Finite Group Databasebeta

← Group #93641

Character table — Group #93641

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444442222444488888888888888888888888888888888
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
χ511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-111
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii11-1-1-1-111
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1
χ17222222222222222222222222-2-2-2-2-2-2-2-222-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-22222-2-222-2-2-2-200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-200000000000000000000000000000000
χ21222-2-22-2-222-2-2000000002i2i−2i−2i2i2i−2i−2i2-2000000i2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ22222-2-22-2-222-2-2000000002i2i−2i−2i2i2i−2i−2i2-2000000−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ23222-2-22-2-222-2-2000000002i2i−2i−2i−2i−2i2i2i-2200000022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ24222-2-22-2-222-2-2000000002i2i−2i−2i−2i−2i2i2i-22000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ25222-2-22-2-222-2-200000000−2i−2i2i2i2i2i−2i−2i-2200000022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ26222-2-22-2-222-2-200000000−2i−2i2i2i2i2i−2i−2i-22000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ27222-2-22-2-222-2-200000000−2i−2i2i2i−2i−2i2i2i2-2000000i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ28222-2-22-2-222-2-200000000−2i−2i2i2i−2i−2i2i2i2-2000000−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ292-2-2222-2-22-22-22i2i−2i−2i2i2i−2i−2i00002i−2i2i−2i002-200000000000000000000i2−i22−2i2−i22−200000000
χ302-2-2222-2-22-22-22i2i−2i−2i2i2i−2i−2i00002i−2i2i−2i002-200000000000000000000−i2i2−22−i2i2−2200000000
χ312-2-2222-2-22-22-22i2i−2i−2i2i2i−2i−2i0000−2i2i−2i2i00-22000000000000000000002−2−i2i2−22i2−i200000000
χ322-2-2222-2-22-22-22i2i−2i−2i2i2i−2i−2i0000−2i2i−2i2i00-2200000000000000000000−22i2−i22−2−i2i200000000
χ332-2-2222-2-22-22-2−2i−2i2i2i−2i−2i2i2i00002i−2i2i−2i00-22000000000000000000002−2i2−i2−22−i2i200000000
χ342-2-2222-2-22-22-2−2i−2i2i2i−2i−2i2i2i00002i−2i2i−2i00-2200000000000000000000−22−i2i22−2i2−i200000000
χ352-2-2222-2-22-22-2−2i−2i2i2i−2i−2i2i2i0000−2i2i−2i2i002-200000000000000000000i2−i2−22i2−i2−2200000000
χ362-2-2222-2-22-22-2−2i−2i2i2i−2i−2i2i2i0000−2i2i−2i2i002-200000000000000000000−i2i22−2−i2i22−200000000
χ372-2-2222-2-2-22-222i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000002-200000000000000000000000000i2−i22−22−2i2−i2
χ382-2-2222-2-2-22-222i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000002-200000000000000000000000000−i2i2−22−22−i2i2
χ392-2-2222-2-2-22-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000-22000000000000000000000000002−2−i2i2i2−i2−22
χ402-2-2222-2-2-22-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000-2200000000000000000000000000−22i2−i2−i2i22−2
χ412-2-2222-2-2-22-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000-22000000000000000000000000002−2i2−i2−i2i2−22
χ422-2-2222-2-2-22-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000-2200000000000000000000000000−22−i2i2i2−i22−2
χ432-2-2222-2-2-22-22−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000002-200000000000000000000000000i2−i2−22−22i2−i2
χ442-2-2222-2-2-22-22−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000002-200000000000000000000000000−i2i22−22−2−i2i2
χ4544444444-4-4-4-44-4-444-4-44000000000000000000000000000000000000000000000000
χ4644444444-4-4-4-4-444-4-444-4000000000000000000000000000000000000000000000000
χ47444-4-44-4-4-4-44400000000000000000000004i−4i00000000000000000000000000000000
χ48444-4-44-4-4-4-4440000000000000000000000−4i4i00000000000000000000000000000000
χ4944-44-4-44-4000004i−4i00−4i4i000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ5044-44-4-44-4000004i−4i00−4i4i00000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ5144-44-4-44-400000−4i4i004i−4i000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ5244-44-4-44-400000−4i4i004i−4i00000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ5344-4-44-4-4400004004-400-400000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ5444-4-44-4-4400004004-400-40000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ5544-4-44-4-440000-400-4400400000000000000002-2-222-2-22000000000000000000000000
χ5644-4-44-4-440000-400-440040000000000000000-222-2-222-2000000000000000000000000
χ574-444-4-4-44000004400-4-400000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ584-444-4-4-44000004400-4-40000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ594-444-4-4-4400000-4-4004400000000000000000000000002-22-2-22-220000000000000000
χ604-444-4-4-4400000-4-400440000000000000000000000000-22-222-22-20000000000000000
χ614-44-44-44-400004i00−4i−4i004i0000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000
χ624-44-44-44-400004i00−4i−4i004i000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000
χ634-44-44-44-40000−4i004i4i00−4i0000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ644-44-44-44-40000−4i004i4i00−4i000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ654-4-4-4-44444-4-440000000000004-4-440000000000000000000000000000000000000000
χ664-4-4-4-44444-4-44000000000000-444-40000000000000000000000000000000000000000
χ674-4-4-4-4444-444-4000000004-4-4400000000000000000000000000000000000000000000
χ684-4-4-4-4444-444-400000000-444-400000000000000000000000000000000000000000000

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