Finite Group Databasebeta

← Group #100340

Character table — Group #100340

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444444888888888888888888888888888844
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
χ911111111-1-1-1111-1-1-1-11-111-1-1-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1-1111-1-1-1-11-111-1-1-1-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-111-11
χ1111111111-1-1-1111-1-1-1-11-111-1-1-1-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-111-11
χ1211111111-1-1-1111-1-1-1-11-111-1-1-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-11-1
χ1311111111-1-1-1111-1-1-1-11-111-1-1-1-11-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii11-1-1-11
χ1411111111-1-1-1111-1-1-1-11-111-1-1-1-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1-1111-1-1-1-11-111-1-1-1-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1-1111-1-1-1-11-111-1-1-1-11-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i11-1-1-11
χ1722222222222222-2-2-222-2-2-22-2-22-222-2-222-2-2000000000000000000000000000000
χ1822222222222222-2-2-222-2-2-22-2-22-2-2-222-2-222000000000000000000000000000000
χ1922222222222-2-2-22222-2222-2-2-2-2-20000000022-2-222-2-20000000000000000000000
χ2022222222222-2-2-22222-2222-2-2-2-2-200000000-2-222-2-2220000000000000000000000
χ2122222222222-2-2-2-2-2-22-2-2-2-2-222-220000000000000000000000002i−2i2i−2i0000000000
χ2222222222222-2-2-2-2-2-22-2-2-2-2-222-22000000000000000000000000−2i2i−2i2i0000000000
χ2322222222-2-2-2222222-222-2-2-222-2-222-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2222222-222-2-2-222-2-2-2-22222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-2222-2-22-2-22-2-2220000000000000000000000002-2-220000000000
χ2622222222-2-2-2-2-2-2222-2-22-2-22-2-222000000000000000000000000-222-20000000000
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
χ29222-2-2-2-2222-2000-22-2-2022-20000000000000002i−2i002i−2i22−2−222−2−200000000i2−i2i2−i200
χ30222-2-2-2-2222-2000-22-2-2022-20000000000000002i−2i002i−2i−2−222−2−22200000000−i2i2−i2i200
χ31222-2-2-2-2222-2000-22-2-2022-2000000000000000−2i2i00−2i2i22−2−222−2−200000000−i2i2−i2i200
χ32222-2-2-2-2222-2000-22-2-2022-2000000000000000−2i2i00−2i2i−2−222−2−22200000000i2−i2i2−i200
χ33222-2-2-2-22-2-220002-2220-22-20000000000000002-200-22i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i200
χ34222-2-2-2-22-2-220002-2220-22-20000000000000002-200-22−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i200
χ35222-2-2-2-22-2-220002-2220-22-2000000000000000-22002-2i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i200
χ36222-2-2-2-22-2-220002-2220-22-2000000000000000-22002-2−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i200
χ372-2-222-2-2200022-22-2-20-220002-200002i−2i2i−2i00000000002−22−22−22−20000i2−i2i2−i2000000
χ382-2-222-2-2200022-22-2-20-220002-200002i−2i2i−2i0000000000−22−22−22−220000−i2i2−i2i2000000
χ392-2-222-2-2200022-22-2-20-220002-20000−2i2i−2i2i00000000002−22−22−22−20000−i2i2−i2i2000000
χ402-2-222-2-2200022-22-2-20-220002-20000−2i2i−2i2i0000000000−22−22−22−220000i2−i2i2−i2000000
χ412-2-222-2-2200022-2-2220-2-2000-2200002i−2i−2i2i0000000000i2−i2i2−i2−i2i2−i2i20000−222−2000000
χ422-2-222-2-2200022-2-2220-2-2000-2200002i−2i−2i2i0000000000−i2i2−i2i2i2−i2i2−i200002−2−22000000
χ432-2-222-2-2200022-2-2220-2-2000-220000−2i2i2i−2i0000000000i2−i2i2−i2−i2i2−i2i200002−2−22000000
χ442-2-222-2-2200022-2-2220-2-2000-220000−2i2i2i−2i0000000000−i2i2−i2i2i2−i2i2−i20000−222−2000000
χ45444-4-4-4-4444-40004-44-40-4-440000000000000000000000000000000000000000000
χ46444-4-4-4-44-4-44000-44-4404-440000000000000000000000000000000000000000000
χ4744-44-44-4-40004-440000-4000000000000004-4000000000000000000000000000000
χ4844-44-44-4-40004-440000-400000000000000-44000000000000000000000000000000
χ4944-44-44-4-4000-44-400004000000004i−4i000000000000000000000000000000000000
χ5044-44-44-4-4000-44-40000400000000−4i4i000000000000000000000000000000000000
χ514-444-4-44-44-444-4-4000-44000400-4000000000000000000000000000000000000000
χ524-444-4-44-44-44-444000-4-4000-4004000000000000000000000000000000000000000
χ534-444-4-44-4-44-44-4-400044000-4004000000000000000000000000000000000000000
χ544-444-4-44-4-44-4-4440004-4000400-4000000000000000000000000000000000000000
χ554-44-444-4-44-4-40000004000000000000000002i2−2i2002i2−2i2000000000000000000000000
χ564-44-444-4-44-4-4000000400000000000000000−2i22i200−2i22i2000000000000000000000000
χ574-44-444-4-4-444000000-40000000000000000022−2200−2222000000000000000000000000
χ584-44-444-4-4-444000000-400000000000000000−22220022−22000000000000000000000000
χ594-4-444-4-44000-4-444-4-4044000-440000000000000000000000000000000000000000
χ604-4-444-4-44000-4-44-44404-40004-40000000000000000000000000000000000000000
χ614-4-4-4-444400000044-400-4000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ624-4-4-4-444400000044-400-400000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ634-4-4-4-4444000000-4-44004000000000000000000000002-2-222-2-2200000000000000
χ644-4-4-4-4444000000-4-4400400000000000000000000000-222-2-222-200000000000000
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000

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