Finite Group Databasebeta

← Group #97133

Character table — Group #97133

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888884444444488888888
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
χ511111111111111111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-11-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-111-11−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-111-11ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1111-1ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1111-1-1-11−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1111-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1-11ii−i−i−i−iii
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222222222-2-2-2-222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000
χ2122222222-2-2-2-2222-2-2-2-2200002-22-2002-200000000000000000000002-22-20000000000
χ2222222222-2-2-2-2222-2-2-2-2200002-22-2002-20000000000000000000000-22-220000000000
χ2322222222-2-2-2-2222-2-2-2-220000-22-2200-2200000000000000000000220000-2-200000000
χ2422222222-2-2-2-2222-2-2-2-220000-22-2200-2200000000000000000000-2-200002200000000
χ2522222222-2-2-2-2-2-2-22222-200002-22-200-22000000000000000000002-20000-2200000000
χ2622222222-2-2-2-2-2-2-22222-200002-22-200-2200000000000000000000-2200002-200000000
χ2722222222-2-2-2-2-2-2-22222-20000-22-22002-200000000000000000000002-2-220000000000
χ2822222222-2-2-2-2-2-2-22222-20000-22-22002-20000000000000000000000-222-20000000000
χ292-222-2-2-2222-2-2000000002i2i−2i−2i2-2-2200002i−2i00i2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ302-222-2-2-2222-2-2000000002i2i−2i−2i2-2-2200002i−2i00−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ312-222-2-2-2222-2-2000000002i2i−2i−2i-222-20000−2i2i0022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ322-222-2-2-2222-2-2000000002i2i−2i−2i-222-20000−2i2i00−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ332-222-2-2-2222-2-200000000−2i−2i2i2i2-2-220000−2i2i00i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ342-222-2-2-2222-2-200000000−2i−2i2i2i2-2-220000−2i2i00−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ352-222-2-2-2222-2-200000000−2i−2i2i2i-222-200002i−2i0022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ362-222-2-2-2222-2-200000000−2i−2i2i2i-222-200002i−2i00−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ372-22-2-222-22-22-222-2-2-222-22i−2i2i−2i00000000002i−2i000000000000000000000000i2−i2i2−i22−22−2
χ382-22-2-222-22-22-222-2-2-222-22i−2i2i−2i00000000002i−2i000000000000000000000000−i2i2−i2i2−22−22
χ392-22-2-222-22-22-222-2-2-222-2−2i2i−2i2i0000000000−2i2i000000000000000000000000i2−i2i2−i2−22−22
χ402-22-2-222-22-22-222-2-2-222-2−2i2i−2i2i0000000000−2i2i000000000000000000000000−i2i2−i2i22−22−2
χ412-22-2-222-22-22-2-2-2222-2-222i−2i2i−2i0000000000−2i2i0000000000000000000000002−2−22−i2i2i2−i2
χ422-22-2-222-22-22-2-2-2222-2-222i−2i2i−2i0000000000−2i2i000000000000000000000000−222−2i2−i2−i2i2
χ432-22-2-222-22-22-2-2-2222-2-22−2i2i−2i2i00000000002i−2i0000000000000000000000002−2−22i2−i2−i2i2
χ442-22-2-222-22-22-2-2-2222-2-22−2i2i−2i2i00000000002i−2i000000000000000000000000−222−2−i2i2i2−i2
χ45444-44-4-4-44-4-44000000004-4-4400000000000000000000000000000000000000000000
χ46444-44-4-4-44-4-4400000000-444-400000000000000000000000000000000000000000000
χ47444-44-4-4-4-444-400000000000000004-400000000000000000000000000000000000000
χ48444-44-4-4-4-444-40000000000000000-4400000000000000000000000000000000000000
χ4944-44-44-4-400004-440000-400000000000000002-22-22-22-2000000000000000000000000
χ5044-44-44-4-400004-440000-40000000000000000-22-22-22-22000000000000000000000000
χ5144-44-44-4-40000-44-40000400000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5244-44-44-4-40000-44-4000040000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5344-4-4-4-44400000004i−4i4i−4i00000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ5444-4-4-4-44400000004i−4i4i−4i0000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ5544-4-4-4-4440000000−4i4i−4i4i00000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ5644-4-4-4-4440000000−4i4i−4i4i0000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ574-444-4-4-44-4-44400000000000044-4-40000000000000000000000000000000000000000
χ584-444-4-4-44-4-444000000000000-4-4440000000000000000000000000000000000000000
χ594-44-4-444-4-44-4444-444-4-4-4000000000000000000000000000000000000000000000000
χ604-44-4-444-4-44-44-4-44-4-4444000000000000000000000000000000000000000000000000
χ614-4-444-44-400000004i−4i−4i4i000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ624-4-444-44-400000004i−4i−4i4i00000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ634-4-444-44-40000000−4i4i4i−4i000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ644-4-444-44-40000000−4i4i4i−4i00000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ654-4-4-444-4400004-4-4000040000000000000000000000002-2-22-222-20000000000000000
χ664-4-4-444-4400004-4-400004000000000000000000000000-222-22-2-220000000000000000
χ674-4-4-444-440000-4440000-40000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ684-4-4-444-440000-4440000-4000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000

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