Finite Group Databasebeta

← Group #224621

Character table — Group #224621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222222224444444444444444444444444488888888888888888888888888816161616161616161616
order12222222444444444444444444444444444444888888884444444888888888888888888882444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111111111-1-111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1iiii−i−i−i−i1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i1-11-11-1ii−i−i
χ10111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1iiii−i−i−i−i1-1-1-1-111−i−iiiii−i−iiiii−i−i−i−i−i−iii-11-11-11−i−iii
χ11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1−i−i−i−iiiii1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii1-11-11-1−i−iii
χ12111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1−i−i−i−iiiii1-1-1-1-111ii−i−i−i−iii−i−i−i−iiiiiii−i−i-11-11-11ii−i−i
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111iiii−i−i−i−i11111-1-1ii−i−iii−i−i−i−i−i−iiiiiii−i−i-111-1-11−i−iii
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111iiii−i−i−i−i111-1-111−i−iiiii−i−i−i−i−i−iiiii−i−iii1-1-111-1ii−i−i
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111−i−i−i−iiiii11111-1-1−i−iii−i−iiiiiii−i−i−i−i−i−iii-111-1-11ii−i−i
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111−i−i−i−iiiii111-1-111ii−i−i−i−iiiiiii−i−i−i−iii−i−i1-1-111-1−i−iii
χ1711111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-11-1
χ1811111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-11-11
χ1911111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-111-1-1111111-1-1-1-111-11-11
χ2011111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-11-11-1
χ2111111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-111111111-11-111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-11-11
χ2211111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111111-11-1
χ2311111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111111-1-111-1-1111111-1-1-1-11-11-1
χ2411111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-11-11
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1iiii−i−i−i−i-11-111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iii-11-111-1i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1iiii−i−i−i−i-11-1-1-111−i−iii−i−iiiii−i−i−i−iiiii−i−i1-11-1-11−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−i−i−iiiii-11-111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i-11-111-1−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−i−i−iiiii-11-1-1-111ii−i−iii−i−i−i−iiiii−i−i−i−iii1-11-1-11i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111iiii−i−i−i−i-1-1111-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iii1-1-11-11−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111iiii−i−i−i−i-1-11-1-111−i−iii−i−iii−i−iiiii−i−iii−i−i-111-11-1i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111−i−i−i−iiiii-1-1111-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−i1-1-11-11i−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111−i−i−i−iiiii-1-11-1-111ii−i−iii−i−iii−i−i−i−iii−i−iii-111-11-1−iii−i
χ3322222222222222-2-222-2-2-2-222-2-22222-2-222-2-22200000000-2-2-20000000000000000000000000000000000
χ3422222222222222-2-222-2-2-2-2-2-222-2-222-2-2-2-222-2-200000000-2220000000000000000000000000000000000
χ35222222222222-2-222-2-222-2-222-2-2-2-2-2-22222-2-2-2-200000000-2220000000000000000000000000000000000
χ36222222222222-2-222-2-222-2-2-2-22222-2-222-2-2222200000000-2-2-20000000000000000000000000000000000
χ3722222222-2-2-2-222-2-222-2-2-2-222-2-2-2-2-2-222-2-222220000000022-20000000000000000000000000000000000
χ3822222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-22222-2-2-2-2000000002-220000000000000000000000000000000000
χ3922222222-2-2-2-2-2-222-2-222-2-222-2-22222-2-2-2-222-2-2000000002-220000000000000000000000000000000000
χ4022222222-2-2-2-2-2-222-2-222-2-2-2-222-2-222-2-222-2-2220000000022-20000000000000000000000000000000000
χ4122-2-222-2-2000022-2-2-2-2222-2000000000000000022-2-222-2-20002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ4222-2-222-2-2000022-2-2-2-2222-2000000000000000022-2-222-2-2000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ4322-2-222-2-2000022-2-2-2-2222-20000000000000000-2-222-2-2220002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ4422-2-222-2-2000022-2-2-2-2222-20000000000000000-2-222-2-222000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ4522-2-222-2-20000-2-22222-2-22-200000000000000002i2i−2i−2i−2i−2i2i2i0002i−2i−2i2i-222-200000000000000000000000000
χ4622-2-222-2-20000-2-22222-2-22-200000000000000002i2i−2i−2i−2i−2i2i2i000−2i2i2i−2i2-2-2200000000000000000000000000
χ4722-2-222-2-20000-2-22222-2-22-20000000000000000−2i−2i2i2i2i2i−2i−2i0002i−2i−2i2i2-2-2200000000000000000000000000
χ4822-2-222-2-20000-2-22222-2-22-20000000000000000−2i−2i2i2i2i2i−2i−2i000−2i2i2i−2i-222-200000000000000000000000000
χ492-22-22-22-222-2-2002i−2i002i−2i00002-22i−2i002i−2i002-22i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000001+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ502-22-22-22-222-2-2002i−2i002i−2i00002-22i−2i002i−2i002-22i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ512-22-22-22-222-2-2002i−2i002i−2i0000-22−2i2i002i−2i00-22−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000001+i−1−i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ522-22-22-22-222-2-2002i−2i002i−2i0000-22−2i2i002i−2i00-22−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000−1−i1+i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ532-22-22-22-222-2-200−2i2i00−2i2i00002-2−2i2i00−2i2i002-2−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000001−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ542-22-22-22-222-2-200−2i2i00−2i2i00002-2−2i2i00−2i2i002-2−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ552-22-22-22-222-2-200−2i2i00−2i2i0000-222i−2i00−2i2i00-222i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000001−i−1+i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ562-22-22-22-222-2-200−2i2i00−2i2i0000-222i−2i00−2i2i00-222i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000−1+i1−i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ572-22-22-22-2-2-222002i−2i002i−2i00002-2−2i2i00−2i2i00-222i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000−1−i1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ582-22-22-22-2-2-222002i−2i002i−2i00002-2−2i2i00−2i2i00-222i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000001+i−1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ592-22-22-22-2-2-222002i−2i002i−2i0000-222i−2i00−2i2i002-2−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000−1−i1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ602-22-22-22-2-2-222002i−2i002i−2i0000-222i−2i00−2i2i002-2−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000001+i−1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ612-22-22-22-2-2-22200−2i2i00−2i2i00002-22i−2i002i−2i00-22−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000−1+i1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ622-22-22-22-2-2-22200−2i2i00−2i2i00002-22i−2i002i−2i00-22−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000001−i−1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ632-22-22-22-2-2-22200−2i2i00−2i2i0000-22−2i2i002i−2i002-22i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000−1+i1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ642-22-22-22-2-2-22200−2i2i00−2i2i0000-22−2i2i002i−2i002-22i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000001−i−1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ6544-4-444-4-400004444-4-4-4-4-440000000000000000000000000000000000000000000000000000000000000
χ6644-4-444-4-40000-4-4-4-44444-440000000000000000000000000000000000000000000000000000000000000
χ6744-4-4-4-4444i−4i4i−4i00000000004i−4i000000004-40000000000000000000000000000000000000000000000000
χ6844-4-4-4-4444i−4i4i−4i0000000000−4i4i00000000-440000000000000000000000000000000000000000000000000
χ6944-4-4-4-444−4i4i−4i4i00000000004i−4i00000000-440000000000000000000000000000000000000000000000000
χ7044-4-4-4-444−4i4i−4i4i0000000000−4i4i000000004-40000000000000000000000000000000000000000000000000
χ714-44-4-44-4400004i−4i004i−4i0000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000
χ724-44-4-44-4400004i−4i004i−4i000000000000000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000
χ734-44-4-44-440000−4i4i00−4i4i0000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000
χ744-44-4-44-440000−4i4i00−4i4i000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000
χ754-4-444-4-440000004i−4i00−4i4i0000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000
χ764-4-444-4-440000004i−4i00−4i4i000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000
χ774-4-444-4-44000000−4i4i004i−4i0000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000
χ784-4-444-4-44000000−4i4i004i−4i000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000
χ794-4-44-444-44i−4i−4i4i4i−4i00−4i4i00000000004-400000000000000000000000000000000000000000000000000000
χ804-4-44-444-44i−4i−4i4i−4i4i004i−4i0000000000-4400000000000000000000000000000000000000000000000000000
χ814-4-44-444-4−4i4i4i−4i4i−4i00−4i4i0000000000-4400000000000000000000000000000000000000000000000000000
χ824-4-44-444-4−4i4i4i−4i−4i4i004i−4i00000000004-400000000000000000000000000000000000000000000000000000
χ838888-8-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000

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