Finite Group Databasebeta

← Group #221704

Character table — Group #221704

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222222224444444444444444444444444488888888888888888888888888816161616161616161616
order12222222222222224444222222444444444444444444442244444444444444444888888882444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1111-1-1-1-1-11111-1-1-1-1111111111-1-11-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1111-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111111111111-111-111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111iiii−i−i−i−i11-1-1-11-1ii−i−iii−i−iii−i−iiiii−i−i−i−i1-1-1-111i−ii−i
χ10111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111iiii−i−i−i−i-1-1-1111-1ii−i−iii−i−iii−i−i−i−i−i−iiiii-1111-1-1−ii−ii
χ11111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111−i−i−i−iiiii11-1-1-11-1−i−iii−i−iii−i−iii−i−i−i−iiiii1-1-1-111−ii−ii
χ12111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111−i−i−i−iiiii-1-1-1111-1−i−iii−i−iii−i−iiiiiii−i−i−i−i-1111-1-1i−ii−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1iiii−i−i−i−i111-1-111−i−iiiii−i−i−i−iiiiiii−i−i−i−i111-1-1-1−ii−ii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1iiii−i−i−i−i-1-111111−i−iiiii−i−i−i−iii−i−i−i−iiiii-1-1-1111i−ii−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1−i−i−i−iiiii111-1-111ii−i−i−i−iiiii−i−i−i−i−i−iiiii111-1-1-1i−ii−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1−i−i−i−iiiii-1-111111ii−i−i−i−iiiii−i−iiiii−i−i−i−i-1-1-1111−ii−ii
χ1711111111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1111111111111-111-11-1-1-1-1-1-1-1-1111111-1-111-1-1-11-1-1-11-1-111
χ1811111111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-1111-1111-111-1-1
χ1911111111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-111-1111111111-1-1-1-1-1-111-1-111-11-1-1-1111-1-1
χ2011111111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-111-1-11-1111-1-1-111
χ2111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-11-111-1-1
χ2211111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-11-11-1-111
χ2311111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-111-1-111-1-11-11-1-1-111
χ2411111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-111-11-1111-1-1
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111iiii−i−i−i−i111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii-1-111-11−iii−i
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111iiii−i−i−i−i-1-1111-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i11-1-11-1i−i−ii
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111−i−i−i−iiiii111-1-1-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−i-1-111-11i−i−ii
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111−i−i−i−iiiii-1-1111-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iii11-1-11-1−iii−i
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1iiii−i−i−i−i11-1-1-1-11ii−i−i−i−iii−i−iiiii−i−i−i−iii-11-111-1i−i−ii
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1iiii−i−i−i−i-1-1-111-11ii−i−i−i−iii−i−iii−i−iiiii−i−i1-11-1-11−iii−i
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1−i−i−i−iiiii11-1-1-1-11−i−iiiii−i−iii−i−i−i−iiiii−i−i-11-111-1−iii−i
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1−i−i−i−iiiii-1-1-111-11−i−iiiii−i−iii−i−iii−i−i−i−iii1-11-1-11i−i−ii
χ332222222222222222-2-2-2-22222222222-2-2-2-2-2-2-2-20000000000-200-2-2000000000000000000000000000000
χ342222222222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-2220000000000200-22000000000000000000000000000000
χ35222222222222-2-2-2-22222-2-222-2-222-2-2-2-2-2-222-2-20000000000200-22000000000000000000000000000000
χ36222222222222-2-2-2-22222-2-2-2-222-2-22222-2-222220000000000-200-2-2000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-222-2-222-2-200000000002002-2000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000-20022000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-20000000000-20022000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-22200000000002002-2000000000000000000000000000000
χ412-2222-2-2-222-2-200002i−2i2i−2i00002-2002-22i−2i002i−2i2i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000001−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000000000
χ422-2222-2-2-222-2-200002i−2i2i−2i00002-2002-22i−2i002i−2i2i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000000000
χ432-2222-2-2-222-2-200002i−2i2i−2i0000-2200-22−2i2i002i−2i−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000000000
χ442-2222-2-2-222-2-200002i−2i2i−2i0000-2200-22−2i2i002i−2i−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000001−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000000000
χ452-2222-2-2-222-2-20000−2i2i−2i2i00002-2002-2−2i2i00−2i2i−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000001+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000000000
χ462-2222-2-2-222-2-20000−2i2i−2i2i00002-2002-2−2i2i00−2i2i−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000000000
χ472-2222-2-2-222-2-20000−2i2i−2i2i0000-2200-222i−2i00−2i2i2i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000000000
χ482-2222-2-2-222-2-20000−2i2i−2i2i0000-2200-222i−2i00−2i2i2i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000001+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000000000
χ492-2222-2-2-2-2-22200002i−2i2i−2i00002-200-22−2i2i00−2i2i2i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000000000
χ502-2222-2-2-2-2-22200002i−2i2i−2i00002-200-22−2i2i00−2i2i2i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000001−i−1+i1+i−1−i1+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000000000
χ512-2222-2-2-2-2-22200002i−2i2i−2i0000-22002-22i−2i00−2i2i−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000001−i−1+i1+i−1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000000000
χ522-2222-2-2-2-2-22200002i−2i2i−2i0000-22002-22i−2i00−2i2i−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000000000
χ532-2222-2-2-2-2-2220000−2i2i−2i2i00002-200-222i−2i002i−2i−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000000000
χ542-2222-2-2-2-2-2220000−2i2i−2i2i00002-200-222i−2i002i−2i−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000001+i−1−i1−i−1+i1−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000000000
χ552-2222-2-2-2-2-2220000−2i2i−2i2i0000-22002-2−2i2i002i−2i2i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000001+i−1−i1−i−1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000000000
χ562-2222-2-2-2-2-2220000−2i2i−2i2i0000-22002-2−2i2i002i−2i2i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000000000
χ572-22-2-22-2200002-22-222-2-20000000000002-200002i−2i2i−2i2i−2i2i−2i2-202-2000000000000002i−2i002i−2i000000000000
χ582-22-2-22-2200002-22-222-2-20000000000002-200002i−2i2i−2i2i−2i2i−2i-220-2200000000000000−2i2i00−2i2i000000000000
χ592-22-2-22-2200002-22-222-2-20000000000002-20000−2i2i−2i2i−2i2i−2i2i2-202-200000000000000−2i2i00−2i2i000000000000
χ602-22-2-22-2200002-22-222-2-20000000000002-20000−2i2i−2i2i−2i2i−2i2i-220-22000000000000002i−2i002i−2i000000000000
χ612-22-2-22-220000-22-22-2-2220000000000002-200002-22-2-22-222-20-22000000000000002-200-22000000000000
χ622-22-2-22-220000-22-22-2-2220000000000002-200002-22-2-22-22-2202-200000000000000-22002-2000000000000
χ632-22-2-22-220000-22-22-2-2220000000000002-20000-22-222-22-22-20-2200000000000000-22002-2000000000000
χ642-22-2-22-220000-22-22-2-2220000000000002-20000-22-222-22-2-2202-2000000000000002-200-22000000000000
χ65444-4-4-44-4000000004i−4i−4i4i0000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000
χ66444-4-4-44-4000000004i−4i−4i4i000000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000
χ67444-4-4-44-400000000−4i4i4i−4i0000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000
χ68444-4-4-44-400000000−4i4i4i−4i000000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000
χ6944-44-44-4-44-44-444-4-400004-40000000000000000000000000000000000000000000000000000000000000
χ7044-44-44-4-44-44-4-4-4440000-440000000000000000000000000000000000000000000000000000000000000
χ7144-44-44-4-4-44-4444-4-40000-440000000000000000000000000000000000000000000000000000000000000
χ7244-44-44-4-4-44-44-4-44400004-40000000000000000000000000000000000000000000000000000000000000
χ734-44-4-44-4400004-44-4-4-444000000000000-440000000000000000000000000000000000000000000000000
χ744-44-4-44-440000-44-4444-4-4000000000000-440000000000000000000000000000000000000000000000000
χ754-4-44-4-4444-4-4400000000004-4004-40000000000000000000000000000000000000000000000000000000
χ764-4-44-4-4444-4-440000000000-4400-440000000000000000000000000000000000000000000000000000000
χ774-4-44-4-444-444-400000000004-400-440000000000000000000000000000000000000000000000000000000
χ784-4-44-4-444-444-40000000000-44004-40000000000000000000000000000000000000000000000000000000
χ794-4-4-4444-400004-4-4400000000000000000000000000000000000000000000000000022−220022−220000000000
χ804-4-4-4444-400004-4-44000000000000000000000000000000000000000000000000000−222200−22220000000000
χ814-4-4-4444-40000-444-40000000000000000000000000000000000000000000000000002i2−2i200−2i22i20000000000
χ824-4-4-4444-40000-444-4000000000000000000000000000000000000000000000000000−2i22i2002i2−2i20000000000
χ8388-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000

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