Finite Group Databasebeta

← Group #72340668

Character table — Group #72340668

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size111122222222224444444444444488888888888888888888888888888888881616161616161616161632323232323232323232323232323232
order1222222222444422224444444444444444444444444444888888888888888822444444448888888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11iiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ121111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1111111iiiiiiii−i−i−i−i−i−i−i−i-1-1−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1
χ141111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1111111iiiiiiii−i−i−i−i−i−i−i−i-1-1−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-111
χ151111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1111111−i−i−i−i−i−i−i−iiiiiiiii-1-1iiii−i−i−i−iii−i−i−i−iii11-1-1-1-111
χ161111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1111111−i−i−i−i−i−i−i−iiiiiiiii-1-1iiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1
χ1711111-1-1-1-1111-1-111-1-111-1-11-1111111-1-111-1-111-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1ii−i−iii−i−i1-11-11-11-1i−ii−ii−ii−i
χ1811111-1-1-1-1111-1-111-1-111-1-11-1111111-1-111-1-111-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1ii−i−iii−i−i-11-11-11-11−ii−ii−ii−ii
χ1911111-1-1-1-1111-1-111-1-111-1-11-1111111-1-111-1-111-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii−i−iii1-11-11-11-1−ii−ii−ii−ii
χ2011111-1-1-1-1111-1-111-1-111-1-11-1111111-1-111-1-111-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii−i−iii-11-11-11-11i−ii−ii−ii−i
χ2111111-1-1-1-1111-1-111-1-111-1-11-1-1-1-1-111-1-111-1-1-1-111-1-11111iiii−i−i−i−iiiii−i−i−i−i-11−i−iii−i−iiii−ii−i−ii−ii-11-111-11-1
χ2211111-1-1-1-1111-1-111-1-111-1-11-1-1-1-1-111-1-111-1-1-1-111-1-11111iiii−i−i−i−iiiii−i−i−i−i-11−i−iii−i−iii−ii−iii−ii−i1-11-1-11-11
χ2311111-1-1-1-1111-1-111-1-111-1-11-1-1-1-1-111-1-111-1-1-1-111-1-11111−i−i−i−iiiii−i−i−i−iiiii-11ii−i−iii−i−ii−ii−i−ii−ii1-11-1-11-11
χ2411111-1-1-1-1111-1-111-1-111-1-11-1-1-1-1-111-1-111-1-1-1-111-1-11111−i−i−i−iiiii−i−i−i−iiiii-11ii−i−iii−i−i−ii−iii−ii−i-11-111-11-1
χ2511111-1-1-1-11-1-111-1-11111-1-1-11111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-111-1-1-1-1111-1-111-1-111-1-111-1-11
χ2611111-1-1-1-11-1-111-1-11111-1-1-11111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-111-1-1-1-111-111-1-111-1-111-1-111-1
χ2711111-1-1-1-11-1-111-1-11111-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-11111-1-11-1-111-1-11-111-1-111-1
χ2811111-1-1-1-11-1-111-1-11111-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-111-1-111-11-1-111-1-11
χ2911111-1-1-1-11-1-111-1-11111-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-11111-1-1i−i−ii−iii−ii−i−ii−iii−i
χ3011111-1-1-1-11-1-111-1-11111-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-11111-1-1−iii−ii−i−ii−iii−ii−i−ii
χ3111111-1-1-1-11-1-111-1-11111-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-111i−i−ii−iii−i−iii−ii−i−ii
χ3211111-1-1-1-11-1-111-1-11111-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-111−iii−ii−i−iii−i−ii−iii−i
χ332222222222222222222222222222-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000-2-2000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-222000000000000000022000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-222222222-2-2-2-2220000000000000000-2-2000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000022000000000000000000000000
χ3722222-2-2-2-2222-2-222-2-222-2-22-22222-2-222-2-222-2-2-2-222-2-2220000000000000000-22000000000000000000000000
χ3822222-2-2-2-2222-2-222-2-222-2-22-2-2-2-2-2-2-222-2-2222222-2-222-2-200000000000000002-2000000000000000000000000
χ3922222-2-2-2-22-2-222-2-22222-2-2-222222-2-22222-2-222-2-2-2-222-2-20000000000000000-22000000000000000000000000
χ4022222-2-2-2-22-2-222-2-22222-2-2-22-2-2-2-2-2-22222-2-2-2-22222-2-22200000000000000002-2000000000000000000000000
χ412-2-22222-2-2-2000000002-22-2002i2i−2i−2i00002i−2i2i−2i2-22i−2i00002-21+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ422-2-22222-2-2-2000000002-22-2002i2i−2i−2i00002i−2i2i−2i2-22i−2i00002-2−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ432-2-22222-2-2-2000000002-22-2002i2i−2i−2i0000−2i2i−2i2i-222i−2i0000-221−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ442-2-22222-2-2-2000000002-22-2002i2i−2i−2i0000−2i2i−2i2i-222i−2i0000-22−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ452-2-22222-2-2-2000000002-22-200−2i−2i2i2i00002i−2i2i−2i-22−2i2i0000-221+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ462-2-22222-2-2-2000000002-22-200−2i−2i2i2i00002i−2i2i−2i-22−2i2i0000-22−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ472-2-22222-2-2-2000000002-22-200−2i−2i2i2i0000−2i2i−2i2i2-2−2i2i00002-21−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ482-2-22222-2-2-2000000002-22-200−2i−2i2i2i0000−2i2i−2i2i2-2−2i2i00002-2−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ492-2-222-2-222-2000000002-2-22002i2i−2i−2i00002i−2i−2i2i2-2−2i2i0000-221−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ502-2-222-2-222-2000000002-2-22002i2i−2i−2i00002i−2i−2i2i2-2−2i2i0000-22−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ512-2-222-2-222-2000000002-2-22002i2i−2i−2i0000−2i2i2i−2i-22−2i2i00002-21+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ522-2-222-2-222-2000000002-2-22002i2i−2i−2i0000−2i2i2i−2i-22−2i2i00002-2−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ532-2-222-2-222-2000000002-2-2200−2i−2i2i2i00002i−2i−2i2i-222i−2i00002-21−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ542-2-222-2-222-2000000002-2-2200−2i−2i2i2i00002i−2i−2i2i-222i−2i00002-2−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ552-2-222-2-222-2000000002-2-2200−2i−2i2i2i0000−2i2i2i−2i2-22i−2i0000-221+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ562-2-222-2-222-2000000002-2-2200−2i−2i2i2i0000−2i2i2i−2i2-22i−2i0000-22−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ5744444444444444-4-4-4-4-4-4-4-4440000000000000000000000000000000000000000000000000000000000000000
χ584444444444-4-4-4-44444-4-4-4-4-4-40000000000000000000000000000000000000000000000000000000000000000
χ5944444-4-4-4-4444-4-4-4-444-4-4444-40000000000000000000000000000000000000000000000000000000000000000
χ6044444-4-4-4-44-4-44444-4-4-4-444-440000000000000000000000000000000000000000000000000000000000000000
χ614444-44-44-4-4444400000000-4-400000000000000000000002-22-22-22-22-22-22-22-200000000000000000000000000
χ624444-44-44-4-4444400000000-4-40000000000000000000000-22-22-22-22-22-22-22-2200000000000000000000000000
χ634444-44-44-4-4-4-4-4-4000000004400000000000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ644444-44-44-4-4-4-4-4-400000000440000000000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ654444-4-44-44-444-4-400000000-4400000000000000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ664444-4-44-44-444-4-400000000-440000000000000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ674444-4-44-44-4-4-444000000004-400000000000000000000002-22-2-22-22-22-222-22-200000000000000000000000000
χ684444-4-44-44-4-4-444000000004-40000000000000000000000-22-222-22-22-22-2-22-2200000000000000000000000000
χ694-4-44444-4-4-400000000-44-440000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ704-4-44444-4-4-400000000-44-44000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ714-4-444-4-444-400000000-444-40000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ724-4-444-4-444-400000000-444-4000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ734-4-44-44-4-44400004-44-400000000000000000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ744-4-44-44-4-44400004-44-40000000000000000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ754-4-44-44-4-4440000-44-4400000000000000000000000000002-2-222-2-222-2-222-2-2200000000000000000000000000
χ764-4-44-44-4-4440000-44-440000000000000000000000000000-222-2-222-2-222-2-222-200000000000000000000000000
χ774-4-44-4-444-4400004-4-4400000000000000000000000000002-2-22-222-2-222-22-2-2200000000000000000000000000
χ784-4-44-4-444-4400004-4-440000000000000000000000000000-222-22-2-222-2-22-222-200000000000000000000000000
χ794-4-44-4-444-440000-444-400000000000000000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ804-4-44-4-444-440000-444-40000000000000000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ8188-8-8000000008i−8i00000000004i−4i4i−4i000000000000004-400000000000000000000000000000000000000000000
χ8288-8-8000000008i−8i0000000000−4i4i−4i4i00000000000000-4400000000000000000000000000000000000000000000
χ8388-8-800000000−8i8i00000000004i−4i4i−4i00000000000000-4400000000000000000000000000000000000000000000
χ8488-8-800000000−8i8i0000000000−4i4i−4i4i000000000000004-400000000000000000000000000000000000000000000
χ858-88-80000008i−8i0000000000004-4-440000000000004i−4i0000000000000000000000000000000000000000000000
χ868-88-80000008i−8i000000000000-444-4000000000000−4i4i0000000000000000000000000000000000000000000000
χ878-88-8000000−8i8i0000000000004-4-44000000000000−4i4i0000000000000000000000000000000000000000000000
χ888-88-8000000−8i8i000000000000-444-40000000000004i−4i0000000000000000000000000000000000000000000000

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