Finite Group Databasebeta

← Group #164402

Character table — Group #164402

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222222224444444444444444444444444488888888888888888888888888816161616161616161616
order12222222444444444444224444444444444444888888882224444888888888888888888882444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ511111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1111-111-1-1-1-11111-1-1-1-1111111111-1-11-1-1-1-1-1-1
χ611111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ711111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-11111
χ811111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1111111111111-111-111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1iiii−i−i−i−i11111-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i-1111-1-1i−ii−i
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-1-11111ii−i−iii−i−iii−i−i−i−i−i−iiiii1-1-1-111−ii−ii
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1−i−i−i−iiiii11111-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii-1111-1-1−ii−ii
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-1-11111−i−iii−i−iii−i−iiiiiii−i−i−i−i1-1-1-111i−ii−i
χ13111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111iiii−i−i−i−i-1111-1-1-1−i−iiiii−i−i−i−iiiiiii−i−i−i−i-1-1-1111−ii−ii
χ14111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111iiii−i−i−i−i-1-1-11-111−i−iiiii−i−i−i−iii−i−i−i−iiiii111-1-1-1i−ii−i
χ15111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111−i−i−i−iiiii-1111-1-1-1ii−i−i−i−iiiii−i−i−i−i−i−iiiii-1-1-1111i−ii−i
χ16111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111−i−i−i−iiiii-1-1-11-111ii−i−i−i−iiiii−i−iiiii−i−i−i−i111-1-1-1−ii−ii
χ1711111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-111-1111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-1-11-1-1-111
χ1811111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-111-1111-1-1
χ1911111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111111-1-1-1-1-1-111-1-111-11-1-11-111-1-1
χ2011111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-111-1-111-1-11-111-11-1-111
χ2111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-1111-1-1
χ2211111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-1-111
χ2311111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-1-1-1-111111111-1-111-1-111-1-11-1-11-1-111
χ2411111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-111-111-1-1
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111iiii−i−i−i−i-111-11-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1-11−iii−i
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111iiii−i−i−i−i-1-1-1-1111−i−iii−i−iiiii−i−i−i−iiiii−i−i-1-1111-1i−i−ii
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111−i−i−i−iiiii-111-11-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-11i−i−ii
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111−i−i−i−iiiii-1-1-1-1111ii−i−iii−i−i−i−iiiii−i−i−i−iii-1-1111-1−iii−i
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i−i−iii1-11-11-1i−i−ii
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i1-1-1-1-111ii−i−i−i−iii−i−iii−i−iiiii−i−i-11-11-11−iii−i
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii111-1-1-1-1−i−iiiii−i−iii−i−i−i−iiiii−i−i1-11-11-1−iii−i
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii1-1-1-1-111−i−iiiii−i−iii−i−iii−i−i−i−iii-11-11-11i−i−ii
χ3322222222222222-2-222-2-222-2-222-2-22222-2-222-2-200000000-200-2-200000000000000000000000000000000
χ3422222222222222-2-222-2-2-2-2-2-222-2-2-2-2-2-222-2-22200000000200-2200000000000000000000000000000000
χ35222222222222-2-222-2-22222-2-2-2-22222-2-222-2-22200000000-200-2-200000000000000000000000000000000
χ36222222222222-2-222-2-222-2-2-2-2-2-222-2-222-2-222-2-200000000200-2200000000000000000000000000000000
χ3722222222-2-2-2-222-2-222-2-222-2-2-2-222-2-222-2-2-2-222000000002002-200000000000000000000000000000000
χ3822222222-2-2-2-222-2-222-2-2-2-2-2-2-2-22222-2-22222-2-200000000-2002200000000000000000000000000000000
χ3922222222-2-2-2-2-2-222-2-22222-2-222-2-2-2-2-2-22222-2-2000000002002-200000000000000000000000000000000
χ4022222222-2-2-2-2-2-222-2-222-2-2-2-222-2-22222-2-2-2-22200000000-2002200000000000000000000000000000000
χ41222-2-22-2-22i2i−2i−2i002i−2i002i−2i2-200002-22i−2i002i−2i002-21+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
χ42222-2-22-2-22i2i−2i−2i002i−2i002i−2i2-200002-22i−2i002i−2i002-2−1−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
χ43222-2-22-2-22i2i−2i−2i002i−2i002i−2i-2200002-2−2i2i00−2i2i00-221+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
χ44222-2-22-2-22i2i−2i−2i002i−2i002i−2i-2200002-2−2i2i00−2i2i00-22−1−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
χ45222-2-22-2-22i2i−2i−2i00−2i2i00−2i2i2-20000-222i−2i00−2i2i00-221−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
χ46222-2-22-2-22i2i−2i−2i00−2i2i00−2i2i2-20000-222i−2i00−2i2i00-22−1+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
χ47222-2-22-2-22i2i−2i−2i00−2i2i00−2i2i-220000-22−2i2i002i−2i002-21−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
χ48222-2-22-2-22i2i−2i−2i00−2i2i00−2i2i-220000-22−2i2i002i−2i002-2−1+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
χ49222-2-22-2-2−2i−2i2i2i002i−2i002i−2i2-20000-22−2i2i002i−2i00-221+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
χ50222-2-22-2-2−2i−2i2i2i002i−2i002i−2i2-20000-22−2i2i002i−2i00-22−1−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
χ51222-2-22-2-2−2i−2i2i2i002i−2i002i−2i-220000-222i−2i00−2i2i002-21+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
χ52222-2-22-2-2−2i−2i2i2i002i−2i002i−2i-220000-222i−2i00−2i2i002-2−1−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
χ53222-2-22-2-2−2i−2i2i2i00−2i2i00−2i2i2-200002-2−2i2i00−2i2i002-21−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
χ54222-2-22-2-2−2i−2i2i2i00−2i2i00−2i2i2-200002-2−2i2i00−2i2i002-2−1+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
χ55222-2-22-2-2−2i−2i2i2i00−2i2i00−2i2i-2200002-22i−2i002i−2i00-221−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
χ56222-2-22-2-2−2i−2i2i2i00−2i2i00−2i2i-2200002-22i−2i002i−2i00-22−1+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
χ572-2222-2-2-200002i−2i2i−2i2i−2i−2i2i002-2000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ02-2002i−2i0000000000002ζ3−2ζ3002ζ−2ζ000000000000
χ582-2222-2-2-200002i−2i2i−2i2i−2i−2i2i002-2000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0-2200−2i2i000000000000−2ζ32ζ300−2ζ2ζ000000000000
χ592-2222-2-2-200002i−2i2i−2i2i−2i−2i2i002-200000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ02-2002i−2i000000000000−2ζ32ζ300−2ζ2ζ000000000000
χ602-2222-2-2-200002i−2i2i−2i2i−2i−2i2i002-200000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0-2200−2i2i0000000000002ζ3−2ζ3002ζ−2ζ000000000000
χ612-2222-2-2-20000−2i2i−2i2i−2i2i2i−2i002-2000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ302-200−2i2i0000000000002ζ−2ζ002ζ3−2ζ3000000000000
χ622-2222-2-2-20000−2i2i−2i2i−2i2i2i−2i002-2000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30-22002i−2i000000000000−2ζ2ζ00−2ζ32ζ3000000000000
χ632-2222-2-2-20000−2i2i−2i2i−2i2i2i−2i002-200000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ302-200−2i2i000000000000−2ζ2ζ00−2ζ32ζ3000000000000
χ642-2222-2-2-20000−2i2i−2i2i−2i2i2i−2i002-200000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30-22002i−2i0000000000002ζ−2ζ002ζ3−2ζ3000000000000
χ6544-44-4-44-44-44-40000000000000000004i−4i004i−4i00000000000000000000000000000000000000000000000
χ6644-44-4-44-44-44-4000000000000000000−4i4i00−4i4i00000000000000000000000000000000000000000000000
χ6744-44-4-44-4-44-440000000000000000004i−4i00−4i4i00000000000000000000000000000000000000000000000
χ6844-44-4-44-4-44-44000000000000000000−4i4i004i−4i00000000000000000000000000000000000000000000000
χ6944-4-44-4-444i−4i−4i4i4i−4i00−4i4i0000004-4000000000000000000000000000000000000000000000000000000000
χ7044-4-44-4-444i−4i−4i4i−4i4i004i−4i000000-44000000000000000000000000000000000000000000000000000000000
χ7144-4-44-4-44−4i4i4i−4i4i−4i00−4i4i000000-44000000000000000000000000000000000000000000000000000000000
χ7244-4-44-4-44−4i4i4i−4i−4i4i004i−4i0000004-4000000000000000000000000000000000000000000000000000000000
χ734-4444-4-4-400004i−4i−4i4i4i−4i4i−4i00-4400000000000000000000000000000000000000000000000000000000000
χ744-4444-4-4-40000−4i4i4i−4i−4i4i−4i4i00-4400000000000000000000000000000000000000000000000000000000000
χ754-44-4-4-4440000004400-4-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ764-44-4-4-4440000004400-4-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ774-44-4-4-444000000-4-4004400000000000000000022−22−2222−222222−220000000000000000000000000000000000000
χ784-44-4-4-444000000-4-40044000000000000000000−222222−2222−22−22220000000000000000000000000000000000000
χ794-4-4-4444-400004400-4-400000000000000000000000000000000000000000000000002i2−2i2002i2−2i20000000000
χ804-4-4-4444-400004400-4-40000000000000000000000000000000000000000000000000−2i22i200−2i22i20000000000
χ814-4-4-4444-40000-4-40044000000000000000000000000000000000000000000000000022−2200−22220000000000
χ824-4-4-4444-40000-4-400440000000000000000000000000000000000000000000000000−22220022−220000000000
χ838-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000000000000

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