Finite Group Databasebeta

← Group #13021059

Character table — Group #13021059

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122224444444444448888888888881010101010101010101010101616161616161616161620202020202020202020202020202020202040404040404040408080
order12222222444444445101010101010102020202020202020202020204444444444444420202020202020204488888888888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii11
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i11
χ911111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i-11
χ1011111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii-11
χ1111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii1-1
χ1211111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i1-1
χ1311111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ1411111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-1
χ1511111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-11
χ1611111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ17222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-22222-2-22222-2-20000000000-2-200000000000000000000000000
χ18222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22200000000002200000000000000000000000000
χ1922222222-2-2-2-222-2-222222222-2-2-2-22222-2-2-2-2222222-2-2-2-2220000000000-2-200000000000000000000000000
χ2022222222-2-2-2-222-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-200000000002200000000000000000000000000
χ2122-2-22-22-22i2i−2i−2i000022-2-22-22-22i2i−2i−2i0000000022-2-2002i2i−2i−2i0000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00
χ2222-2-22-22-22i2i−2i−2i000022-2-22-22-22i2i−2i−2i0000000022-2-2002i2i−2i−2i000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00
χ2322-2-22-22-22i2i−2i−2i000022-2-22-22-22i2i−2i−2i00000000-2-22200−2i−2i2i2i0000000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i00
χ2422-2-22-22-22i2i−2i−2i000022-2-22-22-22i2i−2i−2i00000000-2-22200−2i−2i2i2i000000000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00
χ2522-2-22-22-2−2i−2i2i2i000022-2-22-22-2−2i−2i2i2i0000000022-2-200−2i−2i2i2i0000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00
χ2622-2-22-22-2−2i−2i2i2i000022-2-22-22-2−2i−2i2i2i0000000022-2-200−2i−2i2i2i000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00
χ2722-2-22-22-2−2i−2i2i2i000022-2-22-22-2−2i−2i2i2i00000000-2-222002i2i−2i−2i0000000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i00
χ2822-2-22-22-2−2i−2i2i2i000022-2-22-22-2−2i−2i2i2i00000000-2-222002i2i−2i−2i000000000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i00
χ2922-2-2-22-2200002-2002-2222-2-2-2000022-2-200002i−2i2i−2i2i−2i00002i−2i0000000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000000000
χ3022-2-2-22-2200002-2002-2222-2-2-2000022-2-200002i−2i2i−2i2i−2i00002i−2i000000000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000000000
χ3122-2-2-22-2200002-2002-2222-2-2-2000022-2-20000−2i2i−2i2i−2i2i0000−2i2i0000000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000000000
χ3222-2-2-22-2200002-2002-2222-2-2-2000022-2-20000−2i2i−2i2i−2i2i0000−2i2i000000000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000000000
χ3322-2-2-22-220000-22002-2222-2-2-20000-2-22200002i−2i2i−2i−2i2i0000−2i2i0000000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000000000
χ3422-2-2-22-220000-22002-2222-2-2-20000-2-22200002i−2i2i−2i−2i2i0000−2i2i000000000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000
χ3522-2-2-22-220000-22002-2222-2-2-20000-2-2220000−2i2i−2i2i2i−2i00002i−2i0000000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000000000
χ3622-2-2-22-220000-22002-2222-2-2-20000-2-2220000−2i2i−2i2i2i−2i00002i−2i000000000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000000000
χ372-22-22-2-222-22-20000222-2-22-2-22-22-20000000000002i−2i0000−2i2i00000000002i−2i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000
χ382-22-22-2-222-22-20000222-2-22-2-22-22-20000000000002i−2i0000−2i2i00000000002i−2i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000
χ392-22-22-2-222-22-20000222-2-22-2-22-22-2000000000000−2i2i00002i−2i0000000000−2i2i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000
χ402-22-22-2-222-22-20000222-2-22-2-22-22-2000000000000−2i2i00002i−2i0000000000−2i2i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000
χ412-22-22-2-22-22-220000222-2-22-2-2-22-220000000000002i−2i0000−2i2i0000000000−2i2i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i0000000000
χ422-22-22-2-22-22-220000222-2-22-2-2-22-220000000000002i−2i0000−2i2i0000000000−2i2i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i0000000000
χ432-22-22-2-22-22-220000222-2-22-2-2-22-22000000000000−2i2i00002i−2i00000000002i−2i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i0000000000
χ442-22-22-2-22-22-220000222-2-22-2-2-22-22000000000000−2i2i00002i−2i00000000002i−2i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i0000000000
χ452-2-22-2-2220000002-22-22-2-2-2220000000022-2-20000222-22-2-2-200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ462-2-22-2-2220000002-22-22-2-2-2220000000022-2-20000222-22-2-2-20000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ472-2-22-2-2220000002-22-22-2-2-2220000000022-2-20000-2-2-22-222200000000000000002-2-222-2-2200000000000000
χ482-2-22-2-2220000002-22-22-2-2-2220000000022-2-20000-2-2-22-22220000000000000000-222-2-222-200000000000000
χ492-2-22-2-222000000-222-22-2-2-22200000000-2-222000022-22-22-2-20000000000002i−2i−2i2i00000000−2i2i2i−2i0000000000
χ502-2-22-2-222000000-222-22-2-2-22200000000-2-222000022-22-22-2-2000000000000−2i2i2i−2i000000002i−2i−2i2i0000000000
χ512-2-22-2-222000000-222-22-2-2-22200000000-2-2220000-2-22-22-2220000000000002-2-22000000002-2-220000000000
χ522-2-22-2-222000000-222-22-2-2-22200000000-2-2220000-2-22-22-222000000000000-222-200000000-222-20000000000
χ534444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000044-1-1-1-1-1-1-1-10000000000000000000000000000
χ544444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-4-4111111110000000000000000000000000000
χ55444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000055−5−555−5−50000000000000000000000000000
χ56444444444444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000−5−555−5−5550000000000000000000000000000
χ5744444444-4-4-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-111110000000000000055−5−5−5−5550000000000000000000000000000
χ5844444444-4-4-4-444-4-4-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000−5−55555−5−50000000000000000000000000000
χ5944444444-4-4-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-10000000000004-41111-1-1-1-10000000000000000000000000000
χ6044444444-4-4-4-4-4-444-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000-44-1-1-1-111110000000000000000000000000000
χ614444-4-4-4-4000000004-4-4-444-440000000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ624444-4-4-4-4000000004-4-4-444-44000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ634-44-4-444-4000000004-4-44-444-40000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ644-44-4-444-4000000004-4-44-444-4000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ654-4-4444-4-44i−4i−4i4i000044-44-4-4-444i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ664-4-4444-4-44i−4i−4i4i0000-1-11-1111-1−iii−ii5−i5i5−i55−55−500000000000000−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ180000000000000000000000000000
χ674-4-4444-4-44i−4i−4i4i0000-1-11-1111-1−iii−ii5−i5i5−i55−55−500000000000000ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ180000000000000000000000000000
χ684-4-4444-4-44i−4i−4i4i0000-1-11-1111-1−iii−i−i5i5−i5i5−55−5500000000000000ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ180000000000000000000000000000
χ694-4-4444-4-44i−4i−4i4i0000-1-11-1111-1−iii−i−i5i5−i5i5−55−5500000000000000−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ180000000000000000000000000000
χ704-4-4444-4-4−4i4i4i−4i000044-44-4-4-44−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ714-4-4444-4-4−4i4i4i−4i0000-1-11-1111-1i−i−iii5−i5i5−i5−55−5500000000000000ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ18ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ180000000000000000000000000000
χ724-4-4444-4-4−4i4i4i−4i0000-1-11-1111-1i−i−iii5−i5i5−i5−55−5500000000000000−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ18−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ180000000000000000000000000000
χ734-4-4444-4-4−4i4i4i−4i0000-1-11-1111-1i−i−ii−i5i5−i5i55−55−500000000000000−ζ3+ζ7−ζ11+ζ19ζ3−ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ2−ζ6+ζ14−ζ18−ζ2+ζ6−ζ14+ζ18ζ2+ζ6−ζ14−ζ18−ζ2−ζ6+ζ14+ζ180000000000000000000000000000
χ744-4-4444-4-4−4i4i4i−4i0000-1-11-1111-1i−i−ii−i5i5−i5i55−55−500000000000000ζ3−ζ7+ζ11−ζ19−ζ3+ζ7−ζ11+ζ19−ζ3+ζ7+ζ11−ζ19ζ3−ζ7−ζ11+ζ19−ζ2+ζ6−ζ14+ζ18ζ2−ζ6+ζ14−ζ18−ζ2−ζ6+ζ14+ζ18ζ2+ζ6−ζ14−ζ180000000000000000000000000000
χ758888-8-8-8-800000000-2222-2-22-20000000025−25−252500000000000000000000000000000000000000000000000000
χ768888-8-8-8-800000000-2222-2-22-200000000−252525−2500000000000000000000000000000000000000000000000000
χ7788-8-88-88-88i8i−8i−8i0000-2-222-22-22−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000
χ7888-8-88-88-8−8i−8i8i8i0000-2-222-22-222i2i−2i−2i0000000000000000000000000000000000000000000000000000000000
χ7988-8-8-88-8800008-800-22-2-2-22220000-2-222000000000000000000000000000000000000000000000000000000
χ8088-8-8-88-880000-8800-22-2-2-2222000022-2-2000000000000000000000000000000000000000000000000000000
χ818-88-88-8-888-88-80000-2-2-222-222-22-220000000000000000000000000000000000000000000000000000000000
χ828-88-88-8-88-88-880000-2-2-222-2222-22-20000000000000000000000000000000000000000000000000000000000
χ838-88-8-888-800000000-222-22-2-2200002i5−2i5−2i52i5000000000000000000000000000000000000000000000000000000
χ848-88-8-888-800000000-222-22-2-220000−2i52i52i5−2i5000000000000000000000000000000000000000000000000000000
χ858-8-88-8-8880000008-8-22-2222-2-200000000-2-22200000000000000000000000000000000000000000000000000
χ868-8-88-8-888000000-88-22-2222-2-20000000022-2-200000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.