Finite Group Databasebeta

← Group #101770

Character table — Group #101770

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
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
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
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−iii−i−iii−i−iii−i−i1111-1-1-1-11-11-1ii−i−iii−i−i1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-111111-11-1−i−iii−i−iii-11
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-1-11-11ii−i−i−i−iii-11
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−i−i−iiiii−i−i−i−iii-1-1-1-11111-11-11−i−iiiii−i−i1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-1-11-11−i−iiiii−i−i-11
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iiiii−i−i−i−iiiii−i−i-1-1-1-11111-11-11ii−i−i−i−iii1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iii−i−iii−i−iii−i−iii1111-1-1-1-11-11-1−i−iii−i−iii1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iii−i−iii−i−iii−i−iii-1-1-1-111111-11-1ii−i−iii−i−i-11
χ1722222222222222-2-222-2-222-2-2-2-2-2000022220000-2-2-2-20000000000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-20000-2-2-2-2000022220000000000000000000000
χ19222222222222-2-222-2-222-2-222-2-2-222220000-2-2-2-200000000000000000000000000
χ20222222222222-2-222-2-222-2-222-2-2-2-2-2-2-20000222200000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-222200000000000000000000000022-2-20000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2222000000000000000000000000-2-2220000000000
χ2322222222-2-2-2-222222222-2-2-2-222-20000000000000000000000002-2-220000000000
χ2422222222-2-2-2-222222222-2-2-2-222-2000000000000000000000000-222-20000000000
χ2522222222-2-2-2-222-2-222-2-2-2-222-2-222i2i−2i−2i0000−2i−2i2i2i00000000000000000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-222-2-22−2i−2i2i2i00002i2i−2i−2i00000000000000000000000000
χ2722222222-2-2-2-2-2-222-2-22222-2-2-2-2200002i2i−2i−2i0000−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-222-2-22222-2-2-2-220000−2i−2i2i2i00002i2i−2i−2i0000000000000000000000
χ29222-22-2-2-222-2-2002200-2-2002-20002-22-200000000000022−2−222−2−200002−22−2000000
χ30222-22-2-2-222-2-2002200-2-2002-20002-22-2000000000000−2−222−2−2220000−22−22000000
χ31222-22-2-2-222-2-2002200-2-2002-2000-22-2200000000000022−2−222−2−20000−22−22000000
χ32222-22-2-2-222-2-2002200-2-2002-2000-22-22000000000000−2−222−2−22200002−22−2000000
χ33222-22-2-2-2-2-22200-2-20022002-20002i−2i−2i2i00000000000022−2−2−2−2220000i2−i2−i2i2000000
χ34222-22-2-2-2-2-22200-2-20022002-20002i−2i−2i2i000000000000−2−22222−2−20000−i2i2i2−i2000000
χ35222-22-2-2-2-2-22200-2-20022002-2000−2i2i2i−2i00000000000022−2−2−2−2220000−i2i2i2−i2000000
χ36222-22-2-2-2-2-22200-2-20022002-2000−2i2i2i−2i000000000000−2−22222−2−20000i2−i2−i2i2000000
χ3722-22-22-2-22-22-22200-2-2002-20000000002-22-2000000002−22−22−22−2000000002−22−200
χ3822-22-22-2-22-22-22200-2-2002-20000000002-22-200000000−22−22−22−2200000000−22−2200
χ3922-22-22-2-22-22-22200-2-2002-2000000000-22-22000000002−22−22−22−200000000−22−2200
χ4022-22-22-2-22-22-22200-2-2002-2000000000-22-2200000000−22−22−22−22000000002−22−200
χ4122-22-22-2-2-22-22-2-20022002-20000000002i−2i−2i2i000000002−22−2−22−2200000000i2−i2−i2i200
χ4222-22-22-2-2-22-22-2-20022002-20000000002i−2i−2i2i00000000−22−222−22−200000000−i2i2i2−i200
χ4322-22-22-2-2-22-22-2-20022002-2000000000−2i2i2i−2i000000002−22−2−22−2200000000−i2i2i2−i200
χ4422-22-22-2-2-22-22-2-20022002-2000000000−2i2i2i−2i00000000−22−222−22−200000000i2−i2−i2i200
χ45444-44-4-4-444-4-400-4-4004400-4400000000000000000000000000000000000000000
χ46444-44-4-4-4-4-444004400-4-400-4400000000000000000000000000000000000000000
χ4744-44-44-4-44-44-4-4-4004400-440000000000000000000000000000000000000000000
χ4844-44-44-4-4-44-444400-4-400-440000000000000000000000000000000000000000000
χ4944-4-4-4-4444-4-4400000000000000000000000000000002-2-222-2-2200000000000000
χ5044-4-4-4-4444-4-440000000000000000000000000000000-222-2-222-200000000000000
χ5144-4-4-4-444-444-400000000000000000000000000000002-2-22-222-200000000000000
χ5244-4-4-4-444-444-40000000000000000000000000000000-222-22-2-2200000000000000
χ534-444-4-4-4400004i−4i4i−4i4i−4i4i−4i00004-4000000000000000000000000000000000000000
χ544-444-4-4-4400004i−4i−4i4i4i−4i−4i4i0000-44000000000000000000000000000000000000000
χ554-444-4-4-440000−4i4i4i−4i−4i4i4i−4i0000-44000000000000000000000000000000000000000
χ564-444-4-4-440000−4i4i−4i4i−4i4i−4i4i00004-4000000000000000000000000000000000000000
χ574-44-4-444-40000004i−4i00−4i4i0000000000000002−2i−2+2i2+2i−2−2i00000000000000000000000000
χ584-44-4-444-40000004i−4i00−4i4i000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000
χ594-44-4-444-4000000−4i4i004i−4i0000000000000002+2i−2−2i2−2i−2+2i00000000000000000000000000
χ604-44-4-444-4000000−4i4i004i−4i000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000
χ614-4-444-44-400004i−4i00−4i4i0000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000000000
χ624-4-444-44-400004i−4i00−4i4i000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000000000
χ634-4-444-44-40000−4i4i004i−4i0000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000000000
χ644-4-444-44-40000−4i4i004i−4i000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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