Finite Group Databasebeta

← Group #244151

Character table — Group #244151

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12224444224488888888888844448822444444888888888888888888888888444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-2000022-2-2000022-2-20000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-20000-2-2220000-2-2220000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222-2-2-2-222000022-2-20000-2-2220000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-2220000-2-222000022-2-20000000000000000000000000000
χ2122222222-2-2-2-22222-2-2-2-2222222-2-2-2-200000000000000000000000022-2-222-2-2000000000000
χ2222222222-2-2-2-22222-2-2-2-2222222-2-2-2-2000000000000000000000000-2-222-2-222000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-222-2-200000000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222220000000000000000-2-222-2-22200000000000000000000
χ2522222222-2-2-2-2-2-2-2-222222222-2-222-2-2000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-2-2-222222222-2-222-2-20000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-22200000000000000000000000022-2-2-2-222000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000-2-22222-2-2000000000000
χ292222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2-22-22i−2i000000000000000000000000000000002-200002i−2i0000
χ302222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2-22-22i−2i00000000000000000000000000000000-220000−2i2i0000
χ312222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-22-22−2i2i22-2-200002i2i−2i−2i00000000000000000000000000000000
χ322222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-22-22−2i2i-2-2220000−2i−2i2i2i00000000000000000000000000000000
χ332222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-22-222i−2i22-2-20000−2i−2i2i2i00000000000000000000000000000000
χ342222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-22-222i−2i-2-22200002i2i−2i−2i00000000000000000000000000000000
χ352222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i000000000000000000000000000000002-20000−2i2i0000
χ362222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i00000000000000000000000000000000-2200002i−2i0000
χ372222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2-2-22−2i2i00000000000000000000000000000000002-200002i−2i00
χ382222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2-2-22−2i2i0000000000000000000000000000000000-220000−2i2i00
χ392222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-222-22i−2i0000000000000000000000000000000000002-200002i−2i
χ402222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-222-22i−2i000000000000000000000000000000000000-220000−2i2i
χ412222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-222-2−2i2i0000000000000000000000000000000000002-20000−2i2i
χ422222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-222-2−2i2i000000000000000000000000000000000000-2200002i−2i
χ432222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2-2-222i−2i00000000000000000000000000000000002-20000−2i2i00
χ442222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2-2-222i−2i0000000000000000000000000000000000-2200002i−2i00
χ4522-2-2-2-2222-22-22i−2i2i−2i2i−2i2i−2i00000000000000002i−2i0000002-2i2−i2i2−i22−22−22−22−2i2−i2i2−i2000000000000
χ4622-2-2-2-2222-22-22i−2i2i−2i2i−2i2i−2i00000000000000002i−2i0000002-2−i2i2−i2i2−22−22−22−22−i2i2−i2i2000000000000
χ4722-2-2-2-2222-22-22i−2i2i−2i2i−2i2i−2i0000000000000000−2i2i000000-22i2−i2i2−i22−22−2−22−22−i2i2−i2i2000000000000
χ4822-2-2-2-2222-22-22i−2i2i−2i2i−2i2i−2i0000000000000000−2i2i000000-22−i2i2−i2i2−22−222−22−2i2−i2i2−i2000000000000
χ4922-2-2-2-2222-22-2−2i2i−2i2i−2i2i−2i2i00000000000000002i−2i000000-22i2−i2i2−i2−22−222−22−2−i2i2−i2i2000000000000
χ5022-2-2-2-2222-22-2−2i2i−2i2i−2i2i−2i2i00000000000000002i−2i000000-22−i2i2−i2i22−22−2−22−22i2−i2i2−i2000000000000
χ5122-2-2-2-2222-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000−2i2i0000002-2i2−i2i2−i2−22−22−22−22i2−i2i2−i2000000000000
χ5222-2-2-2-2222-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000−2i2i0000002-2−i2i2−i2i22−22−22−22−2−i2i2−i2i2000000000000
χ5322-2-2-2-222-22-222i−2i2i−2i−2i2i−2i2i000000000000002i−2i0000002-200i2−i2−i2i22−2−222−2−22i2−i2−i2i2000000000000
χ5422-2-2-2-222-22-222i−2i2i−2i−2i2i−2i2i000000000000002i−2i0000002-200−i2i2i2−i2−222−2−222−2−i2i2i2−i2000000000000
χ5522-2-2-2-222-22-222i−2i2i−2i−2i2i−2i2i00000000000000−2i2i000000-2200i2−i2−i2i22−2−22−222−2−i2i2i2−i2000000000000
χ5622-2-2-2-222-22-222i−2i2i−2i−2i2i−2i2i00000000000000−2i2i000000-2200−i2i2i2−i2−222−22−2−22i2−i2−i2i2000000000000
χ5722-2-2-2-222-22-22−2i2i−2i2i2i−2i2i−2i000000000000002i−2i000000-2200i2−i2−i2i2−222−22−2−22−i2i2i2−i2000000000000
χ5822-2-2-2-222-22-22−2i2i−2i2i2i−2i2i−2i000000000000002i−2i000000-2200−i2i2i2−i22−2−22−222−2i2−i2−i2i2000000000000
χ5922-2-2-2-222-22-22−2i2i−2i2i2i−2i2i−2i00000000000000−2i2i0000002-200i2−i2−i2i2−222−2−222−2i2−i2−i2i2000000000000
χ6022-2-2-2-222-22-22−2i2i−2i2i2i−2i2i−2i00000000000000−2i2i0000002-200−i2i2i2−i22−2−222−2−22−i2i2i2−i2000000000000
χ6144-4-444-4-44-4-444-4-444-4-44000000000000000000000000000000000000000000000000000000
χ6244-4-444-4-44-4-44-444-4-444-4000000000000000000000000000000000000000000000000000000
χ6344-4-444-4-4-444-44-4-44-444-4000000000000000000000000000000000000000000000000000000
χ6444-4-444-4-4-444-4-444-44-4-44000000000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i0000000000004ζ3−4ζ34ζ−4ζ0000002-22i−2i00002ζ−2ζ2ζ3−2ζ300000000000000000000000000000000
χ664-44-44i−4i4i−4i0000000000004ζ3−4ζ34ζ−4ζ000000-22−2i2i0000−2ζ2ζ−2ζ32ζ300000000000000000000000000000000
χ674-44-44i−4i4i−4i000000000000−4ζ34ζ3−4ζ4ζ0000002-22i−2i0000−2ζ2ζ−2ζ32ζ300000000000000000000000000000000
χ684-44-44i−4i4i−4i000000000000−4ζ34ζ3−4ζ4ζ000000-22−2i2i00002ζ−2ζ2ζ3−2ζ300000000000000000000000000000000
χ694-44-4−4i4i−4i4i0000000000004ζ−4ζ4ζ3−4ζ30000002-2−2i2i00002ζ3−2ζ32ζ−2ζ00000000000000000000000000000000
χ704-44-4−4i4i−4i4i0000000000004ζ−4ζ4ζ3−4ζ3000000-222i−2i0000−2ζ32ζ3−2ζ2ζ00000000000000000000000000000000
χ714-44-4−4i4i−4i4i000000000000−4ζ4ζ−4ζ34ζ30000002-2−2i2i0000−2ζ32ζ3−2ζ2ζ00000000000000000000000000000000
χ724-44-4−4i4i−4i4i000000000000−4ζ4ζ−4ζ34ζ3000000-222i−2i00002ζ3−2ζ32ζ−2ζ00000000000000000000000000000000
χ738-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000

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