Finite Group Databasebeta

← Group #13027117

Character table — Group #13027117

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444455558888888888881010101010101616161616161616161616162020202020202020404040404040404040404040404040404040
order1244222444510202088882444441010102020208888881010202020202020202020201616161616161616888888161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ5111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ7111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ911111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111iiii−i−i−i−i-1-1-1-1-1-1ii−i−iii−i−iii−i−i
χ1011111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111−i−i−i−iiiii-1-1-1-1-1-1−i−iii−i−iii−i−iii
χ1111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-11111−i−iiiii−i−i−i−iii
χ1211111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-11111ii−i−i−i−iiiii−i−i
χ1311111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-111ii−i−i−i−iii−i−iii
χ1411111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-111−i−iiiii−i−iii−i−i
χ1511111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1111-1-1−i−iii−i−iiiii−i−i
χ1611111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1111-1-1ii−i−iii−i−i−i−iii
χ1722222-2-22-2-222222222002i−2i002-2-22-2-2-2-222-2-200002i2i−2i−2i000000000000002i−2i00000000000000
χ1822222-2-22-2-22222222200−2i2i002-2-22-2-2-2-222-2-20000−2i−2i2i2i00000000000000−2i2i00000000000000
χ1922222-2-22-2-22222-2-2-2-2002i−2i002-2-22-2-222-2-22200002i2i−2i−2i00000000000000−2i2i00000000000000
χ2022222-2-22-2-22222-2-2-2-200−2i2i002-2-22-2-222-2-2220000−2i−2i2i2i000000000000002i−2i00000000000000
χ212222-22-2-22-222222222000000-22-2-22-222-2-2-2-20000000000000000000000000000002i−2i2i−2i0000
χ222222-22-2-22-222222222000000-22-2-22-222-2-2-2-2000000000000000000000000000000−2i2i−2i2i0000
χ232222-22-2-22-22222-2-2-2-2000000-22-2-22-2-2-222220000000000000000000000000000002-2-220000
χ242222-22-2-22-22222-2-2-2-2000000-22-2-22-2-2-22222000000000000000000000000000000-222-20000
χ252222-2-22-2-2222222222000000-2-22-2-22-2-2-2-22200000000000000000000000000000000002-22-2
χ262222-2-22-2-2222222222000000-2-22-2-22-2-2-2-2220000000000000000000000000000000000-22-22
χ272222-2-22-2-222222-2-2-2-2000000-2-22-2-222222-2-200000000000000000000000000000000002i−2i−2i2i
χ282222-2-22-2-222222-2-2-2-2000000-2-22-2-222222-2-20000000000000000000000000000000000−2i2i2i−2i
χ2922-2-2222-2-2-222-2-22i2i−2i−2i00002-2222-2-2-22i−2i2i−2i2i−2i0000000022-2-20000000000002i−2i000000000000
χ3022-2-2222-2-2-222-2-22i2i−2i−2i0000-22222-2-2-22i−2i2i−2i2i−2i00000000-2-222000000000000−2i2i000000000000
χ3122-2-2222-2-2-222-2-2−2i−2i2i2i00002-2222-2-2-2−2i2i−2i2i−2i2i0000000022-2-2000000000000−2i2i000000000000
χ3222-2-2222-2-2-222-2-2−2i−2i2i2i0000-22222-2-2-2−2i2i−2i2i−2i2i00000000-2-2220000000000002i−2i000000000000
χ3322-2-22-2-2-22222-2-22i2i−2i−2i2-200002-2-2-222−2i2i2i−2i−2i2i22-2-200000000000000002i−2i0000000000000000
χ3422-2-22-2-2-22222-2-22i2i−2i−2i-2200002-2-2-222−2i2i2i−2i−2i2i-2-2220000000000000000−2i2i0000000000000000
χ3522-2-22-2-2-22222-2-2−2i−2i2i2i2-200002-2-2-2222i−2i−2i2i2i−2i22-2-20000000000000000−2i2i0000000000000000
χ3622-2-22-2-2-22222-2-2−2i−2i2i2i-2200002-2-2-2222i−2i−2i2i2i−2i-2-22200000000000000002i−2i0000000000000000
χ3722-2-2-22-22-2222-2-22i2i−2i−2i000000-22-22-222i−2i−2i2i−2i2i00000000000000000000000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ7400000000
χ3822-2-2-22-22-2222-2-22i2i−2i−2i000000-22-22-222i−2i−2i2i−2i2i000000000000000000000000002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400000000
χ3922-2-2-22-22-2222-2-2−2i−2i2i2i000000-22-22-22−2i2i2i−2i2i−2i00000000000000000000000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ7800000000
χ4022-2-2-22-22-2222-2-2−2i−2i2i2i000000-22-22-22−2i2i2i−2i2i−2i000000000000000000000000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800000000
χ4122-2-2-2-2222-222-2-22i2i−2i−2i000000-2-2222-2−2i2i−2i2i2i−2i000000000000−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ78000000000000000000
χ4222-2-2-2-2222-222-2-22i2i−2i−2i000000-2-2222-2−2i2i−2i2i2i−2i0000000000002ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ78000000000000000000
χ4322-2-2-2-2222-222-2-2−2i−2i2i2i000000-2-2222-22i−2i2i−2i−2i2i000000000000−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ74000000000000000000
χ4422-2-2-2-2222-222-2-2−2i−2i2i2i000000-2-2222-22i−2i2i−2i−2i2i0000000000002ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ74000000000000000000
χ454444444444-1-1-1-10000444444-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-1-1-1-1000044-4-4-4-4-1-1-1-1-1-1000000-1-1-1-11111111100000000000000000000000000
χ474444444444-1-1-1-10000-4-444-4-4-1-1-1-1-1-10000001111-1-1-1-1111100000000000000000000000000
χ484444444444-1-1-1-10000-4-4-4-444-1-1-1-1-1-100000011111111-1-1-1-100000000000000000000000000
χ4944444-4-44-4-4-1-1-1-10000004i−4i00-111-1110000005−55−5−i−iiii5−i5i5−i500000000000000000000000000
χ5044444-4-44-4-4-1-1-1-10000004i−4i00-111-111000000−55−55−i−iii−i5i5−i5i500000000000000000000000000
χ5144444-4-44-4-4-1-1-1-1000000−4i4i00-111-1110000005−55−5ii−i−i−i5i5−i5i500000000000000000000000000
χ5244444-4-44-4-4-1-1-1-1000000−4i4i00-111-111000000−55−55ii−i−ii5−i5i5−i500000000000000000000000000
χ5344-4-4444-4-4-4-1-111000000004-4-1-1-11110000005−5−555−55−5-1-11100000000000000000000000000
χ5444-4-4444-4-4-4-1-111000000004-4-1-1-1111000000−555−5−55−55-1-11100000000000000000000000000
χ5544-4-4444-4-4-4-1-11100000000-44-1-1-11110000005−5−55−55−5511-1-100000000000000000000000000
χ5644-4-4444-4-4-4-1-11100000000-44-1-1-1111000000−555−55−55−511-1-100000000000000000000000000
χ5744-4-44-4-4-444-1-11100004-40000-1111-1-1000000-1-111i5−i5−i5i5i5−i5−i5i500000000000000000000000000
χ5844-4-44-4-4-444-1-11100004-40000-1111-1-1000000-1-111−i5i5i5−i5−i5i5i5−i500000000000000000000000000
χ5944-4-44-4-4-444-1-1110000-440000-1111-1-100000011-1-1i5−i5−i5i5−i5i5i5−i500000000000000000000000000
χ6044-4-44-4-4-444-1-1110000-440000-1111-1-100000011-1-1−i5i5i5−i5i5−i5−i5i500000000000000000000000000
χ614-44i−4i0000004-44i−4i−4ζ26−4ζ42−4ζ58−4ζ744ζ26+4ζ42+4ζ58+4ζ74−4ζ14−4ζ46−4ζ62−4ζ784ζ14+4ζ46+4ζ62+4ζ780000000000000000000000000000002ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ77−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ73−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ79−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ59000000000000000000
χ624-44i−4i0000004-44i−4i−4ζ26−4ζ42−4ζ58−4ζ744ζ26+4ζ42+4ζ58+4ζ74−4ζ14−4ζ46−4ζ62−4ζ784ζ14+4ζ46+4ζ62+4ζ78000000000000000000000000000000−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ772ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ732ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ792ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ59000000000000000000
χ634-44i−4i0000004-44i−4i4ζ26+4ζ42+4ζ58+4ζ74−4ζ26−4ζ42−4ζ58−4ζ744ζ14+4ζ46+4ζ62+4ζ78−4ζ14−4ζ46−4ζ62−4ζ78000000000000000000000000000000−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ73−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ77−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ592ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ79000000000000000000
χ644-44i−4i0000004-44i−4i4ζ26+4ζ42+4ζ58+4ζ74−4ζ26−4ζ42−4ζ58−4ζ744ζ14+4ζ46+4ζ62+4ζ78−4ζ14−4ζ46−4ζ62−4ζ780000000000000000000000000000002ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ732ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ772ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ59−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ79000000000000000000
χ654-4−4i4i0000004-4−4i4i−4ζ14−4ζ46−4ζ62−4ζ784ζ14+4ζ46+4ζ62+4ζ78−4ζ26−4ζ42−4ζ58−4ζ744ζ26+4ζ42+4ζ58+4ζ74000000000000000000000000000000−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ79−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ59−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ772ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ73000000000000000000
χ664-4−4i4i0000004-4−4i4i−4ζ14−4ζ46−4ζ62−4ζ784ζ14+4ζ46+4ζ62+4ζ78−4ζ26−4ζ42−4ζ58−4ζ744ζ26+4ζ42+4ζ58+4ζ740000000000000000000000000000002ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ792ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ592ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ77−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ73000000000000000000
χ674-4−4i4i0000004-4−4i4i4ζ14+4ζ46+4ζ62+4ζ78−4ζ14−4ζ46−4ζ62−4ζ784ζ26+4ζ42+4ζ58+4ζ74−4ζ26−4ζ42−4ζ58−4ζ74000000000000000000000000000000−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ592ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ792ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ732ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ77000000000000000000
χ684-4−4i4i0000004-4−4i4i4ζ14+4ζ46+4ζ62+4ζ78−4ζ14−4ζ46−4ζ62−4ζ784ζ26+4ζ42+4ζ58+4ζ74−4ζ26−4ζ42−4ζ58−4ζ740000000000000000000000000000002ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ59−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ79−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ73−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ77000000000000000000
χ698888-88-8-88-8-2-2-2-200000000002-222-2200000000000000000000000000000000000000000000
χ708888-8-88-8-88-2-2-2-2000000000022-222-200000000000000000000000000000000000000000000
χ7188-8-8-88-88-88-2-22200000000002-22-22-200000000000000000000000000000000000000000000
χ7288-8-8-8-8888-8-2-222000000000022-2-2-2200000000000000000000000000000000000000000000
χ7316-1616i−16i000000-44−4i4i000000000000000000000000000000000000000000000000000000000000
χ7416-16−16i16i000000-444i−4i000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.