Finite Group Databasebeta

← Group #13018202

Character table — Group #13018202

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111444444444444448888888888888888101010101010101010101010161616161616161620204040404040404040404040404040404040404040
order12222222444444510101010101010444420202020202020202020202044444444444420202020202020204444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ51111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1
χ161111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111
χ1722222222-2-222-2-2222222220000-2-2-2-2-2-2-2-222222222-2-222-2-22200000000-2-200000000000000000000
χ1822222222-2-222-2-2222222220000-2-2-2-2-2-2-2-22222-2-2-2-222-2-222-2-2000000002200000000000000000000
χ1922222222-2-2-2-222222222220000-2-2-2-22222-2-2-2-2222222-2-222-2-200000000-2-200000000000000000000
χ2022222222-2-2-2-222222222220000-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-222000000002200000000000000000000
χ2122-2-2-22-222-2000022-2-22-22-2002-222-2-20000000000002222-2-2-2-222-2-2000000002-20000000000000000
χ2222-2-2-22-222-2000022-2-22-22-2002-222-2-2000000000000-2-2-2-2222222-2-200000000-220000000000000000
χ2322-2-2-22-222-2000022-2-22-22-200-2222-2-20000000000002222-2-2-2-2-2-22200000000-220000000000000000
χ2422-2-2-22-222-2000022-2-22-22-200-2222-2-2000000000000-2-2-2-22222-2-222000000002-20000000000000000
χ2522-2-2-22-22-22000022-2-22-22-22i−2i00-2-22200000000000022-2-2-2-22200002i2i−2i−2i002i−2i000000000000000000
χ2622-2-2-22-22-22000022-2-22-22-22i−2i00-2-222000000000000-2-22222-2-200002i2i−2i−2i00−2i2i000000000000000000
χ2722-2-2-22-22-22000022-2-22-22-2−2i2i00-2-22200000000000022-2-2-2-2220000−2i−2i2i2i00−2i2i000000000000000000
χ2822-2-2-22-22-22000022-2-22-22-2−2i2i00-2-222000000000000-2-22222-2-20000−2i−2i2i2i002i−2i000000000000000000
χ292-2-22-222-2002i−2i002-22-2-222-20000000000002i2i−2i−2i22-2-2002i−2i002i−2i0000000000000000001−i−1+i1+i−1−i00001−i−1+i1+i−1−i
χ302-2-22-222-2002i−2i002-22-2-222-20000000000002i2i−2i−2i22-2-2002i−2i002i−2i000000000000000000−1+i1−i−1−i1+i0000−1+i1−i−1−i1+i
χ312-2-22-222-2002i−2i002-22-2-222-20000000000002i2i−2i−2i-2-22200−2i2i00−2i2i0000000000000000001+i−1−i−1+i1−i0000−1−i1+i1−i−1+i
χ322-2-22-222-2002i−2i002-22-2-222-20000000000002i2i−2i−2i-2-22200−2i2i00−2i2i000000000000000000−1−i1+i1−i−1+i00001+i−1−i−1+i1−i
χ332-2-22-222-200−2i2i002-22-2-222-2000000000000−2i−2i2i2i22-2-200−2i2i00−2i2i0000000000000000001+i−1−i1−i−1+i00001+i−1−i1−i−1+i
χ342-2-22-222-200−2i2i002-22-2-222-2000000000000−2i−2i2i2i22-2-200−2i2i00−2i2i000000000000000000−1−i1+i−1+i1−i0000−1−i1+i−1+i1−i
χ352-2-22-222-200−2i2i002-22-2-222-2000000000000−2i−2i2i2i-2-222002i−2i002i−2i0000000000000000001−i−1+i−1−i1+i0000−1+i1−i1+i−1−i
χ362-2-22-222-200−2i2i002-22-2-222-2000000000000−2i−2i2i2i-2-222002i−2i002i−2i000000000000000000−1+i1−i1+i−1−i00001−i−1+i−1−i1+i
χ372-2-2-22-22200002-222-22-22-2-20000000022-2-200002i−2i2i−2i2i−2i002i−2i00000000000000001+i−1−i1+i−1−i00001−i−1+i1−i−1+i0000
χ382-2-2-22-22200002-222-22-22-2-20000000022-2-200002i−2i2i−2i2i−2i002i−2i0000000000000000−1−i1+i−1−i1+i0000−1+i1−i−1+i1−i0000
χ392-2-2-22-22200002-222-22-22-2-20000000022-2-20000−2i2i−2i2i−2i2i00−2i2i00000000000000001−i−1+i1−i−1+i00001+i−1−i1+i−1−i0000
χ402-2-2-22-22200002-222-22-22-2-20000000022-2-20000−2i2i−2i2i−2i2i00−2i2i0000000000000000−1+i1−i−1+i1−i0000−1−i1+i−1−i1+i0000
χ412-2-2-22-2220000-2222-22-22-2-200000000-2-22200002i−2i2i−2i−2i2i00−2i2i00000000000000001−i−1+i−1+i1−i0000−1−i1+i1+i−1−i0000
χ422-2-2-22-2220000-2222-22-22-2-200000000-2-22200002i−2i2i−2i−2i2i00−2i2i0000000000000000−1+i1−i1−i−1+i00001+i−1−i−1−i1+i0000
χ432-2-2-22-2220000-2222-22-22-2-200000000-2-2220000−2i2i−2i2i2i−2i002i−2i00000000000000001+i−1−i−1−i1+i0000−1+i1−i1−i−1+i0000
χ442-2-2-22-2220000-2222-22-22-2-200000000-2-2220000−2i2i−2i2i2i−2i002i−2i0000000000000000−1−i1+i1+i−1−i00001−i−1+i−1+i1−i0000
χ4544444444444444-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-10000000000000000000000
χ4644444444444444-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111110000000000000000000000
χ474444444444-4-4-4-4-1-1-1-1-1-1-1-144-4-4-1-1-1-1111111110000000000001111-1-1-1-10000000000000000000000
χ484444444444-4-4-4-4-1-1-1-1-1-1-1-1-4-444-1-1-1-111111111000000000000-1-1-1-111110000000000000000000000
χ4944444444-4-444-4-4-1-1-1-1-1-1-1-1000011111111-1-1-1-10000000000005−55−55−55−50000000000000000000000
χ5044444444-4-444-4-4-1-1-1-1-1-1-1-1000011111111-1-1-1-1000000000000−55−55−55−550000000000000000000000
χ5144444444-4-4-4-444-1-1-1-1-1-1-1-100001111-1-1-1-111110000000000005−55−5−55−550000000000000000000000
χ5244444444-4-4-4-444-1-1-1-1-1-1-1-100001111-1-1-1-11111000000000000−55−555−55−50000000000000000000000
χ53444-4-4-44-40000004-4-4-444-4400000000000000004i−4i−4i4i00000000000000000000000000000000000000
χ54444-4-4-44-40000004-4-4-444-440000000000000000−4i4i4i−4i00000000000000000000000000000000000000
χ5544-444-4-4-40000004-4444-4-4-40000000000000000000000000000000000004-400000000000000000000
χ5644-444-4-4-40000004-4444-4-4-4000000000000000000000000000000000000-4400000000000000000000
χ5744-4-4-44-444-40000-1-111-11-11004-4-1-111i5−i5i5−i5i5−i5i5−i5000000000000-1-111i5−i5−i5i50000000000000000000000
χ5844-4-4-44-444-40000-1-111-11-11004-4-1-111−i5i5−i5i5−i5i5−i5i5000000000000-1-111−i5i5i5−i50000000000000000000000
χ5944-4-4-44-444-40000-1-111-11-1100-44-1-111i5−i5i5−i5i5−i5i5−i500000000000011-1-1−i5i5i5−i50000000000000000000000
χ6044-4-4-44-444-40000-1-111-11-1100-44-1-111−i5i5−i5i5−i5i5−i5i500000000000011-1-1i5−i5−i5i50000000000000000000000
χ6144-4-4-44-44-440000-1-111-11-114i−4i0011-1-1i5−i5i5−i5−i5i5−i5i5000000000000−555−5−i−iii0000000000000000000000
χ6244-4-4-44-44-440000-1-111-11-114i−4i0011-1-1−i5i5−i5i5i5−i5i5−i50000000000005−5−55−i−iii0000000000000000000000
χ6344-4-4-44-44-440000-1-111-11-11−4i4i0011-1-1i5−i5i5−i5−i5i5−i5i50000000000005−5−55ii−i−i0000000000000000000000
χ6444-4-4-44-44-440000-1-111-11-11−4i4i0011-1-1−i5i5−i5i5i5−i5i5−i5000000000000−555−5ii−i−i0000000000000000000000
χ654-444-4-4-44000000444-4-4-4-44000000000000000000004i−4i00−4i4i00000000000000000000000000000000
χ664-444-4-4-44000000444-4-4-4-4400000000000000000000−4i4i004i−4i00000000000000000000000000000000
χ674-44-444-4-40000004-4-44-4-44400000000000000000000004i−4i00−4i4i000000000000000000000000000000
χ684-44-444-4-40000004-4-44-4-4440000000000000000000000−4i4i004i−4i000000000000000000000000000000
χ69888-8-8-88-8000000-2222-2-22-2000025−2525−2500000000000000000000000000000000000000000000000000
χ70888-8-8-88-8000000-2222-2-22-20000−2525−252500000000000000000000000000000000000000000000000000
χ7188-888-8-8-8000000-22-2-2-2222000025−25−252500000000000000000000000000000000000000000000000000
χ7288-888-8-8-8000000-22-2-2-22220000−252525−2500000000000000000000000000000000000000000000000000
χ738-888-8-8-88000000-2-2-22222-2000000002i5−2i5−2i52i50000000000000000000000000000000000000000000000
χ748-888-8-8-88000000-2-2-22222-200000000−2i52i52i5−2i50000000000000000000000000000000000000000000000
χ758-88-888-8-8000000-222-222-2-200000000000025−25−2525000000000000000000000000000000000000000000
χ768-88-888-8-8000000-222-222-2-2000000000000−252525−25000000000000000000000000000000000000000000
χ778-8-88-888-8008i−8i00-22-222-2-22000000000000−2i−2i2i2i000000000000000000000000000000000000000000
χ788-8-88-888-800−8i8i00-22-222-2-220000000000002i2i−2i−2i000000000000000000000000000000000000000000
χ798-8-8-88-88800008-8-2-22-22-22200000000-2-2220000000000000000000000000000000000000000000000
χ808-8-8-88-8880000-88-2-22-22-2220000000022-2-20000000000000000000000000000000000000000000000

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