Finite Group Databasebeta

← Group #100421

Character table — Group #100421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222222244444444444444444444444444444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-111-11
χ1111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-111-11
χ1211111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-11-1
χ1311111111-1-1-1-1-1-111-1-11111-1-1-1-11-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii11-1-1-11
χ1411111111-1-1-1-1-1-111-1-11111-1-1-1-11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1-1-1-1-111-1-11111-1-1-1-11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-1-1-111-1-11111-1-1-1-11-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i11-1-1-11
χ1722222222222222-2-222-2-222-2-2-2-2-20000000022-2-222-2-20000000000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-200000000-2-222-2-2220000000000000000000000
χ19222222222222-2-222-2-222-2-222-2-2-22222-2-2-2-2000000000000000000000000000000
χ20222222222222-2-222-2-222-2-222-2-2-2-2-2-2-22222000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22220000000000000000000000002-22-20000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2222000000000000000000000000-22-220000000000
χ2322222222-2-2-2-222222222-2-2-2-222-222-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2-222222222-2-2-2-222-2-2-22222-2-2000000000000000000000000000000
χ2522222222-2-2-2-222-2-222-2-2-2-222-2-220000000000000000000000002i−2i−2i2i0000000000
χ2622222222-2-2-2-222-2-222-2-2-2-222-2-22000000000000000000000000−2i2i2i−2i0000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ292222-2-2-2-222-2-22200-2-2002-20000000000000002-2002-222−2−222−2−2000000002−22−200
χ302222-2-2-2-222-2-22200-2-2002-20000000000000002-2002-2−2−222−2−22200000000−22−2200
χ312222-2-2-2-222-2-22200-2-2002-2000000000000000-2200-2222−2−222−2−200000000−22−2200
χ322222-2-2-2-222-2-22200-2-2002-2000000000000000-2200-22−2−222−2−222000000002−22−200
χ332222-2-2-2-2-2-222-2-20022002-20000000000000002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i2000000002−2−2200
χ342222-2-2-2-2-2-222-2-20022002-20000000000000002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i200000000−222−200
χ352222-2-2-2-2-2-222-2-20022002-2000000000000000−2i2i002i−2ii2i2−i2−i2−i2−i2i2i200000000−222−200
χ362222-2-2-2-2-2-222-2-20022002-2000000000000000−2i2i002i−2i−i2−i2i2i2i2i2−i2−i2000000002−2−2200
χ3722-2-2-2-2222-2-22002200-2-2002-20002i−2i2i−2i0000000000002−22−22−22−20000i2−i2i2−i2000000
χ3822-2-2-2-2222-2-22002200-2-2002-20002i−2i2i−2i000000000000−22−22−22−220000−i2i2−i2i2000000
χ3922-2-2-2-2222-2-22002200-2-2002-2000−2i2i−2i2i0000000000002−22−22−22−20000−i2i2−i2i2000000
χ4022-2-2-2-2222-2-22002200-2-2002-2000−2i2i−2i2i000000000000−22−22−22−220000i2−i2i2−i2000000
χ4122-2-2-2-222-222-2002200-2-200-220002i−2i−2i2i000000000000i2−i2i2−i2−i2i2−i2i20000−222−2000000
χ4222-2-2-2-222-222-2002200-2-200-220002i−2i−2i2i000000000000−i2i2−i2i2i2−i2i2−i200002−2−22000000
χ4322-2-2-2-222-222-2002200-2-200-22000−2i2i2i−2i000000000000i2−i2i2−i2−i2i2−i2i200002−2−22000000
χ4422-2-2-2-222-222-2002200-2-200-22000−2i2i2i−2i000000000000−i2i2−i2i2i2−i2i2−i20000−222−2000000
χ454444-4-4-4-444-4-4-4-4004400-440000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-4444400-4-400-440000000000000000000000000000000000000000000
χ4744-4-444-4-44-44-400000000000000000000000000000002-2-222-2-2200000000000000
χ4844-4-444-4-44-44-40000000000000000000000000000000-222-2-222-200000000000000
χ4944-4-444-4-4-44-4400000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ5044-4-444-4-4-44-440000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ5144-4-4-4-4444-4-4400-4-4004400-4400000000000000000000000000000000000000000
χ5244-4-4-4-444-444-400-4-40044004-400000000000000000000000000000000000000000
χ534-44-44-4-4400004i−4i004i−4i000000000000000002+2i−2−2i002−2i−2+2i000000000000000000000000
χ544-44-44-4-4400004i−4i004i−4i00000000000000000−2−2i2+2i00−2+2i2−2i000000000000000000000000
χ554-44-44-4-440000−4i4i00−4i4i000000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000
χ564-44-44-4-440000−4i4i00−4i4i00000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000
χ574-44-4-444-400004i−4i4-4−4i4i4-400004i−4i000000000000000000000000000000000000000
χ584-44-4-444-400004i−4i-44−4i4i-440000−4i4i000000000000000000000000000000000000000
χ594-44-4-444-40000−4i4i4-44i−4i4-40000−4i4i000000000000000000000000000000000000000
χ604-44-4-444-40000−4i4i-444i−4i-4400004i−4i000000000000000000000000000000000000000
χ614-4-444-44-40000004-400-4400000000000004i−4i000000000000000000000000000000
χ624-4-444-44-40000004-400-440000000000000−4i4i000000000000000000000000000000
χ634-4-444-44-4000000-44004-4000000000004i−4i00000000000000000000000000000000
χ644-4-444-44-4000000-44004-400000000000−4i4i00000000000000000000000000000000
χ658-8-88-88-88000000000000000000000000000000000000000000000000000000000

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