Finite Group Databasebeta

← Group #13021284

Character table — Group #13021284

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
χ911111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-11-11-11-1
χ1011111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-111111-1-11-11
χ1111111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-11-11-11
χ1211111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-111-11-1
χ1311111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-111iiii−i−i−i−i−i−i−i−iiiii-11i−i−ii
χ1411111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-111−i−i−i−iiiiiiiii−i−i−i−i-11−iii−i
χ1511111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1−iii−i
χ1611111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1i−i−ii
χ17222222-2-20000-22002222222-2-2-2-20000000022-2-2-2-20000000000000020000002i2i−2i−2i00002i2i−2i−2i000000
χ18222222-2-20000-22002222222-2-2-2-20000000022-2-2-2-2000000000000002000000−2i−2i2i2i0000−2i−2i2i2i000000
χ19222222-2-20000-22002222222-2-2-2-200000000-2-2222200000000000000-200000022-2-20000-2-222000000
χ20222222-2-20000-22002222222-2-2-2-200000000-2-2222200000000000000-2000000-2-222000022-2-2000000
χ212222-2-2222222-22-2-22-2-2-2-2222-2-222222-2-2-2-22222-2-222220000000000-2-2-20000000000000000000000
χ222222-2-2222222-22-2-22-2-2-2-2222-2-222222-2-2-2-2-2-2-2-222-2-2-2-200000000002220000000000000000000000
χ232222-2-222-2-2-2-2-22222-2-2-2-2222-2-22-2-2-2-222222222-2-2-2-2-2-20000000000-2220000000000000000000000
χ242222-2-222-2-2-2-2-22222-2-2-2-2222-2-22-2-2-2-22222-2-2-2-222222200000000002-2-20000000000000000000000
χ252222-2-2-2-2000022002-2-2-2-222-222-20000000022-2-22200000000000000-20022-2-2000022-2-20000000000
χ262222-2-2-2-2000022002-2-2-2-222-222-20000000022-2-22200000000000000-200-2-2220000-2-2220000000000
χ272222-2-2-2-2000022002-2-2-2-222-222-200000000-2-222-2-2000000000000002002i2i−2i−2i0000−2i−2i2i2i0000000000
χ282222-2-2-2-2000022002-2-2-2-222-222-200000000-2-222-2-200000000000000200−2i−2i2i2i00002i2i−2i−2i0000000000
χ292-2-222-200i2i2−i2−i202i2−i2-222-2-22-20000i2i2−i2−i2i2i2−i2−i2002-22-2i2i2−i2−i200000000000i2−i2i2−i2i2−i2002-2i2−i2i2−i22-200000000
χ302-2-222-200i2i2−i2−i202i2−i2-222-2-22-20000i2i2−i2−i2i2i2−i2−i2002-22-2i2i2−i2−i200000000000i2−i2−i2i2−i2i200-22−i2i2−i2i2-2200000000
χ312-2-222-200i2i2−i2−i202i2−i2-222-2-22-20000i2i2−i2−i2i2i2−i2−i200-22-22−i2−i2i2i200000000000−i2i22−22−200−2i2i−22−222i−2i00000000
χ322-2-222-200i2i2−i2−i202i2−i2-222-2-22-20000i2i2−i2−i2i2i2−i2−i200-22-22−i2−i2i2i200000000000−i2i2−22−22002i−2i2−22−2−2i2i00000000
χ332-2-222-200−i2−i2i2i202−i2i2-222-2-22-20000−i2−i2i2i2−i2−i2i2i2002-22-2−i2−i2i2i200000000000−i2i2i2−i2i2−i200-22i2−i2i2−i2-2200000000
χ342-2-222-200−i2−i2i2i202−i2i2-222-2-22-20000−i2−i2i2i2−i2−i2i2i2002-22-2−i2−i2i2i200000000000−i2i2−i2i2−i2i2002-2−i2i2−i2i22-200000000
χ352-2-222-200−i2−i2i2i202−i2i2-222-2-22-20000−i2−i2i2i2−i2−i2i2i200-22-22i2i2−i2−i200000000000i2−i22−22−2002i−2i−22−22−2i2i00000000
χ362-2-222-200−i2−i2i2i202−i2i2-222-2-22-20000−i2−i2i2i2−i2−i2i2i200-22-22i2i2−i2−i200000000000i2−i2−22−2200−2i2i2−22−22i−2i00000000
χ372-2-22-2200i2i2−i2−i202−i2i2-2-2-2222-20000i2i2−i2−i2−i2−i2i2i2002-2-22i2i2−i2−i200000000000−i2i22−2−222i−2i00−222−2002i−2i000000
χ382-2-22-2200i2i2−i2−i202−i2i2-2-2-2222-20000i2i2−i2−i2−i2−i2i2i2002-2-22i2i2−i2−i200000000000−i2i2−222−2−2i2i002−2−2200−2i2i000000
χ392-2-22-2200i2i2−i2−i202−i2i2-2-2-2222-20000i2i2−i2−i2−i2−i2i2i200-222-2−i2−i2i2i200000000000i2−i2i2−i2−i2i2-2200i2−i2−i2i2002-2000000
χ402-2-22-2200i2i2−i2−i202−i2i2-2-2-2222-20000i2i2−i2−i2−i2−i2i2i200-222-2−i2−i2i2i200000000000i2−i2−i2i2i2−i22-200−i2i2i2−i200-22000000
χ412-2-22-2200−i2−i2i2i202i2−i2-2-2-2222-20000−i2−i2i2i2i2i2−i2−i2002-2-22−i2−i2i2i200000000000i2−i22−2−22−2i2i00−222−200−2i2i000000
χ422-2-22-2200−i2−i2i2i202i2−i2-2-2-2222-20000−i2−i2i2i2i2i2−i2−i2002-2-22−i2−i2i2i200000000000i2−i2−222−22i−2i002−2−22002i−2i000000
χ432-2-22-2200−i2−i2i2i202i2−i2-2-2-2222-20000−i2−i2i2i2i2i2−i2−i200-222-2i2i2−i2−i200000000000−i2i2i2−i2−i2i22-200i2−i2−i2i200-22000000
χ442-2-22-2200−i2−i2i2i202i2−i2-2-2-2222-20000−i2−i2i2i2i2i2−i2−i200-222-2i2i2−i2−i200000000000−i2i2−i2i2i2−i2-2200−i2i2i2−i2002-2000000
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
χ4744444444-4-4-4-44-1-4-4-1-1-1-1-1-1-1-1-1-1-11111111100000000004-41111-1-1-1-10000000000000000000000000
χ4844444444-4-4-4-44-1-4-4-1-1-1-1-1-1-1-1-1-1-1111111110000000000-44-1-1-1-111110000000000000000000000000
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
χ5344-4-4000022−2222−22040040000-4-4000022−2222−2200004-4000022−2222−2200000000000000000000000000000000000
χ5444-4-4000022−2222−22040040000-4-4000022−2222−220000-440000−2222−222200000000000000000000000000000000000
χ5544-4-40000−2222−2222040040000-4-40000−2222−222200004-40000−2222−222200000000000000000000000000000000000
χ5644-4-40000−2222−2222040040000-4-40000−2222−22220000-44000022−2222−2200000000000000000000000000000000000
χ574-44-4004-400000400-40000-44-4004000000000000004i−4i−4i4i00000000000000000000000000000000000
χ584-44-4004-400000400-40000-44-400400000000000000−4i4i4i−4i00000000000000000000000000000000000
χ594-44-400-444i−4i−4i4i0400-40000-44400-44i−4i−4i4i0000000000000000000000000000000000000000000000000
χ604-44-400-444i−4i−4i4i0-10015−55−51-1-15−51−iii−ii5−i5i5−i5000000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ360000000000000000000000000
χ614-44-400-444i−4i−4i4i0-10015−55−51-1-15−51−iii−ii5−i5i5−i5000000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000000000000000
χ624-44-400-444i−4i−4i4i0-1001−55−551-1-1−551−iii−i−i5i5−i5i5000000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ360000000000000000000000000
χ634-44-400-444i−4i−4i4i0-1001−55−551-1-1−551−iii−i−i5i5−i5i5000000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000000000000000
χ644-44-400-44−4i4i4i−4i0400-40000-44400-4−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ654-44-400-44−4i4i4i−4i0-10015−55−51-1-15−51i−i−ii−i5i5−i5i5000000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ360000000000000000000000000
χ664-44-400-44−4i4i4i−4i0-10015−55−51-1-15−51i−i−ii−i5i5−i5i5000000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ360000000000000000000000000
χ674-44-400-44−4i4i4i−4i0-1001−55−551-1-1−551i−i−iii5−i5i5−i5000000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ360000000000000000000000000
χ684-44-400-44−4i4i4i−4i0-1001−55−551-1-1−551i−i−iii5−i5i5−i5000000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ360000000000000000000000000
χ69888888-8-80000-8-200-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000
χ708888-8-8-8-800008-200-22222-2-22-2-2200000000000000000000000000000000000000000000000000000
χ7188-8-8000042−4242−420-200-225−25−2525220000−22−2210−10−1010000000000000000000000000000000000000000000000
χ7288-8-8000042−4242−420-200-2−252525−25220000−22−22−101010−10000000000000000000000000000000000000000000000
χ7388-8-80000−4242−42420-200-225−25−25252200002−22−2−101010−10000000000000000000000000000000000000000000000
χ7488-8-80000−4242−42420-200-2−252525−252200002−22−210−10−1010000000000000000000000000000000000000000000000
χ758-88-8008-800000-200225−2525−252-22−2525-200000000000000000000000000000000000000000000000000000
χ768-88-8008-800000-2002−2525−25252-2225−25-200000000000000000000000000000000000000000000000000000
χ778-8-888-8004i24i2−4i2−4i20-24i2−4i22-2-222-220000−i2−i2i2i2−i2−i2i2i2000000000000000000000000000000000000000000000
χ788-8-888-800−4i2−4i24i24i20-2−4i24i22-2-222-220000i2i2−i2−i2i2i2−i2−i2000000000000000000000000000000000000000000000
χ798-8-88-88004i24i2−4i2−4i20-2−4i24i2222-2-2-220000−i2−i2i2i2i2i2−i2−i2000000000000000000000000000000000000000000000
χ808-8-88-8800−4i2−4i24i24i20-24i2−4i2222-2-2-220000i2i2−i2−i2−i2−i2i2i2000000000000000000000000000000000000000000000

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