Finite Group Databasebeta

← Group #211208

Character table — Group #211208

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444422224444444444888888884444888888888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ5111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-111
χ911111111-1-1-1-11-1-1-1-11111111111111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ1011111111-1-1-1-11-1-1-1-11111111111111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1
χ1111111111-1-1-1-11-1-1-1-11111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1211111111-1-1-1-11-1-1-1-11111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1311111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ1411111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111
χ1511111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1611111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1711-11-11-1-1ii−i−i1ii−i−i1-1-1-11-1111-1-11-1i−i11-1-1i−i11-1-1ii−i−ii−ii−i1-1i−iii−i−iii−i−i11-1-1ii−i−i11-1-111-1-11-1i−i1-1i−i
χ1811-11-11-1-1ii−i−i1ii−i−i1-1-1-11-1111-1-11-1i−i11-1-1i−i11-1-1ii−i−ii−ii−i1-1i−i−i−iii−i−iii11-1-1ii−i−i-1-111-1-111-11−ii-11−ii
χ1911-11-11-1-1ii−i−i1ii−i−i1-1-1-11-1111-1-11-1i−i11-1-1i−i-1-111−i−iiii−ii−i-11−iiii−i−i−i−iii-1-111−i−iii11-1-1-1-1111-1−ii-11i−i
χ2011-11-11-1-1ii−i−i1ii−i−i1-1-1-11-1111-1-11-1i−i11-1-1i−i-1-111−i−iiii−ii−i-11−ii−i−iiiii−i−i-1-111−i−iii-1-11111-1-1-11i−i1-1−ii
χ2111-11-11-1-1ii−i−i1ii−i−i1-1-1-11-11-1-1111-1i−i-1-111i−i11-1-1ii−i−i−ii−ii1-1i−iii−i−iii−i−i-1-111−i−iii11-1-111-1-1-11−ii-11−ii
χ2211-11-11-1-1ii−i−i1ii−i−i1-1-1-11-11-1-1111-1i−i-1-111i−i11-1-1ii−i−i−ii−ii1-1i−i−i−iii−i−iii-1-111−i−iii-1-111-1-1111-1i−i1-1i−i
χ2311-11-11-1-1ii−i−i1ii−i−i1-1-1-11-11-1-1111-1i−i-1-111i−i-1-111−i−iii−ii−ii-11−iiii−i−i−i−iii11-1-1ii−i−i11-1-1-1-111-11i−i1-1−ii
χ2411-11-11-1-1ii−i−i1ii−i−i1-1-1-11-11-1-1111-1i−i-1-111i−i-1-111−i−iii−ii−ii-11−ii−i−iiiii−i−i11-1-1ii−i−i-1-11111-1-11-1−ii-11i−i
χ2511-11-11-1-1−i−iii1−i−iii1-1-1-11-1111-1-11-1−ii11-1-1−ii11-1-1−i−iii−ii−ii1-1−iiii−i−iii−i−i11-1-1−i−iii-1-111-1-111-11i−i-11i−i
χ2611-11-11-1-1−i−iii1−i−iii1-1-1-11-1111-1-11-1−ii11-1-1−ii11-1-1−i−iii−ii−ii1-1−ii−i−iii−i−iii11-1-1−i−iii11-1-111-1-11-1−ii1-1−ii
χ2711-11-11-1-1−i−iii1−i−iii1-1-1-11-1111-1-11-1−ii11-1-1−ii-1-111ii−i−i−ii−ii-11i−iii−i−i−i−iii-1-111ii−i−i-1-11111-1-1-11−ii1-1i−i
χ2811-11-11-1-1−i−iii1−i−iii1-1-1-11-1111-1-11-1−ii11-1-1−ii-1-111ii−i−i−ii−ii-11i−i−i−iiiii−i−i-1-111ii−i−i11-1-1-1-1111-1i−i-11−ii
χ2911-11-11-1-1−i−iii1−i−iii1-1-1-11-11-1-1111-1−ii-1-111−ii11-1-1−i−iiii−ii−i1-1−iiii−i−iii−i−i-1-111ii−i−i-1-111-1-1111-1−ii1-1−ii
χ3011-11-11-1-1−i−iii1−i−iii1-1-1-11-11-1-1111-1−ii-1-111−ii11-1-1−i−iiii−ii−i1-1−ii−i−iii−i−iii-1-111ii−i−i11-1-111-1-1-11i−i-11i−i
χ3111-11-11-1-1−i−iii1−i−iii1-1-1-11-11-1-1111-1−ii-1-111−ii-1-111ii−i−ii−ii−i-11i−iii−i−i−i−iii11-1-1−i−iii-1-11111-1-11-1i−i-11−ii
χ3211-11-11-1-1−i−iii1−i−iii1-1-1-11-11-1-1111-1−ii-1-111−ii-1-111ii−i−ii−ii−i-11i−i−i−iiiii−i−i11-1-1−i−iii11-1-1-1-111-11−ii1-1i−i
χ332222222222222-2-2-2-2-2-222-2-222222-2-2-2-2-2-2-2-2220000000022-2-2000000000000000000000000000000000000
χ342222222222222-2-2-2-2-2-222-2-22-2-2-2-2-2-2-2-222222200000000-2-222000000000000000000000000000000000000
χ35222222222222-2222222-2-222-20000-2-2-2-20000-2-2222222220000-2-2-2-200000000000000000000000000000000
χ36222222222222-2222222-2-222-20000-2-2-2-20000-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2000022220000-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2000022220000-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ3922222222-2-2-2-222222-2-222-2-222222-2-222-2-2-2-2-2-200000000-2-222000000000000000000000000000000000000
χ4022222222-2-2-2-222222-2-222-2-22-2-2-2-2-2-2222222-2-20000000022-2-2000000000000000000000000000000000000
χ4122222222-2-2-2-2-22222-2-2-2-2-2-2-2000022-2-20000220000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ4222222222-2-2-2-2-22222-2-2-2-2-2-2-2000022-2-2000022000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ4322222222-2-2-2-2-2-2-2-2-222-2-222-20000-2-2220000222222-2-2-2-20000-2-22200000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-222-2-222-20000-2-222000022-2-2-2-22222000022-2-200000000000000000000000000000000
χ4522-22-22-2-22i2i−2i−2i2−2i−2i2i2i-22-2-2-22222-2-2-22−2i2i-2-2222i−2i000000002i−2i−2i2i000000000000000000000000000000000000
χ4622-22-22-2-22i2i−2i−2i2−2i−2i2i2i-22-2-2-222-2-222-22−2i2i22-2-22i−2i00000000−2i2i2i−2i000000000000000000000000000000000000
χ4722-22-22-2-22i2i−2i−2i-22i2i−2i−2i2-2222-2-20000-22−2i2i0000−2i2i22-2-22i2i−2i−2i0000-22−2i2i00000000000000000000000000000000
χ4822-22-22-2-22i2i−2i−2i-22i2i−2i−2i2-2222-2-20000-22−2i2i0000−2i2i-2-222−2i−2i2i2i00002-22i−2i00000000000000000000000000000000
χ4922-22-22-2-22i2i−2i−2i-2−2i−2i2i2i-2222-22-200002-22i−2i0000−2i2i0000000000000000000000002i−2i−2i2i-222-20000000000000000
χ5022-22-22-2-22i2i−2i−2i-2−2i−2i2i2i-2222-22-200002-22i−2i0000−2i2i000000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ5122-22-22-2-2−2i−2i2i2i22i2i−2i−2i-22-2-2-22222-2-2-222i−2i-2-222−2i2i00000000−2i2i2i−2i000000000000000000000000000000000000
χ5222-22-22-2-2−2i−2i2i2i22i2i−2i−2i-22-2-2-222-2-222-222i−2i22-2-2−2i2i000000002i−2i−2i2i000000000000000000000000000000000000
χ5322-22-22-2-2−2i−2i2i2i-22i2i−2i−2i-2222-22-200002-2−2i2i00002i−2i0000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ5422-22-22-2-2−2i−2i2i2i-22i2i−2i−2i-2222-22-200002-2−2i2i00002i−2i000000000000000000000000−2i2i2i−2i-222-20000000000000000
χ5522-22-22-2-2−2i−2i2i2i-2−2i−2i2i2i2-2222-2-20000-222i−2i00002i−2i22-2-2−2i−2i2i2i0000-222i−2i00000000000000000000000000000000
χ5622-22-22-2-2−2i−2i2i2i-2−2i−2i2i2i2-2222-2-20000-222i−2i00002i−2i-2-2222i2i−2i−2i00002-2−2i2i00000000000000000000000000000000
χ572-222-2-22-22i−2i2i−2i02i−2i2i−2i2-200-220000000000000002i−2i2i−2i2-22-200000000i2−i2i2−i22−22−2000000002−22−2i2−i2i2−i200000000
χ582-222-2-22-22i−2i2i−2i02i−2i2i−2i2-200-220000000000000002i−2i2i−2i2-22-200000000−i2i2−i2i2−22−2200000000−22−22−i2i2−i2i200000000
χ592-222-2-22-22i−2i2i−2i02i−2i2i−2i2-200-22000000000000000−2i2i−2i2i-22-2200000000i2−i2i2−i2−22−22000000002−22−2−i2i2−i2i200000000
χ602-222-2-22-22i−2i2i−2i02i−2i2i−2i2-200-22000000000000000−2i2i−2i2i-22-2200000000−i2i2−i2i22−22−200000000−22−22i2−i2i2−i200000000
χ612-222-2-22-2−2i2i−2i2i0−2i2i−2i2i2-200-220000000000000002i−2i2i−2i-22-2200000000i2−i2i2−i22−22−200000000−22−22−i2i2−i2i200000000
χ622-222-2-22-2−2i2i−2i2i0−2i2i−2i2i2-200-220000000000000002i−2i2i−2i-22-2200000000−i2i2−i2i2−22−22000000002−22−2i2−i2i2−i200000000
χ632-222-2-22-2−2i2i−2i2i0−2i2i−2i2i2-200-22000000000000000−2i2i−2i2i2-22-200000000i2−i2i2−i2−22−2200000000−22−22i2−i2i2−i200000000
χ642-222-2-22-2−2i2i−2i2i0−2i2i−2i2i2-200-22000000000000000−2i2i−2i2i2-22-200000000−i2i2−i2i22−22−2000000002−22−2−i2i2−i2i200000000
χ652-2-222-2-222-2-2202-2-222200-2-20000000000000002i−2i−2i2i−2i2i2i−2i000000002−2−22−i2i2i2−i2000000002−2−22i2−i2−i2i200000000
χ662-2-222-2-222-2-2202-2-222200-2-20000000000000002i−2i−2i2i−2i2i2i−2i00000000−222−2i2−i2−i2i200000000−222−2−i2i2i2−i200000000
χ672-2-222-2-222-2-2202-2-222200-2-2000000000000000−2i2i2i−2i2i−2i−2i2i000000002−2−22i2−i2−i2i2000000002−2−22−i2i2i2−i200000000
χ682-2-222-2-222-2-2202-2-222200-2-2000000000000000−2i2i2i−2i2i−2i−2i2i00000000−222−2−i2i2i2−i200000000−222−2i2−i2−i2i200000000
χ692-2-222-2-22-222-20-222-22200-2-20000000000000002i−2i−2i2i2i−2i−2i2i000000002−2−22−i2i2i2−i200000000−222−2−i2i2i2−i200000000
χ702-2-222-2-22-222-20-222-22200-2-20000000000000002i−2i−2i2i2i−2i−2i2i00000000−222−2i2−i2−i2i2000000002−2−22i2−i2−i2i200000000
χ712-2-222-2-22-222-20-222-22200-2-2000000000000000−2i2i2i−2i−2i2i2i−2i000000002−2−22i2−i2−i2i200000000−222−2i2−i2−i2i200000000
χ722-2-222-2-22-222-20-222-22200-2-2000000000000000−2i2i2i−2i−2i2i2i−2i00000000−222−2−i2i2i2−i2000000002−2−22−i2i2i2−i200000000
χ734-444-4-44-44i−4i4i−4i0−4i4i−4i4i-44004-4000000000000000000000000000000000000000000000000000000000000000
χ744-444-4-44-4−4i4i−4i4i04i−4i4i−4i-44004-4000000000000000000000000000000000000000000000000000000000000000
χ754-44-4-44-44000040000004-400-4000000004i−4i4i−4i00000000000000000000000000000000000000000000000000
χ764-44-4-44-44000040000004-400-400000000−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ774-44-4-44-440000-4000000-440044-44-40000000000000000000000000000000000000000000000000000000000
χ784-44-4-44-440000-4000000-44004-44-440000000000000000000000000000000000000000000000000000000000
χ794-4-444-4-444-4-440-444-4-4-40044000000000000000000000000000000000000000000000000000000000000000
χ804-4-444-4-44-444-404-4-44-4-40044000000000000000000000000000000000000000000000000000000000000000
χ814-4-4-4444-400004000000-4400-4000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ824-4-4-4444-400004000000-4400-400000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ834-4-4-4444-40000-40000004-40044-4-440000000000000000000000000000000000000000000000000000000000
χ844-4-4-4444-40000-40000004-4004-444-40000000000000000000000000000000000000000000000000000000000
χ85888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).