Finite Group Databasebeta

← Group #135679

Character table — Group #135679

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444224444444444888888888888161616161616161616161616161616164444888816161616161616168888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-2-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-22222-2-2000000000000000000000000
χ2122222222-2-2-2-22222-2-2-2-20000000000002222−2−2−2−22222−2−2−2−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i20000000000000000
χ2222222222-2-2-2-22222-2-2-2-20000000000002222−2−2−2−22222−2−2−2−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i20000000000000000
χ2322222222-2-2-2-22222-2-2-2-2000000000000−2−2−2−22222−2−2−2−222222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i20000000000000000
χ2422222222-2-2-2-22222-2-2-2-2000000000000−2−2−2−22222−2−2−2−22222−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i20000000000000000
χ2522222222-2-2-2-2-2-2-2-222220000000000002222−2−2−2−2−2−2−2−222222i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i20000000000000000
χ2622222222-2-2-2-2-2-2-2-222220000000000002222−2−2−2−2−2−2−2−22222−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i20000000000000000
χ2722222222-2-2-2-2-2-2-2-22222000000000000−2−2−2−222222222−2−2−2−22i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i20000000000000000
χ2822222222-2-2-2-2-2-2-2-22222000000000000−2−2−2−222222222−2−2−2−2−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i20000000000000000
χ292222-2-2-2-222-2-222-2-222-2-2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002i−2i2i−2i2−22−22−22−20000000000000000
χ302222-2-2-2-222-2-222-2-222-2-2000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−2i2i−2i2i−22−22−22−220000000000000000
χ312222-2-2-2-222-2-222-2-222-2-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002i−2i2i−2i−22−22−22−220000000000000000
χ322222-2-2-2-222-2-222-2-222-2-2000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−2i2i−2i2i2−22−22−22−20000000000000000
χ332222-2-2-2-222-2-2-2-222-2-222000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002i−2i−2i2i2−22−2−22−220000000000000000
χ342222-2-2-2-222-2-2-2-222-2-222000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000−2i2i2i−2i−22−222−22−20000000000000000
χ352222-2-2-2-222-2-2-2-222-2-222000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002i−2i−2i2i−22−222−22−20000000000000000
χ362222-2-2-2-222-2-2-2-222-2-222000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−2i2i2i−2i2−22−2−22−220000000000000000
χ372222-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-222-2-20000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ382222-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-222-2-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ392222-2-2-2-2-2-22222-2-2-2-222-2-2-2-22222-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ402222-2-2-2-2-2-22222-2-2-2-222-2-2-2-22222-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ412222-2-2-2-2-2-222-2-22222-2-22222-2-2-2-2-2-2220000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ422222-2-2-2-2-2-222-2-22222-2-22222-2-2-2-2-2-222000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ432222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2222222-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ442222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2222222-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ4522-2-222-2-22-22-22i−2i2i−2i2i−2i2i−2i22-2-222-2-22i−2i2i−2i000000000000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ2
χ4622-2-222-2-22-22-22i−2i2i−2i2i−2i2i−2i22-2-222-2-22i−2i2i−2i00000000000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ2
χ4722-2-222-2-22-22-22i−2i2i−2i2i−2i2i−2i-2-222-2-222−2i2i−2i2i0000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ200000000
χ4822-2-222-2-22-22-22i−2i2i−2i2i−2i2i−2i-2-222-2-222−2i2i−2i2i000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ200000000
χ4922-2-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i22-2-222-2-2−2i2i−2i2i000000000000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ6
χ5022-2-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i22-2-222-2-2−2i2i−2i2i00000000000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ6
χ5122-2-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i-2-222-2-2222i−2i2i−2i0000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ600000000
χ5222-2-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i-2-222-2-2222i−2i2i−2i000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ600000000
χ5322-2-2-2-222-222-22i−2i−2i2i−2i2i2i−2i22-2-2-2-2222i−2i−2i2i000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ6000000000000
χ5422-2-2-2-222-222-22i−2i−2i2i−2i2i2i−2i22-2-2-2-2222i−2i−2i2i00000000000000000000000000000000−2ζ22ζ2−2ζ62ζ6000000000000
χ5522-2-2-2-222-222-22i−2i−2i2i−2i2i2i−2i-2-22222-2-2−2i2i2i−2i00000000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ20000
χ5622-2-2-2-222-222-22i−2i−2i2i−2i2i2i−2i-2-22222-2-2−2i2i2i−2i0000000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ20000
χ5722-2-2-2-222-222-2−2i2i2i−2i2i−2i−2i2i22-2-2-2-222−2i2i2i−2i000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ2000000000000
χ5822-2-2-2-222-222-2−2i2i2i−2i2i−2i−2i2i22-2-2-2-222−2i2i2i−2i00000000000000000000000000000000−2ζ62ζ6−2ζ22ζ2000000000000
χ5922-2-2-2-222-222-2−2i2i2i−2i2i−2i−2i2i-2-22222-2-22i−2i−2i2i00000000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ60000
χ6022-2-2-2-222-222-2−2i2i2i−2i2i−2i−2i2i-2-22222-2-22i−2i−2i2i0000000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ60000
χ6144-4-444-4-4-44-444i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-44-44−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ6344-4-4-4-4444-4-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-4-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i0000000000002i2−2i22i2−2i222−2222−2200002ζ+2ζ3−2ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ72ζ−2ζ3−2ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000000000000000
χ664-44-44i−4i4i−4i0000000000002i2−2i22i2−2i222−2222−220000−2ζ−2ζ32ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ7−2ζ+2ζ32ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000000000000000
χ674-44-44i−4i4i−4i000000000000−2i22i2−2i22i2−2222−222200002ζ5−2ζ7−2ζ5+2ζ7−2ζ+2ζ32ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ−2ζ32ζ+2ζ30000000000000000000000000000000000000000
χ684-44-44i−4i4i−4i000000000000−2i22i2−2i22i2−2222−22220000−2ζ5+2ζ72ζ5−2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ+2ζ3−2ζ−2ζ30000000000000000000000000000000000000000
χ694-44-4−4i4i−4i4i0000000000002i2−2i22i2−2i2−2222−222200002ζ−2ζ3−2ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ−2ζ32ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ70000000000000000000000000000000000000000
χ704-44-4−4i4i−4i4i0000000000002i2−2i22i2−2i2−2222−22220000−2ζ+2ζ32ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ+2ζ3−2ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ70000000000000000000000000000000000000000
χ714-44-4−4i4i−4i4i000000000000−2i22i2−2i22i222−2222−2200002ζ5+2ζ7−2ζ5−2ζ72ζ+2ζ3−2ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ+2ζ32ζ−2ζ30000000000000000000000000000000000000000
χ724-44-4−4i4i−4i4i000000000000−2i22i2−2i22i222−2222−220000−2ζ5−2ζ72ζ5+2ζ7−2ζ−2ζ32ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ−2ζ3−2ζ+2ζ30000000000000000000000000000000000000000
χ734-4-444i−4i−4i4i0000000000002i2−2i2−2i22i222−22−22220000000000002ζ5−2ζ7−2ζ5+2ζ72ζ−2ζ3−2ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ72ζ+2ζ3−2ζ−2ζ300000000000000000000000000000000
χ744-4-444i−4i−4i4i0000000000002i2−2i2−2i22i222−22−2222000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ+2ζ32ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ7−2ζ−2ζ32ζ+2ζ300000000000000000000000000000000
χ754-4-444i−4i−4i4i000000000000−2i22i22i2−2i2−222222−220000000000002ζ+2ζ3−2ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000
χ764-4-444i−4i−4i4i000000000000−2i22i22i2−2i2−222222−22000000000000−2ζ−2ζ32ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ+2ζ32ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000
χ774-4-44−4i4i4i−4i0000000000002i2−2i2−2i22i2−222222−220000000000002ζ5+2ζ7−2ζ5−2ζ7−2ζ−2ζ32ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ72ζ−2ζ3−2ζ+2ζ300000000000000000000000000000000
χ784-4-44−4i4i4i−4i0000000000002i2−2i2−2i22i2−222222−22000000000000−2ζ5−2ζ72ζ5+2ζ72ζ+2ζ3−2ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ7−2ζ+2ζ32ζ−2ζ300000000000000000000000000000000
χ794-4-44−4i4i4i−4i000000000000−2i22i22i2−2i222−22−22220000000000002ζ−2ζ3−2ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ7−2ζ−2ζ32ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000
χ804-4-44−4i4i4i−4i000000000000−2i22i22i2−2i222−22−2222000000000000−2ζ+2ζ32ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ72ζ+2ζ3−2ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.