Finite Group Databasebeta

← Group #13019706

Character table — Group #13019706

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122224444444444448888888888881010101010101010101010101616161616161616161620202020202020202020202020202020202040404040404040408080
order12222222444422445101010101010101010101020202020202020202222444444444420202020202020202244444444444444448888888824
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
χ911111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-1
χ1111111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11
χ1211111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ1311111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-11
χ1411111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-11
χ1511111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i1-1
χ1611111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii1-1
χ17222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-20000000000-2-200000000000000000000000000
χ18222222222222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000002200000000000000000000000000
χ1922222222-2-2-2-222-2-2222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000002200000000000000000000000000
χ2022222222-2-2-2-222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000-2-200000000000000000000000000
χ21222-22-2-2-22i2i−2i−2i0000222-2-22-2-2000000002i2i−2i−2i000000002i2i−2i−2i00000000002-21+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000
χ22222-22-2-2-22i2i−2i−2i0000222-2-22-2-2000000002i2i−2i−2i000000002i2i−2i−2i00000000002-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000
χ23222-22-2-2-22i2i−2i−2i0000222-2-22-2-2000000002i2i−2i−2i00000000−2i−2i2i2i0000000000-221−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i0000000000
χ24222-22-2-2-22i2i−2i−2i0000222-2-22-2-2000000002i2i−2i−2i00000000−2i−2i2i2i0000000000-22−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i0000000000
χ25222-22-2-2-2−2i−2i2i2i0000222-2-22-2-200000000−2i−2i2i2i000000002i2i−2i−2i0000000000-221+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i0000000000
χ26222-22-2-2-2−2i−2i2i2i0000222-2-22-2-200000000−2i−2i2i2i000000002i2i−2i−2i0000000000-22−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i0000000000
χ27222-22-2-2-2−2i−2i2i2i0000222-2-22-2-200000000−2i−2i2i2i00000000−2i−2i2i2i00000000002-21−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000
χ28222-22-2-2-2−2i−2i2i2i0000222-2-22-2-200000000−2i−2i2i2i00000000−2i−2i2i2i00000000002-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000
χ2922-22-22-2-22i−2i2i−2i000022-22-2-22-2000000002i−2i2i−2i2-22-22i2i−2i−2i000000000000000000000000000000002−2i2−i22−2i2−i200
χ3022-22-22-2-22i−2i2i−2i000022-22-2-22-2000000002i−2i2i−2i2-22-22i2i−2i−2i00000000000000000000000000000000−22−i2i2−22−i2i200
χ3122-22-22-2-22i−2i2i−2i000022-22-2-22-2000000002i−2i2i−2i-22-22−2i−2i2i2i00000000000000000000000000000000i2−i2−22−i2i22−200
χ3222-22-22-2-22i−2i2i−2i000022-22-2-22-2000000002i−2i2i−2i-22-22−2i−2i2i2i00000000000000000000000000000000−i2i22−2i2−i2−2200
χ3322-22-22-2-2−2i2i−2i2i000022-22-2-22-200000000−2i2i−2i2i2-22-2−2i−2i2i2i000000000000000000000000000000002−2−i2i22−2−i2i200
χ3422-22-22-2-2−2i2i−2i2i000022-22-2-22-200000000−2i2i−2i2i2-22-2−2i−2i2i2i00000000000000000000000000000000−22i2−i2−22i2−i200
χ3522-22-22-2-2−2i2i−2i2i000022-22-2-22-200000000−2i2i−2i2i-22-222i2i−2i−2i00000000000000000000000000000000i2−i22−2−i2i2−2200
χ3622-22-22-2-2−2i2i−2i2i000022-22-2-22-200000000−2i2i−2i2i-22-222i2i−2i−2i00000000000000000000000000000000−i2i2−22i2−i22−200
χ372-222-2-22-200002-2002-2222-2-2-222-2-20000000000002i−2i2i−2i2i−2i2i−2i0000000000001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000
χ382-222-2-22-200002-2002-2222-2-2-222-2-20000000000002i−2i2i−2i2i−2i2i−2i000000000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000
χ392-222-2-22-200002-2002-2222-2-2-222-2-2000000000000−2i2i−2i2i−2i2i−2i2i0000000000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000
χ402-222-2-22-200002-2002-2222-2-2-222-2-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000
χ412-222-2-22-20000-22002-2222-2-2-2-2-2220000000000002i−2i2i−2i−2i2i−2i2i0000000000001−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i0000000000
χ422-222-2-22-20000-22002-2222-2-2-2-2-2220000000000002i−2i2i−2i−2i2i−2i2i000000000000−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i0000000000
χ432-222-2-22-20000-22002-2222-2-2-2-2-222000000000000−2i2i−2i2i2i−2i2i−2i0000000000001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i0000000000
χ442-222-2-22-20000-22002-2222-2-2-2-2-222000000000000−2i2i−2i2i2i−2i2i−2i000000000000−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i0000000000
χ452-22-2-22-220000002-22-22-2-2-222000022-2-2000022-2-200002-2-2200000000000000002i−2i−2i2i0000−2i2i2i−2i0000000000
χ462-22-2-22-220000002-22-22-2-2-222000022-2-2000022-2-200002-2-220000000000000000−2i2i2i−2i00002i−2i−2i2i0000000000
χ472-22-2-22-220000002-22-22-2-2-222000022-2-20000-2-2220000-222-200000000000000002-2-2200002-2-220000000000
χ482-22-2-22-220000002-22-22-2-2-222000022-2-20000-2-2220000-222-20000000000000000-222-20000-222-20000000000
χ492-22-2-22-22000000-222-22-2-2-2220000-2-222000022-2-20000-222-20000000000002i−2i−2i2i0000−2i2i2i−2i00000000000000
χ502-22-2-22-22000000-222-22-2-2-2220000-2-222000022-2-20000-222-2000000000000−2i2i2i−2i00002i−2i−2i2i00000000000000
χ512-22-2-22-22000000-222-22-2-2-2220000-2-2220000-2-22200002-2-220000000000002-2-2200002-2-2200000000000000
χ522-22-2-22-22000000-222-22-2-2-2220000-2-2220000-2-22200002-2-22000000000000-222-20000-222-200000000000000
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
χ55444444444444-4-4-4-4-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000055−5−555−5−50000000000000000000000000000
χ56444444444444-4-4-4-4-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000−5−555−5−5550000000000000000000000000000
χ5744444444-4-4-4-444-4-4-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000055−5−5−5−5550000000000000000000000000000
χ5844444444-4-4-4-444-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000−5−55555−5−50000000000000000000000000000
χ5944444444-4-4-4-4-4-444-1-1-1-1-1-1-1-11111-1-1-1-111110000000000004-4-1-1-1-111110000000000000000000000000000
χ6044444444-4-4-4-4-4-444-1-1-1-1-1-1-1-11111-1-1-1-11111000000000000-441111-1-1-1-10000000000000000000000000000
χ6144-4-4-4-4444-4-44000044-4-44-4-44000000004-4-4400000000000000000000000000000000000000000000000000
χ6244-4-4-4-4444-4-440000-1-111-111-15−55−55−55−5-111-100000000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000000000
χ6344-4-4-4-4444-4-440000-1-111-111-15−55−55−55−5-111-100000000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000000000
χ6444-4-4-4-4444-4-440000-1-111-111-1−55−55−55−55-111-100000000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000000000
χ6544-4-4-4-4444-4-440000-1-111-111-1−55−55−55−55-111-100000000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000000000
χ6644-4-4-4-444-444-4000044-4-44-4-4400000000-444-400000000000000000000000000000000000000000000000000
χ6744-4-4-4-444-444-40000-1-111-111-15−55−5−55−551-1-1100000000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000000000
χ6844-4-4-4-444-444-40000-1-111-111-15−55−5−55−551-1-1100000000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000000000
χ6944-4-4-4-444-444-40000-1-111-111-1−55−555−55−51-1-1100000000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000000000
χ7044-4-4-4-444-444-40000-1-111-111-1−55−555−55−51-1-1100000000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000000000
χ714-4-444-4-44000000004-4-44-44-4400000000000000004-4-44000000000000000000000000000000000000000000
χ724-4-444-4-44000000004-4-44-44-440000000000000000-444-4000000000000000000000000000000000000000000
χ734-4-4-4444-4000000004-4-4-4444-40000000000004-4-440000000000000000000000000000000000000000000000
χ744-4-4-4444-4000000004-4-4-4444-4000000000000-444-40000000000000000000000000000000000000000000000
χ75888-88-8-8-88i8i−8i−8i0000-2-2-222-22200000000−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ76888-88-8-8-8−8i−8i8i8i0000-2-2-222-222000000002i2i−2i−2i00000000000000000000000000000000000000000000000000
χ7788-88-88-8-88i−8i8i−8i0000-2-22-222-2200000000−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ7888-88-88-8-8−8i8i−8i8i0000-2-22-222-22000000002i−2i2i−2i00000000000000000000000000000000000000000000000000
χ798-888-8-88-800008-800-22-2-2-2222-2-2220000000000000000000000000000000000000000000000000000000000
χ808-888-8-88-80000-8800-22-2-2-222222-2-20000000000000000000000000000000000000000000000000000000000
χ818-88-8-88-880000008-8-22-2222-2-20000-2-222000000000000000000000000000000000000000000000000000000
χ828-88-8-88-88000000-88-22-2222-2-2000022-2-2000000000000000000000000000000000000000000000000000000
χ838-8-888-8-8800000000-222-22-22-2000025−25−2525000000000000000000000000000000000000000000000000000000
χ848-8-888-8-8800000000-222-22-22-20000−252525−25000000000000000000000000000000000000000000000000000000
χ858-8-8-8888-800000000-2222-2-2-2225−25−25250000000000000000000000000000000000000000000000000000000000
χ868-8-8-8888-800000000-2222-2-2-22−252525−250000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.