Finite Group Databasebeta

← Group #290397

Character table — Group #290397

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444444888888888888888888888881616161616161616161616163232
order12222222444444444444444488884444488888888888888888822444488888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1
χ7111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-111-1-1-1-1
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ9111111111111111111-1-1-1-1-1-11111-1111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1
χ10111111111111111111-1-1-1-1-1-11111-1111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11
χ11111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-11
χ12111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-111-1-1-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1111-1
χ17222222222-222-2-22-2-2-22222-2-20000-222-2-2000000000000000000002-20000000000
χ18222222222-222-2-22-2-2-22222-2-20000-2-2-22200000000000000000000-220000000000
χ19222222222-222-2-22-2-2-2-2-2-2-2220000222-2-200000000000000000000-220000000000
χ20222222222-222-2-22-2-2-2-2-2-2-22200002-2-222000000000000000000002-20000000000
χ2122222222-22-2-222-22-2-222-2-2222222-20000-2-22200000000-2-2000000000000000000
χ2222222222-22-2-222-22-2-222-2-222-2-2-2-2-2000022-2-20000000022000000000000000000
χ2322222222-22-2-222-22-2-2-2-222-2-2222220000-2-2-2-20000000022000000000000000000
χ2422222222-22-2-222-22-2-2-2-222-2-2-2-2-2-220000222200000000-2-2000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-200002000000002i2i−2i−2i0000000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-20000200000000−2i−2i2i2i000000000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-222220000-2000000002i2i−2i−2i000000000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-222-2-222220000-200000000−2i−2i2i2i0000000000000000002i−2i0000
χ292222-2-2-2-2222-22-2-2-22-200000000000000000002-22-222-2-20000002-2000000000000
χ302222-2-2-2-2222-22-2-2-22-200000000000000000002-22-2-2-222000000-22000000000000
χ312222-2-2-2-2222-22-2-2-22-20000000000000000000-22-2222-2-2000000-22000000000000
χ322222-2-2-2-2222-22-2-2-22-20000000000000000000-22-22-2-2220000002-2000000000000
χ332222-2-2-2-2-2-2-22-22222-200000000000000000002i−2i−2i2i00000022-2-200002i−2i00000000
χ342222-2-2-2-2-2-2-22-22222-200000000000000000002i−2i−2i2i000000-2-2220000−2i2i00000000
χ352222-2-2-2-2-2-2-22-22222-20000000000000000000−2i2i2i−2i00000022-2-20000−2i2i00000000
χ362222-2-2-2-2-2-2-22-22222-20000000000000000000−2i2i2i−2i000000-2-22200002i−2i00000000
χ3722-2-222-2-20200-2-202002i−2i002i−2i22-2-200000002i−2i0000i2−i2i2−i2002−22−20000002−200i2−i200
χ3822-2-222-2-20200-2-202002i−2i002i−2i22-2-200000002i−2i0000−i2i2−i2i200−22−22000000−2200−i2i200
χ3922-2-222-2-20200-2-202002i−2i002i−2i-2-2220000000−2i2i0000i2−i2i2−i2002−22−2000000−2200−i2i200
χ4022-2-222-2-20200-2-202002i−2i002i−2i-2-2220000000−2i2i0000−i2i2−i2i200−22−220000002−200i2−i200
χ4122-2-222-2-20200-2-20200−2i2i00−2i2i22-2-20000000−2i2i0000i2−i2i2−i200−22−22000000−2200i2−i200
χ4222-2-222-2-20200-2-20200−2i2i00−2i2i22-2-20000000−2i2i0000−i2i2−i2i2002−22−20000002−200−i2i200
χ4322-2-222-2-20200-2-20200−2i2i00−2i2i-2-22200000002i−2i0000i2−i2i2−i200−22−220000002−200−i2i200
χ4422-2-222-2-20200-2-20200−2i2i00−2i2i-2-22200000002i−2i0000−i2i2−i2i2002−22−2000000−2200i2−i200
χ454444-4-4-4-44-44-4-44-44-4400000000000000000000000000000000000000000000000
χ464444-4-4-4-4-44-444-44-4-4400000000000000000000000000000000000000000000000
χ4744-4-444-4-40-400440-4004i−4i00−4i4i00000000000000000000000000000000000000000
χ4844-4-444-4-40-400440-400−4i4i004i−4i00000000000000000000000000000000000000000
χ4944-4-4-4-4440400-440-400000000000000000000000002i2−2i2−2i22i200000000000000000000
χ5044-4-4-4-4440400-440-40000000000000000000000000−2i22i22i2−2i200000000000000000000
χ5144-4-4-4-4440-4004-404000000000000000000000000000000022−22−222200000000000000
χ5244-4-4-4-4440-4004-4040000000000000000000000000000000−222222−2200000000000000
χ534-44-44-44-40000000000004i−4i002i2−2i22i2−2i20000000000000000022−22000000000000000000
χ544-44-44-44-40000000000004i−4i00−2i22i2−2i22i200000000000000000−2222000000000000000000
χ554-44-44-44-4000000000000−4i4i002i2−2i22i2−2i200000000000000000−2222000000000000000000
χ564-44-44-44-4000000000000−4i4i00−2i22i2−2i22i20000000000000000022−22000000000000000000
χ574-4-444-4-4440-4-40040000000002i2−2i2−2i22i2000002i2−2i2000000000000000000000000000000
χ584-4-444-4-4440-4-4004000000000−2i22i22i2−2i200000−2i22i2000000000000000000000000000000
χ594-4-444-4-44-404400-40000000002i2−2i2−2i22i200000−2i22i2000000000000000000000000000000
χ604-4-444-4-44-404400-4000000000−2i22i22i2−2i2000002i2−2i2000000000000000000000000000000
χ614-4-44-444-440-4400-4000000000000004i−4i0000000000000000000000000000000000
χ624-4-44-444-440-4400-400000000000000−4i4i0000000000000000000000000000000000
χ634-4-44-444-4-404-400400000000000000004-400000000000000000000000000000000
χ644-4-44-444-4-404-40040000000000000000-4400000000000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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