Finite Group Databasebeta

← Group #97121

Character table — Group #97121

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444222244442244444488888888888888882444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-111-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i1-1-1-1-1111ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i-11111-1-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii1-1-1-1-1111−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-11111-1-1-1ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-111−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-111ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222222222-2-2-2-222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2122222222-2-2-2-222-2-222-2-22-22-200000000002-200000000000000000002-202-200000000
χ2222222222-2-2-2-222-2-222-2-22-22-200000000002-20000000000000000000-220-2200000000
χ2322222222-2-2-2-222-2-222-2-2-22-220000000000-22000000000000000022-200-20000000000
χ2422222222-2-2-2-222-2-222-2-2-22-220000000000-220000000000000000-2-220020000000000
χ2522222222-2-2-2-2-2-222-2-2222-22-20000000000-2200000000000000002-2200-20000000000
χ2622222222-2-2-2-2-2-222-2-2222-22-20000000000-220000000000000000-22-20020000000000
χ2722222222-2-2-2-2-2-222-2-222-22-2200000000002-200000000000000000002-20-2200000000
χ2822222222-2-2-2-2-2-222-2-222-22-2200000000002-20000000000000000000-2202-200000000
χ29222-2-22-2-222-2-2000000002-2-222i2i−2i−2i00002i−2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ30222-2-22-2-222-2-2000000002-2-222i2i−2i−2i00002i−2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000
χ31222-2-22-2-222-2-2000000002-2-22−2i−2i2i2i0000−2i2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ32222-2-22-2-222-2-2000000002-2-22−2i−2i2i2i0000−2i2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000
χ33222-2-22-2-222-2-200000000-222-22i2i−2i−2i0000−2i2i00i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ34222-2-22-2-222-2-200000000-222-22i2i−2i−2i0000−2i2i00−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ35222-2-22-2-222-2-200000000-222-2−2i−2i2i2i00002i−2i00i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ36222-2-22-2-222-2-200000000-222-2−2i−2i2i2i00002i−2i00−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ372-2-2222-2-22-22-22i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i2-20000000000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ382-2-2222-2-22-22-22i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i2-2000000000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ392-2-2222-2-22-22-22i−2i2i−2i2i−2i2i−2i0000−2i2i−2i2i-220000000000000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ402-2-2222-2-22-22-22i−2i2i−2i2i−2i2i−2i0000−2i2i−2i2i-22000000000000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ412-2-2222-2-22-22-2−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i-220000000000000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ422-2-2222-2-22-22-2−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i-22000000000000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ432-2-2222-2-22-22-2−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i2-20000000000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ442-2-2222-2-22-22-2−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i2-2000000000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ45444-4-44-4-4-4-4440000000044-4-400000000000000000000000000000000000000000000
χ46444-4-44-4-4-4-44400000000-4-44400000000000000000000000000000000000000000000
χ4744-44-4-44-40000004i−4i00−4i4i00000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ4844-44-4-44-40000004i−4i00−4i4i0000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ4944-44-4-44-4000000−4i4i004i−4i00000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ5044-44-4-44-4000000−4i4i004i−4i0000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ5144-4-44-4-4400004400-4-40000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ5244-4-44-4-4400004400-4-4000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ5344-4-44-4-440000-4-400440000000000000000002-2-22-222-2000000000000000000000000
χ5444-4-44-4-440000-4-40044000000000000000000-222-22-2-22000000000000000000000000
χ554-444-4-4-440000004400-4-40000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ564-444-4-4-440000004400-4-4000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ574-444-4-4-44000000-4-400440000000000000000000000002-22-2-22-220000000000000000
χ584-444-4-4-44000000-4-40044000000000000000000000000-22-222-22-20000000000000000
χ594-44-44-44-400004i−4i00−4i4i000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ604-44-44-44-400004i−4i00−4i4i00000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ614-44-44-44-40000−4i4i004i−4i000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ624-44-44-44-40000−4i4i004i−4i00000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ634-4-4444-4-4-44-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000
χ644-4-4444-4-4-44-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000
χ654-4-4-4-44444-4-440000000000004-4-440000000000000000000000000000000000000000
χ664-4-4-4-44444-4-44000000000000-444-40000000000000000000000000000000000000000
χ674-4-4-4-4444-444-40000000000000000004-4000000000000000000000000000000000000
χ684-4-4-4-4444-444-4000000000000000000-44000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.