Finite Group Databasebeta

← Group #244113

Character table — Group #244113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12224444888888882244888844448888222244444444888888888888888888888888888824448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-111
χ41111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1
χ511111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1
χ611111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1111-1-1
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-111
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-111
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1
χ17222222222222222222222222-2-2-2-2-2-2-2-20000000022-2-20000000022-2-2000000000000000000000000
χ18222222222222222222222222-2-2-2-2-2-2-2-200000000-2-22200000000-2-222000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-222-2-222-2-20000000000000000000000000000000022-2-222-2-200000000
χ202222222222222222-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000-2-222-2-22200000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000022-2-222-2-20000000000000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000-2-222-2-2220000000000000000
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000022-2-200000000-2-222000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000-2-2220000000022-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2220000000000000000000000000000000022-2-2-2-22200000000
χ2622222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000-2-22222-2-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000022-2-2-2-2220000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000-2-22222-2-20000000000000000
χ292222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-22i2i−2i−2i2-22-22i−2i2i−2i002200-2-2000000002i2i−2i−2i0000000000000000000000000000
χ302222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-22i2i−2i−2i2-22-22i−2i2i−2i00-2-2002200000000−2i−2i2i2i0000000000000000000000000000
χ312222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-22i2i−2i−2i-22-22−2i2i−2i2i2200-2-20000002i2i−2i−2i00000000000000000000000000000000
χ322222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-22i2i−2i−2i-22-22−2i2i−2i2i-2-20022000000−2i−2i2i2i00000000000000000000000000000000
χ332222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i2-2-222i−2i−2i2i0000000000000000000000000000000000000000200-2002i−2i
χ342222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i2-2-222i−2i−2i2i0000000000000000000000000000000000000000-200200−2i2i
χ352222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i-222-2−2i2i2i−2i000000000000000000000000000000000000000002-202i−2i00
χ362222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i-222-2−2i2i2i−2i00000000000000000000000000000000000000000-220−2i2i00
χ372222-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-2−2i−2i2i2i2-22-2−2i2i−2i2i002200-2-200000000−2i−2i2i2i0000000000000000000000000000
χ382222-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-2−2i−2i2i2i2-22-2−2i2i−2i2i00-2-20022000000002i2i−2i−2i0000000000000000000000000000
χ392222-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-2−2i−2i2i2i-22-222i−2i2i−2i2200-2-2000000−2i−2i2i2i00000000000000000000000000000000
χ402222-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-2−2i−2i2i2i-22-222i−2i2i−2i-2-200220000002i2i−2i−2i00000000000000000000000000000000
χ412222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i2-2-22−2i2i2i−2i0000000000000000000000000000000000000000200-200−2i2i
χ422222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i2-2-22−2i2i2i−2i0000000000000000000000000000000000000000-2002002i−2i
χ432222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i-222-22i−2i−2i2i000000000000000000000000000000000000000002-20−2i2i00
χ442222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i-222-22i−2i−2i2i00000000000000000000000000000000000000000-2202i−2i00
χ452-2-2222-2-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i0000000000000000002-200000000002i−2i2−22−2i2−i2i2−i22−22−2i2−i2i2−i200000000
χ462-2-2222-2-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i0000000000000000002-200000000002i−2i−22−22−i2i2−i2i2−22−22−i2i2−i2i200000000
χ472-2-2222-2-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i000000000000000000-220000000000−2i2i2−22−2i2−i2i2−i2−22−22−i2i2−i2i200000000
χ482-2-2222-2-22i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i000000000000000000-220000000000−2i2i−22−22−i2i2−i2i22−22−2i2−i2i2−i200000000
χ492-2-2222-2-22i2i−2i−2i2i2i−2i−2i-22-22−2i2i−2i2i00000000000000002-200000000002i−2i002−2−22i2−i2−i2i22−2−22i2−i2−i2i200000000
χ502-2-2222-2-22i2i−2i−2i2i2i−2i−2i-22-22−2i2i−2i2i00000000000000002-200000000002i−2i00−222−2−i2i2i2−i2−222−2−i2i2i2−i200000000
χ512-2-2222-2-22i2i−2i−2i2i2i−2i−2i-22-22−2i2i−2i2i0000000000000000-220000000000−2i2i002−2−22i2−i2−i2i2−222−2−i2i2i2−i200000000
χ522-2-2222-2-22i2i−2i−2i2i2i−2i−2i-22-22−2i2i−2i2i0000000000000000-220000000000−2i2i00−222−2−i2i2i2−i22−2−22i2−i2−i2i200000000
χ532-2-2222-2-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i0000000000000000002-20000000000−2i2i2−22−2−i2i2−i2i22−22−2−i2i2−i2i200000000
χ542-2-2222-2-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i0000000000000000002-20000000000−2i2i−22−22i2−i2i2−i2−22−22i2−i2i2−i200000000
χ552-2-2222-2-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i000000000000000000-2200000000002i−2i2−22−2−i2i2−i2i2−22−22i2−i2i2−i200000000
χ562-2-2222-2-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i000000000000000000-2200000000002i−2i−22−22i2−i2i2−i22−22−2−i2i2−i2i200000000
χ572-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-22-222i−2i2i−2i00000000000000002-20000000000−2i2i002−2−22−i2i2i2−i22−2−22−i2i2i2−i200000000
χ582-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-22-222i−2i2i−2i00000000000000002-20000000000−2i2i00−222−2i2−i2−i2i2−222−2i2−i2−i2i200000000
χ592-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-22-222i−2i2i−2i0000000000000000-2200000000002i−2i002−2−22−i2i2i2−i2−222−2i2−i2−i2i200000000
χ602-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-22-222i−2i2i−2i0000000000000000-2200000000002i−2i00−222−2i2−i2−i2i22−2−22−i2i2i2−i200000000
χ6144-4-44i−4i4i−4i4ζ−4ζ4ζ−4ζ4ζ3−4ζ34ζ3−4ζ30000000000000000002-2002i−2i000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ6244-4-44i−4i4i−4i4ζ−4ζ4ζ−4ζ4ζ3−4ζ34ζ3−4ζ3000000000000000000-2200−2i2i00000000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ6344-4-44i−4i4i−4i−4ζ4ζ−4ζ4ζ−4ζ34ζ3−4ζ34ζ30000000000000000002-2002i−2i00000000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ6444-4-44i−4i4i−4i−4ζ4ζ−4ζ4ζ−4ζ34ζ3−4ζ34ζ3000000000000000000-2200−2i2i000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ6544-4-4−4i4i−4i4i4ζ3−4ζ34ζ3−4ζ34ζ−4ζ4ζ−4ζ0000000000000000002-200−2i2i000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ6644-4-4−4i4i−4i4i4ζ3−4ζ34ζ3−4ζ34ζ−4ζ4ζ−4ζ000000000000000000-22002i−2i00000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ6744-4-4−4i4i−4i4i−4ζ34ζ3−4ζ34ζ3−4ζ4ζ−4ζ4ζ0000000000000000002-200−2i2i00000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ6844-4-4−4i4i−4i4i−4ζ34ζ3−4ζ34ζ3−4ζ4ζ−4ζ4ζ000000000000000000-22002i−2i000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ694-44-44i−4i−4i4i4ζ3−4ζ3−4ζ34ζ3−4ζ4ζ4ζ−4ζ00000000000000002-2002i−2i0000002ζ3−2ζ32ζ−2ζ00000000000000000000000000000000
χ704-44-44i−4i−4i4i4ζ3−4ζ3−4ζ34ζ3−4ζ4ζ4ζ−4ζ0000000000000000-2200−2i2i000000−2ζ32ζ3−2ζ2ζ00000000000000000000000000000000
χ714-44-44i−4i−4i4i−4ζ34ζ34ζ3−4ζ34ζ−4ζ−4ζ4ζ00000000000000002-2002i−2i000000−2ζ32ζ3−2ζ2ζ00000000000000000000000000000000
χ724-44-44i−4i−4i4i−4ζ34ζ34ζ3−4ζ34ζ−4ζ−4ζ4ζ0000000000000000-2200−2i2i0000002ζ3−2ζ32ζ−2ζ00000000000000000000000000000000
χ734-44-4−4i4i4i−4i4ζ−4ζ−4ζ4ζ−4ζ34ζ34ζ3−4ζ300000000000000002-200−2i2i0000002ζ−2ζ2ζ3−2ζ300000000000000000000000000000000
χ744-44-4−4i4i4i−4i4ζ−4ζ−4ζ4ζ−4ζ34ζ34ζ3−4ζ30000000000000000-22002i−2i000000−2ζ2ζ−2ζ32ζ300000000000000000000000000000000
χ754-44-4−4i4i4i−4i−4ζ4ζ4ζ−4ζ4ζ3−4ζ3−4ζ34ζ300000000000000002-200−2i2i000000−2ζ2ζ−2ζ32ζ300000000000000000000000000000000
χ764-44-4−4i4i4i−4i−4ζ4ζ4ζ−4ζ4ζ3−4ζ3−4ζ34ζ30000000000000000-22002i−2i0000002ζ−2ζ2ζ3−2ζ300000000000000000000000000000000
χ774-4-44-4-44444-4-4-4-4444-4-444-4-4400000000000000000000000000000000000000000000000000000000
χ784-4-44-4-44444-4-4-4-444-444-4-444-400000000000000000000000000000000000000000000000000000000
χ794-4-44-4-444-4-44444-4-44-4-44-444-400000000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-4-44444-4-4-444-44-4-4400000000000000000000000000000000000000000000000000000000

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