Finite Group Databasebeta

← Group #13027157

Character table — Group #13027157

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1122222444444455888881010101010101010101010101016161616161616202020202020202020202020202020202032323232808080808080
order1224488581016161616221020204040244881616161616161616484080808080444488888161616161616161620204040444888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-11111-1-1-1-111111-1-11-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-111-111
χ511111111111111-1-111111-1-1-1-1-1iiii−i−i−i−i1111111i−ii−i-1ii−i−i-1-1-1-1ii−i−i1111-1i−i-1i−i
χ611111111111111-1-111111-1-1-1-1-1iiii−i−i−i−i-1-111111i−ii−i-1ii−i−i-1-1-1-1ii−i−i-1-1-1-11−ii1−ii
χ711111111111111-1-111111-1-1-1-1-1−i−i−i−iiiii1111111−ii−ii-1−i−iii-1-1-1-1−i−iii1111-1−ii-1−ii
χ811111111111111-1-111111-1-1-1-1-1−i−i−i−iiiii-1-111111−ii−ii-1−i−iii-1-1-1-1−i−iii-1-1-1-11i−i1i−i
χ91111111111-1-1-1-1111111111111111111111-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1111-1-1-1
χ101111111111-1-1-1-111111111111111111111-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-1-1111
χ111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-11-1-1-111
χ121111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1111-1-1
χ131111111111-1-1-1-1-1-111111-1-1-1-1-1iiii−i−i−i−i1-11-1-1-1-1−ii−ii-1−i−iii1111ii−i−i11-1-1-1i−i1−ii
χ141111111111-1-1-1-1-1-111111-1-1-1-1-1iiii−i−i−i−i-111-1-1-1-1−ii−ii-1−i−iii1111ii−i−i-1-1111−ii-1i−i
χ151111111111-1-1-1-1-1-111111-1-1-1-1-1−i−i−i−iiiii1-11-1-1-1-1i−ii−i-1ii−i−i1111−i−iii11-1-1-1−ii1i−i
χ161111111111-1-1-1-1-1-111111-1-1-1-1-1−i−i−i−iiiii-111-1-1-1-1i−ii−i-1ii−i−i1111−i−iii-1-1111i−i-1−ii
χ1722222-2-22-22000022222-2-2222-2-20000000000-200002222-2-2-2-2-2000000000000000000
χ1822222-2-22-22000022222-2-2222-2-20000000000-20000-2-2-2-2-22222000000000000000000
χ1922222-2-22-220000-2-2222-2-2-2-2-2220000000000-200002i−2i2i−2i2−2i−2i2i2i000000000000000000
χ2022222-2-22-220000-2-2222-2-2-2-2-2220000000000-20000−2i2i−2i2i22i2i−2i−2i000000000000000000
χ21222-2-200202i2i2−i2−i2222-2-2002-2-20022−2−222−2−2000i2i2−i2−i2000002i−2i2i−2ii2i2−i2−i22−22−20000000000
χ22222-2-200202i2i2−i2−i2222-2-2002-2-200−2−222−2−222000i2i2−i2−i200000−2i2i−2i2ii2i2−i2−i2−22−220000000000
χ23222-2-200202i2i2−i2−i2-2-22-2-200-22200i2i2−i2−i2−i2−i2i2i2000i2i2−i2−i200000-222-2−i2−i2i2i2i2−i2−i2i20000000000
χ24222-2-200202i2i2−i2−i2-2-22-2-200-22200−i2−i2i2i2i2i2−i2−i2000i2i2−i2−i2000002-2-22−i2−i2i2i2−i2i2i2−i20000000000
χ25222-2-200202−i2−i2i2i2222-2-2002-2-20022−2−222−2−2000−i2−i2i2i200000−2i2i−2i2i−i2−i2i2i22−22−20000000000
χ26222-2-200202−i2−i2i2i2222-2-2002-2-200−2−222−2−222000−i2−i2i2i2000002i−2i2i−2i−i2−i2i2i2−22−220000000000
χ27222-2-200202−i2−i2i2i2-2-22-2-200-22200i2i2−i2−i2−i2−i2i2i2000−i2−i2i2i2000002-2-22i2i2−i2−i2i2−i2−i2i20000000000
χ28222-2-200202−i2−i2i2i2-2-22-2-200-22200−i2−i2i2i2i2i2−i2−i2000−i2−i2i2i200000-222-2i2i2−i2−i2−i2i2i2−i20000000000
χ2922-22-2222-22000022-22-222-22-2222222222200-200000000-200000000-2-2-2-20000000000
χ3022-22-2222-22000022-22-222-22-222-2-2-2-2-2-2-2-200-200000000-20000000022220000000000
χ3122-22-2222-220000-2-2-22-2222-22-2-22i2i2i2i−2i−2i−2i−2i00-200000000200000000−2i−2i2i2i0000000000
χ3222-22-2222-220000-2-2-22-2222-22-2-2−2i−2i−2i−2i2i2i2i2i00-2000000002000000002i2i−2i−2i0000000000
χ3322-22-2-2-22222i−2i2i−2i22-22-2-2-2-22-2-2-2000000000022i−2i2i−2i0000200002i−2i2i−2i00000000000000
χ3422-22-2-2-22222i−2i2i−2i-2-2-22-2-2-22-2222000000000022i−2i2i−2i0000-20000−2i2i−2i2i00000000000000
χ3522-22-2-2-2222−2i2i−2i2i22-22-2-2-2-22-2-2-200000000002−2i2i−2i2i000020000−2i2i−2i2i00000000000000
χ3622-22-2-2-2222−2i2i−2i2i-2-2-22-2-2-22-222200000000002−2i2i−2i2i0000-200002i−2i2i−2i00000000000000
χ3722-2-22002022−2−2222-2-2200-2-220022−2−222−2−20002−2−2222-2-2000002−2−22−22−220000000000
χ3822-2-22002022−2−2222-2-2200-2-2200−2−222−2−2220002−2−22-2-222000002−2−222−22−20000000000
χ3922-2-22002022−2−22-2-2-2-220022-200i2i2−i2−i2−i2−i2i2i20002−2−222i−2i−2i2i00000−222−2−i2i2i2−i20000000000
χ4022-2-22002022−2−22-2-2-2-220022-200−i2−i2i2i2i2i2−i2−i20002−2−22−2i2i2i−2i00000−222−2i2−i2−i2i20000000000
χ4122-2-2200202−222−222-2-2200-2-220022−2−222−2−2000−222−2-2-22200000−222−2−22−220000000000
χ4222-2-2200202−222−222-2-2200-2-2200−2−222−2−222000−222−222-2-200000−222−22−22−20000000000
χ4322-2-2200202−222−2-2-2-2-220022-200i2i2−i2−i2−i2−i2i2i2000−222−2−2i2i2i−2i000002−2−22−i2i2i2−i20000000000
χ4422-2-2200202−222−2-2-2-2-220022-200−i2−i2i2i2i2i2−i2−i2000−222−22i−2i−2i2i000002−2−22i2−i2−i2i20000000000
χ454444444-14-1444400-1-1-1-1-1000000000000044-1-1-1-1-100000000000000000-1-1-1-1000000
χ464444444-14-1444400-1-1-1-1-10000000000000-4-4-1-1-1-1-1000000000000000001111000000
χ474444444-14-1-4-4-4-400-1-1-1-1-100000000000004-4-1111100000000000000000-1-111000000
χ484444444-14-1-4-4-4-400-1-1-1-1-10000000000000-44-111110000000000000000011-1-1000000
χ4944-44-4-4-4-14-14i−4i4i−4i001-1111000000000000000-1−ii−ii000000000000000005−5i5−i5000000
χ5044-44-4-4-4-14-14i−4i4i−4i001-1111000000000000000-1−ii−ii00000000000000000−55−i5i5000000
χ5144-44-4-4-4-14-1−4i4i−4i4i001-1111000000000000000-1i−ii−i000000000000000005−5−i5i5000000
χ5244-44-4-4-4-14-1−4i4i−4i4i001-1111000000000000000-1i−ii−i00000000000000000−55i5−i5000000
χ534-400022−2240-400004-400022−2200022−22−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ772ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ79−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ772ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ790000000000000000000000000000000000
χ544-400022−2240-400004-400022−2200022−222ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ77−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ792ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ77−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ790000000000000000000000000000000000
χ554-400022−2240-40000-4400022−22000−2222−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ792ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ792ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ79−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ79−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ770000000000000000000000000000000000
χ564-400022−2240-40000-4400022−22000−22222ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ79−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ79−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ792ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ792ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ770000000000000000000000000000000000
χ574-4000−222240-400004-4000−2222000−22222ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ770000000000000000000000000000000000
χ584-4000−222240-400004-4000−2222000−2222−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ770000000000000000000000000000000000
χ594-4000−222240-40000-44000−222200022−22−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ792ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ792ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ79−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ790000000000000000000000000000000000
χ604-4000−222240-40000-44000−222200022−222ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ79−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ79−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ792ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ790000000000000000000000000000000000
χ6188888-8-8-2-8-2000000-2-2-22200000000000000020000000000000000000000000000000
χ62888-8-800-20-24i24i2−4i2−4i200-222000000000000000000−i2−i2i2i2000000000000000000000000000
χ63888-8-800-20-2−4i2−4i24i24i200-222000000000000000000i2i2−i2−i2000000000000000000000000000
χ6488-88-888-2-8-20000002-22-2-200000000000000020000000000000000000000000000000
χ6588-8-8800-20-242−42−42420022-2000000000000000000−222−2000000000000000000000000000
χ6688-8-8800-20-2−424242−420022-20000000000000000002−2−22000000000000000000000000000
χ6716-1600082−82-404000000000−222200000000000000000000000000000000000000000000000
χ6816-16000−8282-40400000000022−2200000000000000000000000000000000000000000000000

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