Finite Group Databasebeta

← Group #13018176

Character table — Group #13018176

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111444444444444448888888888888888101010101010101010101010161616161616161620204040404040404040404040404040404040404040
order12222222444444510101010101010224420202020202020202020202022224444444410101010202020204444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−iiiii−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−iiiii−i−i−i−iiiii
χ51111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ91111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ121111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ131111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111
χ141111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-1
χ151111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222-2-222-2-2222222220000-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2000000002200000000000000000000
χ1822222222-2-222-2-2222222220000-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000-2-200000000000000000000
χ1922222222-2-2-2-222222222220000-2-2-2-2-2-2-2-222222222-2-22222-2-200000000-2-200000000000000000000
χ2022222222-2-2-2-222222222220000-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-222000000002200000000000000000000
χ2122-222-2-2-2002-20022-2-22-2-220000000022-2-2000000002i−2i2i2i−2i−2i2i−2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ2222-222-2-2-2002-20022-2-22-2-220000000022-2-2000000002i−2i2i2i−2i−2i2i−2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ2322-222-2-2-2002-20022-2-22-2-220000000022-2-200000000−2i2i−2i−2i2i2i−2i2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ2422-222-2-2-2002-20022-2-22-2-220000000022-2-200000000−2i2i−2i−2i2i2i−2i2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ2522-222-2-2-200-220022-2-22-2-2200000000-2-222000000002i−2i−2i−2i2i2i2i−2i000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ2622-222-2-2-200-220022-2-22-2-2200000000-2-222000000002i−2i−2i−2i2i2i2i−2i00000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ2722-222-2-2-200-220022-2-22-2-2200000000-2-22200000000−2i2i2i2i−2i−2i−2i2i000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ2822-222-2-2-200-220022-2-22-2-2200000000-2-22200000000−2i2i2i2i−2i−2i−2i2i00000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ2922-2-2-222-22-20000222-2-22-2-2002i−2i22-2-20000000022-2-2-2-200002200002i2i−2i−2i00002i−2i0000000000000000
χ3022-2-2-222-22-20000222-2-22-2-2002i−2i22-2-200000000-2-222220000-2-200002i2i−2i−2i0000−2i2i0000000000000000
χ3122-2-2-222-22-20000222-2-22-2-200−2i2i22-2-20000000022-2-2-2-20000220000−2i−2i2i2i0000−2i2i0000000000000000
χ3222-2-2-222-22-20000222-2-22-2-200−2i2i22-2-200000000-2-222220000-2-20000−2i−2i2i2i00002i−2i0000000000000000
χ3322-2-2-222-2-220000222-2-22-2-22-200-2-2220000000022-2-2220000-2-222-2-20000002-2000000000000000000
χ3422-2-2-222-2-220000222-2-22-2-22-200-2-22200000000-2-222-2-200002222-2-2000000-22000000000000000000
χ3522-2-2-222-2-220000222-2-22-2-2-2200-2-2220000000022-2-2220000-2-2-2-222000000-22000000000000000000
χ3622-2-2-222-2-220000222-2-22-2-2-2200-2-22200000000-2-222-2-2000022-2-2220000002-2000000000000000000
χ372-22-22-22-200002i−2i2-2222-2-2-20000000000002i2i−2i−2i2-22-2002i−2i2i−2i0000000000000000000000002−2i2−i22−2i2−i2
χ382-22-22-22-200002i−2i2-2222-2-2-20000000000002i2i−2i−2i2-22-2002i−2i2i−2i000000000000000000000000−22−i2i2−22−i2i2
χ392-22-22-22-200002i−2i2-2222-2-2-20000000000002i2i−2i−2i-22-2200−2i2i−2i2i000000000000000000000000i2−i2−22−i2i22−2
χ402-22-22-22-200002i−2i2-2222-2-2-20000000000002i2i−2i−2i-22-2200−2i2i−2i2i000000000000000000000000−i2i22−2i2−i2−22
χ412-22-22-22-20000−2i2i2-2222-2-2-2000000000000−2i−2i2i2i2-22-200−2i2i−2i2i0000000000000000000000002−2−i2i22−2−i2i2
χ422-22-22-22-20000−2i2i2-2222-2-2-2000000000000−2i−2i2i2i2-22-200−2i2i−2i2i000000000000000000000000−22i2−i2−22i2−i2
χ432-22-22-22-20000−2i2i2-2222-2-2-2000000000000−2i−2i2i2i-22-22002i−2i2i−2i000000000000000000000000i2−i22−2−i2i2−22
χ442-22-22-22-20000−2i2i2-2222-2-2-2000000000000−2i−2i2i2i-22-22002i−2i2i−2i000000000000000000000000−i2i2−22i2−i22−2
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
χ474444444444-4-4-4-4-1-1-1-1-1-1-1-144-4-4-1-1-1-111111111000000000000-1-1-1-111110000000000000000000000
χ484444444444-4-4-4-4-1-1-1-1-1-1-1-1-4-444-1-1-1-1111111110000000000001111-1-1-1-10000000000000000000000
χ4944444444-4-444-4-4-1-1-1-1-1-1-1-100001111-1-1-1-111110000000000005−55−55−55−50000000000000000000000
χ5044444444-4-444-4-4-1-1-1-1-1-1-1-100001111-1-1-1-11111000000000000−55−55−55−550000000000000000000000
χ5144444444-4-4-4-444-1-1-1-1-1-1-1-1000011111111-1-1-1-10000000000005−55−5−55−550000000000000000000000
χ5244444444-4-4-4-444-1-1-1-1-1-1-1-1000011111111-1-1-1-1000000000000−55−555−55−50000000000000000000000
χ53444-4-4-4-4400000044-44-4-44-4000000000000000000004i−4i0000−4i4i000000000000000000000000000000
χ54444-4-4-4-4400000044-44-4-44-400000000000000000000−4i4i00004i−4i000000000000000000000000000000
χ5544-4-4-444-44-40000-1-1-111-111004i−4i-1-111i5−i5i5−i5i5−i5i5−i50000000000005−5−55−i−iii0000000000000000000000
χ5644-4-4-444-44-40000-1-1-111-111004i−4i-1-111−i5i5−i5i5−i5i5−i5i5000000000000−555−5−i−iii0000000000000000000000
χ5744-4-4-444-44-40000-1-1-111-11100−4i4i-1-111i5−i5i5−i5i5−i5i5−i5000000000000−555−5ii−i−i0000000000000000000000
χ5844-4-4-444-44-40000-1-1-111-11100−4i4i-1-111−i5i5−i5i5−i5i5−i5i50000000000005−5−55ii−i−i0000000000000000000000
χ5944-4-4-444-4-440000-1-1-111-1114-40011-1-1i5−i5i5−i5−i5i5−i5i5000000000000-1-111i5−i5−i5i50000000000000000000000
χ6044-4-4-444-4-440000-1-1-111-1114-40011-1-1−i5i5−i5i5i5−i5i5−i5000000000000-1-111−i5i5i5−i50000000000000000000000
χ6144-4-4-444-4-440000-1-1-111-111-440011-1-1i5−i5i5−i5−i5i5−i5i500000000000011-1-1−i5i5i5−i50000000000000000000000
χ6244-4-4-444-4-440000-1-1-111-111-440011-1-1−i5i5−i5i5i5−i5i5−i500000000000011-1-1i5−i5−i5i50000000000000000000000
χ634-444-44-4-40000004-4-44-44-440000000000000000000000000000000000004i−4i00000000000000000000
χ644-444-44-4-40000004-4-44-44-44000000000000000000000000000000000000−4i4i00000000000000000000
χ654-4-44-4-4440000004-44-4-4-44400000000000000004-4-4400000000000000000000000000000000000000
χ664-4-44-4-4440000004-44-4-4-4440000000000000000-444-400000000000000000000000000000000000000
χ674-4-4-444-440000004-4-4-4444-400000000000000000000004-4-4400000000000000000000000000000000
χ684-4-4-444-440000004-4-4-4444-40000000000000000000000-444-400000000000000000000000000000000
χ69888-8-8-8-88000000-2-22-222-22000000002i5−2i5−2i52i50000000000000000000000000000000000000000000000
χ70888-8-8-8-88000000-2-22-222-2200000000−2i52i52i5−2i50000000000000000000000000000000000000000000000
χ7188-888-8-8-8008-800-2-222-222-200000000-2-2220000000000000000000000000000000000000000000000
χ7288-888-8-8-800-8800-2-222-222-20000000022-2-20000000000000000000000000000000000000000000000
χ738-888-88-8-8000000-222-22-22-2000025−2525−2500000000000000000000000000000000000000000000000000
χ748-888-88-8-8000000-222-22-22-20000−2525−252500000000000000000000000000000000000000000000000000
χ758-88-88-88-800008i−8i-22-2-2-2222000000000000−2i−2i2i2i000000000000000000000000000000000000000000
χ768-88-88-88-80000−8i8i-22-2-2-22220000000000002i2i−2i−2i000000000000000000000000000000000000000000
χ778-8-88-8-888000000-22-2222-2-200000000000025−25−2525000000000000000000000000000000000000000000
χ788-8-88-8-888000000-22-2222-2-2000000000000−252525−25000000000000000000000000000000000000000000
χ798-8-8-888-88000000-2222-2-2-22000025−25−252500000000000000000000000000000000000000000000000000
χ808-8-8-888-88000000-2222-2-2-220000−252525−2500000000000000000000000000000000000000000000000000

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