Finite Group Databasebeta

← Group #13021286

Character table — Group #13021286

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222222244444444444888888888888101010101010101010101616161616161616161620202020202020202020202020202020202020808080808080
order12222244888845881010101010101020202020404040404040404044444488884420202020202020204888888888888888888448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1ii−i−i
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1−i−iii
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11−i−iii
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11ii−i−i
χ911111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11-11-11-1
χ1011111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111-1-11-11
χ1111111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-1-11-11-11
χ1211111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-111-11-1
χ1311111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11i−i−ii
χ1411111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11−iii−i
χ1511111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-111iiii−i−i−i−i−i−i−i−iiiii1-1−iii−i
χ1611111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-111−i−i−i−iiiiiiiii−i−i−i−i1-1i−i−ii
χ17222222-2-20000-22002222222-2-2-2-2000000002-2-222200000000000000-200000022-2-2000022-2-2000000
χ18222222-2-20000-22002222222-2-2-2-2000000002-2-222200000000000000-2000000-2-2220000-2-222000000
χ19222222-2-20000-22002222222-2-2-2-200000000-222-2-2-20000000000000020000002i2i−2i−2i0000−2i−2i2i2i000000
χ20222222-2-20000-22002222222-2-2-2-200000000-222-2-2-2000000000000002000000−2i−2i2i2i00002i2i−2i−2i000000
χ212222-2-2222222-22-2-22-2-2-2-2222-2-222222-2-2-2-22-2-2-2-22-2-2-2-200000000002220000000000000000000000
χ222222-2-2222222-22-2-22-2-2-2-2222-2-222222-2-2-2-2-22222-222220000000000-2-2-20000000000000000000000
χ232222-2-222-2-2-2-2-22222-2-2-2-2222-2-22-2-2-2-222222-2-2-2-22222200000000002-2-20000000000000000000000
χ242222-2-222-2-2-2-2-22222-2-2-2-2222-2-22-2-2-2-22222-22222-2-2-2-2-20000000000-2220000000000000000000000
χ252222-2-2-2-2000022002-2-2-2-222-222-200000000222-2-2200000000000000-20022-2-2000022-2-20000000000
χ262222-2-2-2-2000022002-2-2-2-222-222-200000000222-2-2200000000000000-200-2-2220000-2-2220000000000
χ272222-2-2-2-2000022002-2-2-2-222-222-200000000-2-2-222-2000000000000002002i2i−2i−2i0000−2i−2i2i2i0000000000
χ282222-2-2-2-2000022002-2-2-2-222-222-200000000-2-2-222-200000000000000200−2i−2i2i2i00002i2i−2i−2i0000000000
χ292-2-222-20022−2−2022−2-222-2-2-22000022−2−222−2−22002-2-222−2−2000000000002−2i2−i2i2−i2002i−2ii2−i2i2−i2002i−2i000000
χ302-2-222-20022−2−2022−2-222-2-2-22000022−2−222−2−22002-2-222−2−2000000000002−2−i2i2−i2i200−2i2i−i2i2−i2i200−2i2i000000
χ312-2-222-20022−2−2022−2-222-2-2-22000022−2−222−2−2-200-222−2−22200000000000−222−22−2002-2−22−2200-22000000
χ322-2-222-20022−2−2022−2-222-2-2-22000022−2−222−2−2-200-222−2−22200000000000−22−22−2200-222−22−2002-2000000
χ332-2-222-200−2−22202−22-222-2-2-220000−2−222−2−2222002-2-2−2−22200000000000−22i2−i2i2−i200−2i2ii2−i2i2−i200−2i2i000000
χ342-2-222-200−2−22202−22-222-2-2-220000−2−222−2−2222002-2-2−2−22200000000000−22−i2i2−i2i2002i−2i−i2i2−i2i2002i−2i000000
χ352-2-222-200−2−22202−22-222-2-2-220000−2−222−2−222-200-22222−2−2000000000002−22−22−200-22−22−22002-2000000
χ362-2-222-200−2−22202−22-222-2-2-220000−2−222−2−222-200-22222−2−2000000000002−2−22−22002-22−22−200-22000000
χ372-2-22-220022−2−202−22-2-2-222-22000022−2−2−2−222200-22-2−2−222000000000002−2i2−i2−i2i22i−2i00i2−i2−i2i22i−2i00000000
χ382-2-22-220022−2−202−22-2-2-222-22000022−2−2−2−222200-22-2−2−222000000000002−2−i2i2i2−i2−2i2i00−i2i2i2−i2−2i2i00000000
χ392-2-22-220022−2−202−22-2-2-222-22000022−2−2−2−222-2002-2222−2−200000000000−222−2−222-200−222−2-2200000000
χ402-2-22-220022−2−202−22-2-2-222-22000022−2−2−2−222-2002-2222−2−200000000000−22−222−2-22002−2−222-200000000
χ412-2-22-2200−2−222022−2-2-2-222-220000−2−22222−2−2200-22-222−2−200000000000−22i2−i2−i2i2−2i2i00i2−i2−i2i2−2i2i00000000
χ422-2-22-2200−2−222022−2-2-2-222-220000−2−22222−2−2200-22-222−2−200000000000−22−i2i2i2−i22i−2i00−i2i2i2−i22i−2i00000000
χ432-2-22-2200−2−222022−2-2-2-222-220000−2−22222−2−2-2002-22−2−222000000000002−22−2−22-2200−222−22-200000000
χ442-2-22-2200−2−222022−2-2-2-222-220000−2−22222−2−2-2002-22−2−222000000000002−2−222−22-2002−2−22-2200000000
χ454444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000044-1-1-1-1-1-1-1-10000000000000000000000000
χ464444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000-4-4111111110000000000000000000000000
χ4744444444-4-4-4-44-1-4-4-1-1-1-1-1-1-1-1-1-1-11111111100000000004-4-1-1-1-111110000000000000000000000000
χ4844444444-4-4-4-44-1-4-4-1-1-1-1-1-1-1-1-1-1-1111111110000000000-441111-1-1-1-10000000000000000000000000
χ494444-4-4444444-4-1-4-4-11111-1-1-111-1-1-1-1-1111100000000000055−5−555−5−50000000000000000000000000
χ504444-4-4444444-4-1-4-4-11111-1-1-111-1-1-1-1-11111000000000000−5−555−5−5550000000000000000000000000
χ514444-4-444-4-4-4-4-4-144-11111-1-1-111-11111-1-1-1-100000000000055−5−5−5−5550000000000000000000000000
χ524444-4-444-4-4-4-4-4-144-11111-1-1-111-11111-1-1-1-1000000000000−5−55555−5−50000000000000000000000000
χ5344-4-4004-44-44-40400-400004-4-40044-44-40000000000000000000000000000000000000000000000000
χ5444-4-4004-44-44-40-10015−55−5-1115−5-1-11-115−55−5000000000000−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−ζ380000000000000000000000000
χ5544-4-4004-44-44-40-10015−55−5-1115−5-1-11-115−55−5000000000000ζ6−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+ζ380000000000000000000000000
χ5644-4-4004-44-44-40-1001−55−55-111−55-1-11-11−55−55000000000000ζ6−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+ζ380000000000000000000000000
χ5744-4-4004-44-44-40-1001−55−55-111−55-1-11-11−55−55000000000000−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−ζ380000000000000000000000000
χ5844-4-4004-4-44-440400-400004-4-4004-44-440000000000000000000000000000000000000000000000000
χ5944-4-4004-4-44-440-10015−55−5-1115−5-11-11-1−55−55000000000000−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+ζ380000000000000000000000000
χ6044-4-4004-4-44-440-10015−55−5-1115−5-11-11-1−55−55000000000000ζ6−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−ζ380000000000000000000000000
χ6144-4-4004-4-44-440-1001−55−55-111−55-11-11-15−55−5000000000000ζ6−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−ζ380000000000000000000000000
χ6244-4-4004-4-44-440-1001−55−55-111−55-11-11-15−55−5000000000000−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+ζ380000000000000000000000000
χ6344-4-400-4400000400-400004-4400-4000000000000004-44-400000000000000000000000000000000000
χ6444-4-400-4400000400-400004-4400-400000000000000-44-4400000000000000000000000000000000000
χ654-44-4000022−22−2222040040000-4-4000022−22−2222000004-400022−22−222200000000000000000000000000000000000
χ664-44-4000022−22−2222040040000-4-4000022−22−222200000-44000−222222−2200000000000000000000000000000000000
χ674-44-40000−222222−22040040000-4-40000−222222−22000004-4000−222222−2200000000000000000000000000000000000
χ684-44-40000−222222−22040040000-4-40000−222222−2200000-4400022−22−222200000000000000000000000000000000000
χ69888888-8-80000-8-200-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000
χ708888-8-8-8-800008-200-22222-2-22-2-2200000000000000000000000000000000000000000000000000000
χ7188-8-800-8800000-200225−2525−25-22-2−2525200000000000000000000000000000000000000000000000000000
χ7288-8-800-8800000-2002−2525−2525-22-225−25200000000000000000000000000000000000000000000000000000
χ738-88-8000042−42−42420-200-225−25−2525220000−222−210−10−1010000000000000000000000000000000000000000000000
χ748-88-8000042−42−42420-200-2−252525−25220000−222−2−101010−10000000000000000000000000000000000000000000000
χ758-88-80000−424242−420-200-225−25−25252200002−2−22−101010−10000000000000000000000000000000000000000000000
χ768-88-80000−424242−420-200-2−252525−252200002−2−2210−10−1010000000000000000000000000000000000000000000000
χ778-8-888-8004242−42−420-242−422-2-2222-20000−2−222−2−222000000000000000000000000000000000000000000000
χ788-8-888-800−42−4242420-2−42422-2-2222-2000022−2−222−2−2000000000000000000000000000000000000000000000
χ798-8-88-88004242−42−420-2−4242222-2-22-20000−2−22222−2−2000000000000000000000000000000000000000000000
χ808-8-88-8800−42−4242420-242−42222-2-22-2000022−2−2−2−222000000000000000000000000000000000000000000000

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