Finite Group Databasebeta

← Group #97142

Character table — Group #97142

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444442244444488888888888888882244444488888888
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
χ51111111111111111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111ii−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−iiiii1-11-1-1-111ii−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-11-1111-1-1−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−i1-11-1-1-111−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-11-1111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-22222-2-2-2-222-2-2-2-200000000000000000000000000000000
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
χ20222222222222-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2-2-200000000000000000000000000000000
χ2122222222-2-2-2-2222-2-2-2-222-200002-20000002-2000000000000000000002-22-200000000
χ2222222222-2-2-2-2222-2-2-2-222-200002-20000002-200000000000000000000-22-2200000000
χ2322222222-2-2-2-2222-2-2-2-22-220000-22000000-22000000000000000022-2-2000000000000
χ2422222222-2-2-2-2222-2-2-2-22-220000-22000000-220000000000000000-2-222000000000000
χ2522222222-2-2-2-2-2-2-22222-22-200002-2000000-2200000000000000002-2-22000000000000
χ2622222222-2-2-2-2-2-2-22222-22-200002-2000000-220000000000000000-222-2000000000000
χ2722222222-2-2-2-2-2-2-22222-2-220000-220000002-2000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-22222-2-220000-220000002-200000000000000000000-222-200000000
χ2922-2-222-2-222-2-222-2-2-222-2002i2i−2i−2i00002i−2i00000000000000000000000000002−22−2i2−i2i2−i2
χ3022-2-222-2-222-2-222-2-2-222-2002i2i−2i−2i00002i−2i0000000000000000000000000000−22−22−i2i2−i2i2
χ3122-2-222-2-222-2-222-2-2-222-200−2i−2i2i2i0000−2i2i00000000000000000000000000002−22−2−i2i2−i2i2
χ3222-2-222-2-222-2-222-2-2-222-200−2i−2i2i2i0000−2i2i0000000000000000000000000000−22−22i2−i2i2−i2
χ3322-2-222-2-222-2-2-2-2222-2-22002i2i−2i−2i0000−2i2i0000000000000000000000000000i2−i2−i2i2−222−2
χ3422-2-222-2-222-2-2-2-2222-2-22002i2i−2i−2i0000−2i2i0000000000000000000000000000−i2i2i2−i22−2−22
χ3522-2-222-2-222-2-2-2-2222-2-2200−2i−2i2i2i00002i−2i0000000000000000000000000000i2−i2−i2i22−2−22
χ3622-2-222-2-222-2-2-2-2222-2-2200−2i−2i2i2i00002i−2i0000000000000000000000000000−i2i2i2−i2−222−2
χ372-2222-2-2-22-22-2000000002-22i−2i2i−2i-2200002i−2i00i2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ382-2222-2-2-22-22-2000000002-22i−2i2i−2i-2200002i−2i00−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ392-2222-2-2-22-22-2000000002-2−2i2i−2i2i-220000−2i2i00i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ402-2222-2-2-22-22-2000000002-2−2i2i−2i2i-220000−2i2i00−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ412-2222-2-2-22-22-200000000-222i−2i2i−2i2-20000−2i2i0022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ422-2222-2-2-22-22-200000000-222i−2i2i−2i2-20000−2i2i00−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ432-2222-2-2-22-22-200000000-22−2i2i−2i2i2-200002i−2i0022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ442-2222-2-2-22-22-200000000-22−2i2i−2i2i2-200002i−2i00−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ45444-4-4-44-400000004i−4i4i−4i00000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ46444-4-4-44-400000004i−4i4i−4i0000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ47444-4-4-44-40000000−4i4i−4i4i00000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ48444-4-4-44-40000000−4i4i−4i4i0000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ4944-44-4-4-4400000004i−4i−4i4i000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ5044-44-4-4-4400000004i−4i−4i4i00000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ5144-44-4-4-440000000−4i4i4i−4i000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ5244-44-4-4-440000000−4i4i4i−4i00000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ5344-4-444-4-4-4-44444-444-4-4-4000000000000000000000000000000000000000000000000
χ5444-4-444-4-4-4-444-4-44-4-4444000000000000000000000000000000000000000000000000
χ554-4444-4-4-4-44-4400000000440000-4-40000000000000000000000000000000000000000
χ564-4444-4-4-4-44-4400000000-4-40000440000000000000000000000000000000000000000
χ574-44-4-44-4400004-440000-40000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ584-44-4-44-4400004-440000-4000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ594-44-4-44-440000-44-4000040000000000000000000000002-2-22-222-20000000000000000
χ604-44-4-44-440000-44-400004000000000000000000000000-222-22-2-220000000000000000
χ614-4-44-444-400004-4-40000400000000000000002-2-222-2-22000000000000000000000000
χ624-4-44-444-400004-4-4000040000000000000000-222-2-222-2000000000000000000000000
χ634-4-44-444-40000-4440000-400000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ644-4-44-444-40000-4440000-40000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ654-4-4-44-4444-4-4400000000004-4-44000000000000000000000000000000000000000000
χ664-4-4-44-4444-4-440000000000-444-4000000000000000000000000000000000000000000
χ674-4-4-44-444-444-400000000000000004-400000000000000000000000000000000000000
χ684-4-4-44-444-444-40000000000000000-4400000000000000000000000000000000000000

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