Finite Group Databasebeta

← Group #224166

Character table — Group #224166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222222224444444444444444444444444488888888888888888888888888816161616161616161616
order12222222444444444444444444444444444444888888882244444888888888888888888884444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-111111111111111-1-111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1iiii−i−i−i−i11-1-1-11-1ii−i−iii−i−iiiii−i−i−i−iii−i−i1-11-11-1ii−i−i
χ10111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1iiii−i−i−i−i-1-111-11-1−i−iiiii−i−iiiii−i−i−i−i−i−iii-11-11-11−i−iii
χ11111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1−i−i−i−iiiii11-1-1-11-1−i−iii−i−iii−i−i−i−iiiii−i−iii1-11-11-1−i−iii
χ12111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1−i−i−i−iiiii-1-111-11-1ii−i−i−i−iii−i−i−i−iiiiiii−i−i-11-11-11ii−i−i
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i11-1-1111ii−i−iii−i−i−i−i−i−iiiiiii−i−i-111-1-11−i−iii
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i-1-111111−i−iiiii−i−i−i−i−i−iiiii−i−iii1-1-111-1ii−i−i
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiii11-1-1111−i−iii−i−iiiiiii−i−i−i−i−i−iii-111-1-11ii−i−i
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiii-1-111111ii−i−i−i−iiiiiii−i−i−i−iii−i−i1-1-111-1−i−iii
χ1711111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111111111111111-1-111111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-11-11-1
χ1811111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-11-11
χ1911111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11-1-1-1-11111-1-111-1-111111111-1-1-1-1-11-11
χ2011111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-111111-11-1
χ2111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-11111111111111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-11-11
χ2211111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-11-11-1
χ2311111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1111-11-1
χ2411111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111111-1-111-1-1-1-1-1-11111-1-1-11-11
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1iiii−i−i−i−i11-1-11-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iii1-1-11-11i−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-1-1111-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-11-1−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−i−i−iiiii11-1-11-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i1-1-11-11−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-1-1111-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iii-111-11-1i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111iiii−i−i−i−i11-1-1-1-11ii−i−i−i−iii−i−iiiii−i−i−i−iii-11-111-1−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111iiii−i−i−i−i-1-111-1-11−i−iii−i−iii−i−iiiii−i−iii−i−i1-11-1-11i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111−i−i−i−iiiii11-1-1-1-11−i−iiiii−i−iii−i−i−i−iiiii−i−i-11-111-1i−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111−i−i−i−iiiii-1-111-1-11ii−i−iii−i−iii−i−i−i−iii−i−iii1-11-1-11−iii−i
χ3322222222222222-2-222-2-2-2-222-2-222-2-22222-2-222000000000000-2-2-2000000000000000000000000000000
χ3422222222222222-2-222-2-2-2-222-2-2-2-222-2-2-2-222-2-20000000000002-22000000000000000000000000000000
χ35222222222222-2-222-2-222-2-2-2-22222-2-2-2-222-2-2-2-20000000000002-22000000000000000000000000000000
χ36222222222222-2-222-2-222-2-2-2-222-2-22222-2-22222000000000000-2-2-2000000000000000000000000000000
χ3722222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-2-2-2222200000000000022-2000000000000000000000000000000
χ3822222222-2-2-2-222-2-222-2-2-2-2-2-222-2-2222222-2-2-2-2000000000000-222000000000000000000000000000000
χ3922222222-2-2-2-2-2-222-2-222-2-222-2-222-2-222-2-222-2-2000000000000-222000000000000000000000000000000
χ4022222222-2-2-2-2-2-222-2-222-2-222-2-2-2-222-2-222-2-22200000000000022-2000000000000000000000000000000
χ412222-2-2-2-200002222-2-2-2-22-2000000000000000022-2-222-2-22-22-20002-22-200000000000000000000000000
χ422222-2-2-2-200002222-2-2-2-22-2000000000000000022-2-222-2-2-22-22000-22-2200000000000000000000000000
χ432222-2-2-2-200002222-2-2-2-22-20000000000000000-2-222-2-2222-22-2000-22-2200000000000000000000000000
χ442222-2-2-2-200002222-2-2-2-22-20000000000000000-2-222-2-222-22-220002-22-200000000000000000000000000
χ452222-2-2-2-20000-2-2-2-222222-200000000000000002i2i−2i−2i−2i−2i2i2i2-2-220002i−2i−2i2i00000000000000000000000000
χ462222-2-2-2-20000-2-2-2-222222-200000000000000002i2i−2i−2i−2i−2i2i2i-222-2000−2i2i2i−2i00000000000000000000000000
χ472222-2-2-2-20000-2-2-2-222222-20000000000000000−2i−2i2i2i2i2i−2i−2i2-2-22000−2i2i2i−2i00000000000000000000000000
χ482222-2-2-2-20000-2-2-2-222222-20000000000000000−2i−2i2i2i2i2i−2i−2i-222-20002i−2i−2i2i00000000000000000000000000
χ4922-2-22-22-222-2-2002i−2i002i−2i00002i−2i002i−2i2-2002i−2i2-21+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
χ5022-2-22-22-222-2-2002i−2i002i−2i00002i−2i002i−2i2-2002i−2i2-2−1−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
χ5122-2-22-22-222-2-2002i−2i002i−2i00002i−2i00−2i2i-2200−2i2i-221+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
χ5222-2-22-22-222-2-2002i−2i002i−2i00002i−2i00−2i2i-2200−2i2i-22−1−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
χ5322-2-22-22-222-2-200−2i2i00−2i2i0000−2i2i002i−2i-22002i−2i-221−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
χ5422-2-22-22-222-2-200−2i2i00−2i2i0000−2i2i002i−2i-22002i−2i-22−1+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
χ5522-2-22-22-222-2-200−2i2i00−2i2i0000−2i2i00−2i2i2-200−2i2i2-21−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
χ5622-2-22-22-222-2-200−2i2i00−2i2i0000−2i2i00−2i2i2-200−2i2i2-2−1+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
χ5722-2-22-22-2-2-222002i−2i002i−2i0000−2i2i002i−2i-2200−2i2i2-21+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
χ5822-2-22-22-2-2-222002i−2i002i−2i0000−2i2i002i−2i-2200−2i2i2-2−1−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
χ5922-2-22-22-2-2-222002i−2i002i−2i0000−2i2i00−2i2i2-2002i−2i-221+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
χ6022-2-22-22-2-2-222002i−2i002i−2i0000−2i2i00−2i2i2-2002i−2i-22−1−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
χ6122-2-22-22-2-2-22200−2i2i00−2i2i00002i−2i002i−2i2-200−2i2i-221−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
χ6222-2-22-22-2-2-22200−2i2i00−2i2i00002i−2i002i−2i2-200−2i2i-22−1+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
χ6322-2-22-22-2-2-22200−2i2i00−2i2i00002i−2i00−2i2i-22002i−2i2-21−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
χ6422-2-22-22-2-2-22200−2i2i00−2i2i00002i−2i00−2i2i-22002i−2i2-2−1+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
χ654444-4-4-4-4000044-4-4-4-444-440000000000000000000000000000000000000000000000000000000000000
χ664444-4-4-4-40000-4-44444-4-4-440000000000000000000000000000000000000000000000000000000000000
χ6744-4-4-44-440000004i−4i00−4i4i0000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000
χ6844-4-4-44-440000004i−4i00−4i4i000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000
χ6944-4-4-44-44000000−4i4i004i−4i0000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000
χ7044-4-4-44-44000000−4i4i004i−4i000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000
χ714-44-44-4-444i−4i4i−4i4i−4i004i−4i00004-400000000000000000000000000000000000000000000000000000000000
χ724-44-44-4-444i−4i4i−4i−4i4i00−4i4i0000-4400000000000000000000000000000000000000000000000000000000000
χ734-44-44-4-44−4i4i−4i4i4i−4i004i−4i0000-4400000000000000000000000000000000000000000000000000000000000
χ744-44-44-4-44−4i4i−4i4i−4i4i00−4i4i00004-400000000000000000000000000000000000000000000000000000000000
χ754-44-4-444-400004i−4i00−4i4i0000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000
χ764-44-4-444-400004i−4i00−4i4i000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000
χ774-44-4-444-40000−4i4i004i−4i0000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000
χ784-44-4-444-40000−4i4i004i−4i000000000000000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000
χ794-4-4444-4-44i−4i−4i4i000000000000004-400004i−4i0000000000000000000000000000000000000000000000000
χ804-4-4444-4-44i−4i−4i4i00000000000000-440000−4i4i0000000000000000000000000000000000000000000000000
χ814-4-4444-4-4−4i4i4i−4i000000000000004-40000−4i4i0000000000000000000000000000000000000000000000000
χ824-4-4444-4-4−4i4i4i−4i00000000000000-4400004i−4i0000000000000000000000000000000000000000000000000
χ838-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000000

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