-2-2-2-20022-2-200000000000000-200002000000000000
χ2822222222-2-2-2-2-2-2222222-2-2-2-200-2-2220000000000000020000-2000000000000
χ292-222-2-22-22i2i−2i−2i002i−2i00002-2002-2000000002i−2ii2i2−i2−i222−2−20000000000i2−i22−20000
χ302-222-2-22-22i2i−2i−2i002i−2i00002-2002-2000000002i−2i−i2−i2i2i2−2−2220000000000−i2i2−220000
χ312-222-2-22-22i2i−2i−2i002i−2i00002-200-2200000000−2i2ii2i2−i2−i222−2−20000000000−i2i2−220000
χ322-222-2-22-22i2i−2i−2i002i−2i00002-200-2200000000−2i2i−i2−i2i2i2−2−2220000000000i2−i22−20000
χ332-222-2-22-2−2i−2i2i2i00−2i2i00002-2002-200000000−2i2ii2i2−i2−i2−2−2220000000000i2−i2−220000
χ342-222-2-22-2−2i−2i2i2i00−2i2i00002-2002-200000000−2i2i−i2−i2i2i222−2−20000000000−i2i22−20000
χ352-222-2-22-2−2i−2i2i2i00−2i2i00002-200-22000000002i−2ii2i2−i2−i2−2−2220000000000−i2i22−20000
χ362-222-2-22-2−2i−2i2i2i00−2i2i00002-200-22000000002i−2i−i2−i2i2i222−2−20000000000i2−i2−220000
χ372-2-2-2222-22i−2i2i−2i2i−2i00002-20000002-22i−2i0000002−22−2i2−i2i2−i2000000000000002−2i2−i2
χ382-2-2-2222-22i−2i2i−2i2i−2i00002-20000002-22i−2i000000−22−22−i2i2−i2i200000000000000−22−i2i2
χ392-2-2-2222-22i−2i2i−2i2i−2i00002-2000000-22−2i2i0000002−22−2i2−i2i2−i200000000000000−22−i2i2
χ402-2-2-2222-22i−2i2i−2i2i−2i00002-2000000-22−2i2i000000−22−22−i2i2−i2i2000000000000002−2i2−i2
χ412-2-2-2222-2−2i2i−2i2i−2i2i00002-20000002-2−2i2i0000002−22−2−i2i2−i2i2000000000000002−2−i2i2
χ422-2-2-2222-2−2i2i−2i2i−2i2i00002-20000002-2−2i2i000000−22−22i2−i2i2−i200000000000000−22i2−i2
χ432-2-2-2222-2−2i2i−2i2i−2i2i00002-2000000-222i−2i0000002−22−2−i2i2−i2i200000000000000−22i2−i2
χ442-2-2-2222-2−2i2i−2i2i−2i2i00002-2000000-222i−2i000000−22−22i2−i2i2−i2000000000000002−2−i2i2
χ4544-4-4-4-4444-4-440000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ4644-4-4-4-4444-4-44000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ4744-4-4-4-444-444-40000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ4844-4-4-4-444-444-4000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ494-444-4-44-44i4i−4i−4i00−4i4i0000-440000000000000000000000000000000000000000
χ504-444-4-44-4−4i−4i4i4i004i−4i0000-440000000000000000000000000000000000000000
χ514-44-44-4-44000000000000004-4000000004i−4i0000000000000000000000000000
χ524-44-44-4-44000000000000004-400000000−4i4i0000000000000000000000000000
χ534-44-44-4-4400000000000000-440000004i−4i000000000000000000000000000000
χ544-44-44-4-4400000000000000-44000000−4i4i000000000000000000000000000000
χ554-4-44-44-44000000004i−4i000000000000000000000000000000002i−2i2-200000000
χ564-4-44-44-44000000004i−4i00000000000000000000000000000000−2i2i-2200000000
χ574-4-44-44-4400000000−4i4i000000000000000000000000000000002i−2i-2200000000
χ584-4-44-44-4400000000−4i4i00000000000000000000000000000000−2i2i2-200000000
χ594-4-4-4444-44i−4i4i−4i−4i4i0000-44000000000000000000000000000000000000000000
χ604-4-4-4444-4−4i4i−4i4i4i−4i0000-44000000000000000000000000000000000000000000
χ61888-8-88-8-8000000000000000000000000000000000000000000000000000000
χ6288-888-8-8-8000000000000000000000000000000000000000000000000000000

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