Finite Group Databasebeta

← Group #13026945

Character table — Group #13026945

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1122222444444455888881010101010101010101010101016161616161616202020202020202020202020202020202032323232808080808080
order1224488245888104410202040402248816161616161616162810204040402488816161616161616161616161610104040444888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ511111111111111-1-111111-1-1-1-1-1iiii−i−i−i−i1111111-1-1-1-1-1iiiiii−i−i−i−i−i−i1111-1i−i-1i−i
χ611111111111111-1-111111-1-1-1-1-1iiii−i−i−i−i-1-111111-1-1-1-1-1iiiiii−i−i−i−i−i−i-1-1-1-11−ii1−ii
χ711111111111111-1-111111-1-1-1-1-1−i−i−i−iiiii1111111-1-1-1-1-1−i−i−i−i−i−iiiiiii1111-1−ii-1−ii
χ811111111111111-1-111111-1-1-1-1-1−i−i−i−iiiii-1-111111-1-1-1-1-1−i−i−i−i−i−iiiiiii-1-1-1-11i−i1i−i
χ91111111-1-111-1-11111111111111111111111-1-1-11-1-1-1-11-1-111-1-1-1-111-1-1-1-111-1-11-1-1-111
χ101111111-1-111-1-1111111111111111111111-11-1-11-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-111-1111-1-1
χ111111111-1-111-1-11111111111111-1-1-1-1-1-1-1-11-1-1-11-1-1-1-11-1-1-1-11111-1-1111111-1-1111-1-1-1
χ121111111-1-111-1-11111111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11-1-1-1-11111-1-11111-1-111-1-1-1111
χ131111111-1-111-1-11-1-111111-1-1-1-1-1iiii−i−i−i−i1-1-1-11-1-111-111ii−i−i−i−i−i−iiiii11-1-1-1−ii1i−i
χ141111111-1-111-1-11-1-111111-1-1-1-1-1iiii−i−i−i−i-11-1-11-1-111-111ii−i−i−i−i−i−iiiii-1-1111i−i-1−ii
χ151111111-1-111-1-11-1-111111-1-1-1-1-1−i−i−i−iiiii1-1-1-11-1-111-111−i−iiiiiii−i−i−i−i11-1-1-1i−i1−ii
χ161111111-1-111-1-11-1-111111-1-1-1-1-1−i−i−i−iiiii-11-1-11-1-111-111−i−iiiiiii−i−i−i−i-1-1111−ii-1i−i
χ1722222-2-2222-2-2-2222222-2-2222-2-2000000000022-2-2-222-2-2-20000000000000000000000
χ1822222-2-2222-2-2-22-2-2222-2-2-2-2-222000000000022-2-2-2-2-22220000000000000000000000
χ1922222-2-2-2-22-222222222-2-2222-2-20000000000-2-2-222-2-2-2220000000000000000000000
χ2022222-2-2-2-22-2222-2-2222-2-2-2-2-2220000000000-2-2-222222-2-20000000000000000000000
χ21222-2-20000202i−2i2222-2-200-2-220022−2−222−2−2000002i−2i0002i−2i2−2i2i2−i2−i22−2i2i2−i2−i20000000000
χ22222-2-20000202i−2i2222-2-200-2-2200−2−222−2−222000002i−2i0002i−2i−22−i2−i2i2i2−22−i2−i2i2i20000000000
χ23222-2-20000202i−2i2-2-22-2-20022-200i2i2−i2−i2−i2−i2i2i2000002i−2i000−2i2ii2−i2−2−222−i2i222−2−20000000000
χ24222-2-20000202i−2i2-2-22-2-20022-200−i2−i2i2i2i2i2−i2−i2000002i−2i000−2i2i−i2i222−2−2i2−i2−2−2220000000000
χ25222-2-2000020−2i2i2222-2-200-2-220022−2−222−2−200000−2i2i000−2i2i2−2−i2−i2i2i22−2−i2−i2i2i20000000000
χ26222-2-2000020−2i2i2222-2-200-2-2200−2−222−2−22200000−2i2i000−2i2i−22i2i2−i2−i2−22i2i2−i2−i20000000000
χ27222-2-2000020−2i2i2-2-22-2-20022-200i2i2−i2−i2−i2−i2i2i200000−2i2i0002i−2ii2−i222−2−2−i2i2−2−2220000000000
χ28222-2-2000020−2i2i2-2-22-2-20022-200−i2−i2i2i2i2i2−i2−i200000−2i2i0002i−2i−i2i2−2−222i2−i222−2−20000000000
χ2922-22-2002-22000222-22-200-22-20022−2−222−2−2002-2000-22000−222−22−2−222−22−20000000000
χ3022-22-2002-22000222-22-200-22-200−2−222−2−222002-2000-220002−2−22−222−2−22−220000000000
χ3122-22-2002-220002-2-2-22-2002-2200i2i2−i2−i2−i2−i2i2i2002-20002-2000−i2i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ3222-22-2002-220002-2-2-22-2002-2200−i2−i2i2i2i2i2−i2−i2002-20002-2000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ3322-22-200-222000222-22-200-22-20022−2−222−2−200-220002-2000−22−22−22−22−22−220000000000
χ3422-22-200-222000222-22-200-22-200−2−222−2−22200-220002-20002−22−22−22−22−22−20000000000
χ3522-22-200-2220002-2-2-22-2002-2200i2i2−i2−i2−i2−i2i2i200-22000-22000−i2i2−i2i2−i2i2i2−i2i2−i2i2−i20000000000
χ3622-22-200-2220002-2-2-22-2002-2200−i2−i2i2i2i2i2−i2−i200-22000-22000i2−i2i2−i2i2−i2−i2i2−i2i2−i2i20000000000
χ3722-2-2222002-200222-2-22222-2-222222222220000-20000-200-2-20000-2-200000000000000
χ3822-2-2222002-200222-2-22222-2-222-2-2-2-2-2-2-2-20000-20000-2002200002200000000000000
χ3922-2-2222002-2002-2-2-2-2222-222-2-22i2i2i2i−2i−2i−2i−2i0000-20000200−2i−2i00002i2i00000000000000
χ4022-2-2222002-2002-2-2-2-2222-222-2-2−2i−2i−2i−2i2i2i2i2i0000-200002002i2i0000−2i−2i00000000000000
χ4122-2-22-2-2002200222-2-22-2-22-2-2-2-200000000000020000200002i−2i−2i2i002i−2i−2i2i0000000000
χ4222-2-22-2-2002200222-2-22-2-22-2-2-2-20000000000002000020000−2i2i2i−2i00−2i2i2i−2i0000000000
χ4322-2-22-2-20022002-2-2-2-22-2-2-2222200000000000020000-200002-2-2200-222-20000000000
χ4422-2-22-2-20022002-2-2-2-22-2-2-2222200000000000020000-20000-222-2002-2-220000000000
χ45444444444-1444-100-1-1-1-1-1000000000000044-1-1-1-1-100000000000000000-1-1-1-1000000
χ46444444444-1444-100-1-1-1-1-10000000000000-4-4-1-1-1-1-1000000000000000001111000000
χ474444444-4-4-14-4-4-100-1-1-1-1-100000000000004-411-11100000000000000000-1-111000000
χ484444444-4-4-14-4-4-100-1-1-1-1-10000000000000-4411-1110000000000000000011-1-1000000
χ4944444-4-444-1-4-4-4-100-1-1-111000000000000000-1-1111000000000000000005−55−5000000
χ5044444-4-444-1-4-4-4-100-1-1-111000000000000000-1-111100000000000000000−55−55000000
χ5144444-4-4-4-4-1-444-100-1-1-111000000000000000111-1-1000000000000000005−5−55000000
χ5244444-4-4-4-4-1-444-100-1-1-111000000000000000111-1-100000000000000000−555−5000000
χ534-400022−22004000-44i−4i00022−220002i2−2i22ζ13+2ζ29−2ζ31−2ζ47+2ζ61−2ζ63+2ζ77−2ζ79−2ζ13−2ζ29+2ζ31+2ζ47−2ζ61+2ζ63−2ζ77+2ζ79−2ζ9−2ζ11−2ζ27−2ζ41−2ζ43−2ζ57−2ζ59−2ζ732ζ9+2ζ11+2ζ27+2ζ41+2ζ43+2ζ57+2ζ59+2ζ732ζ9−2ζ11−2ζ27+2ζ41−2ζ43+2ζ57−2ζ59+2ζ73−2ζ9+2ζ11+2ζ27−2ζ41+2ζ43−2ζ57+2ζ59−2ζ732ζ13+2ζ29+2ζ31+2ζ47+2ζ61+2ζ63+2ζ77+2ζ79−2ζ13−2ζ29−2ζ31−2ζ47−2ζ61−2ζ63−2ζ77−2ζ790000000000000000000000000000000000
χ544-400022−22004000-44i−4i00022−220002i2−2i2−2ζ13−2ζ29+2ζ31+2ζ47−2ζ61+2ζ63−2ζ77+2ζ792ζ13+2ζ29−2ζ31−2ζ47+2ζ61−2ζ63+2ζ77−2ζ792ζ9+2ζ11+2ζ27+2ζ41+2ζ43+2ζ57+2ζ59+2ζ73−2ζ9−2ζ11−2ζ27−2ζ41−2ζ43−2ζ57−2ζ59−2ζ73−2ζ9+2ζ11+2ζ27−2ζ41+2ζ43−2ζ57+2ζ59−2ζ732ζ9−2ζ11−2ζ27+2ζ41−2ζ43+2ζ57−2ζ59+2ζ73−2ζ13−2ζ29−2ζ31−2ζ47−2ζ61−2ζ63−2ζ77−2ζ792ζ13+2ζ29+2ζ31+2ζ47+2ζ61+2ζ63+2ζ77+2ζ790000000000000000000000000000000000
χ554-400022−22004000-4−4i4i00022−22000−2i22i22ζ9−2ζ11−2ζ27+2ζ41−2ζ43+2ζ57−2ζ59+2ζ73−2ζ9+2ζ11+2ζ27−2ζ41+2ζ43−2ζ57+2ζ59−2ζ732ζ13+2ζ29+2ζ31+2ζ47+2ζ61+2ζ63+2ζ77+2ζ79−2ζ13−2ζ29−2ζ31−2ζ47−2ζ61−2ζ63−2ζ77−2ζ792ζ13+2ζ29−2ζ31−2ζ47+2ζ61−2ζ63+2ζ77−2ζ79−2ζ13−2ζ29+2ζ31+2ζ47−2ζ61+2ζ63−2ζ77+2ζ79−2ζ9−2ζ11−2ζ27−2ζ41−2ζ43−2ζ57−2ζ59−2ζ732ζ9+2ζ11+2ζ27+2ζ41+2ζ43+2ζ57+2ζ59+2ζ730000000000000000000000000000000000
χ564-400022−22004000-4−4i4i00022−22000−2i22i2−2ζ9+2ζ11+2ζ27−2ζ41+2ζ43−2ζ57+2ζ59−2ζ732ζ9−2ζ11−2ζ27+2ζ41−2ζ43+2ζ57−2ζ59+2ζ73−2ζ13−2ζ29−2ζ31−2ζ47−2ζ61−2ζ63−2ζ77−2ζ792ζ13+2ζ29+2ζ31+2ζ47+2ζ61+2ζ63+2ζ77+2ζ79−2ζ13−2ζ29+2ζ31+2ζ47−2ζ61+2ζ63−2ζ77+2ζ792ζ13+2ζ29−2ζ31−2ζ47+2ζ61−2ζ63+2ζ77−2ζ792ζ9+2ζ11+2ζ27+2ζ41+2ζ43+2ζ57+2ζ59+2ζ73−2ζ9−2ζ11−2ζ27−2ζ41−2ζ43−2ζ57−2ζ59−2ζ730000000000000000000000000000000000
χ574-4000−2222004000-44i−4i000−2222000−2i22i2−2ζ9−2ζ11−2ζ27−2ζ41−2ζ43−2ζ57−2ζ59−2ζ732ζ9+2ζ11+2ζ27+2ζ41+2ζ43+2ζ57+2ζ59+2ζ73−2ζ13−2ζ29+2ζ31+2ζ47−2ζ61+2ζ63−2ζ77+2ζ792ζ13+2ζ29−2ζ31−2ζ47+2ζ61−2ζ63+2ζ77−2ζ792ζ13+2ζ29+2ζ31+2ζ47+2ζ61+2ζ63+2ζ77+2ζ79−2ζ13−2ζ29−2ζ31−2ζ47−2ζ61−2ζ63−2ζ77−2ζ79−2ζ9+2ζ11+2ζ27−2ζ41+2ζ43−2ζ57+2ζ59−2ζ732ζ9−2ζ11−2ζ27+2ζ41−2ζ43+2ζ57−2ζ59+2ζ730000000000000000000000000000000000
χ584-4000−2222004000-44i−4i000−2222000−2i22i22ζ9+2ζ11+2ζ27+2ζ41+2ζ43+2ζ57+2ζ59+2ζ73−2ζ9−2ζ11−2ζ27−2ζ41−2ζ43−2ζ57−2ζ59−2ζ732ζ13+2ζ29−2ζ31−2ζ47+2ζ61−2ζ63+2ζ77−2ζ79−2ζ13−2ζ29+2ζ31+2ζ47−2ζ61+2ζ63−2ζ77+2ζ79−2ζ13−2ζ29−2ζ31−2ζ47−2ζ61−2ζ63−2ζ77−2ζ792ζ13+2ζ29+2ζ31+2ζ47+2ζ61+2ζ63+2ζ77+2ζ792ζ9−2ζ11−2ζ27+2ζ41−2ζ43+2ζ57−2ζ59+2ζ73−2ζ9+2ζ11+2ζ27−2ζ41+2ζ43−2ζ57+2ζ59−2ζ730000000000000000000000000000000000
χ594-4000−2222004000-4−4i4i000−22220002i2−2i22ζ13+2ζ29+2ζ31+2ζ47+2ζ61+2ζ63+2ζ77+2ζ79−2ζ13−2ζ29−2ζ31−2ζ47−2ζ61−2ζ63−2ζ77−2ζ79−2ζ9+2ζ11+2ζ27−2ζ41+2ζ43−2ζ57+2ζ59−2ζ732ζ9−2ζ11−2ζ27+2ζ41−2ζ43+2ζ57−2ζ59+2ζ73−2ζ9−2ζ11−2ζ27−2ζ41−2ζ43−2ζ57−2ζ59−2ζ732ζ9+2ζ11+2ζ27+2ζ41+2ζ43+2ζ57+2ζ59+2ζ73−2ζ13−2ζ29+2ζ31+2ζ47−2ζ61+2ζ63−2ζ77+2ζ792ζ13+2ζ29−2ζ31−2ζ47+2ζ61−2ζ63+2ζ77−2ζ790000000000000000000000000000000000
χ604-4000−2222004000-4−4i4i000−22220002i2−2i2−2ζ13−2ζ29−2ζ31−2ζ47−2ζ61−2ζ63−2ζ77−2ζ792ζ13+2ζ29+2ζ31+2ζ47+2ζ61+2ζ63+2ζ77+2ζ792ζ9−2ζ11−2ζ27+2ζ41−2ζ43+2ζ57−2ζ59+2ζ73−2ζ9+2ζ11+2ζ27−2ζ41+2ζ43−2ζ57+2ζ59−2ζ732ζ9+2ζ11+2ζ27+2ζ41+2ζ43+2ζ57+2ζ59+2ζ73−2ζ9−2ζ11−2ζ27−2ζ41−2ζ43−2ζ57−2ζ59−2ζ732ζ13+2ζ29−2ζ31−2ζ47+2ζ61−2ζ63+2ζ77−2ζ79−2ζ13−2ζ29+2ζ31+2ζ47−2ζ61+2ζ63−2ζ77+2ζ790000000000000000000000000000000000
χ61888-8-80000-208i−8i-200-22200000000000000000000−2i2i000000000000000000000000000
χ62888-8-80000-20−8i8i-200-222000000000000000000002i−2i000000000000000000000000000
χ6388-88-8008-8-2000-2002-2200000000000000000-22000000000000000000000000000000
χ6488-88-800-88-2000-2002-22000000000000000002-2000000000000000000000000000000
χ6588-8-888800-2-800-20022-2-2-200000000000000000200000000000000000000000000000
χ6688-8-88-8-800-2800-20022-22200000000000000000-200000000000000000000000000000
χ6716-1600082−8200-4000400000−222200000000000000000000000000000000000000000000000
χ6816-16000−828200-400040000022−2200000000000000000000000000000000000000000000000

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