Finite Group Databasebeta

← Group #13026260

Character table — Group #13026260

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444444448888888888810101010101010101616161616161616161616162020202020202020202040404040404040404080808080
order12442424588102020224481010102020202244888810101010202020204040404024161616161616161622448161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1iiii−i−i−i−i-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1−i−i−i−iiiii-1-1-1-1-1−i−iii−i−iii
χ511111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111111-1-1-1-1
χ611111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ711111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i1111-1ii−i−i−i−iii
χ811111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii1111-1−i−iiiii−i−i
χ9111111-1-11111111-11-1-11-1-1-1-111111111111-1-111-1-111-1-1-1-1111111111-11-1-1-1-1-1-11-11-1
χ10111111-1-11111111-11-1-11-1-1-1-111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-11-11
χ11111111-1-11111111-11-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111-1-111iiii−i−i−i−i-11-111−i−iiii−i−ii
χ12111111-1-11111111-11-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111-1-111−i−i−i−iiiii-11-111ii−i−i−iii−i
χ13111111-1-1111111-11-11-11-1-1-1-1111111111-1-111-1-11111-1-1-1-111111111-11-11-1-1-1-1-1-11-11
χ14111111-1-1111111-11-11-11-1-1-1-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111111-11-1
χ15111111-1-1111111-11-11-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-111iiii−i−i−i−i1-11-11−i−iii−iii−i
χ16111111-1-1111111-11-11-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-111−i−i−i−iiiii1-11-11ii−i−ii−i−ii
χ17222222222-2-22220000-22222222222-2-2-2-200000000-2-2-2-222000000000000-200000000
χ18222222222-2-22220000-2222222-2-2-2-2222200000000-2-2-2-2-2-2000000000000200000000
χ19222222-2-22-2-2222000022-2-2-2-222222-2-2-2-200000000-2-222-2-2000000000000200000000
χ20222222-2-22-2-2222000022-2-2-2-22-2-2-2-2222200000000-2-22222000000000000-200000000
χ2122-2-22-22-22002-2-200000222-2-2-222-2-20000000000000000-2222−2−222−2−2000002−22−20000
χ2222-2-22-22-22002-2-200000222-2-2-222-2-20000000000000000-22−2−222−2−22200000−22−220000
χ2322-2-22-22-22002-2-200000222-2-2-2-2-22200000000000000002-2i2i2−i2−i2−i2−i2i2i200000i2−i2−i2i20000
χ2422-2-22-22-22002-2-200000222-2-2-2-2-22200000000000000002-2−i2−i2i2i2i2i2−i2−i200000−i2i2i2−i20000
χ2522-2-22-2-222002-2-2000002-2-222-222-2-200000000000000002-222−2−222−2−200000−22−220000
χ2622-2-22-2-222002-2-2000002-2-222-222-2-200000000000000002-2−2−222−2−222000002−22−20000
χ2722-2-22-2-222002-2-2000002-2-222-2-2-2220000000000000000-22i2i2−i2−i2−i2−i2i2i200000−i2i2i2−i20000
χ2822-2-22-2-222002-2-2000002-2-222-2-2-2220000000000000000-22−i2−i2i2i2i2i2−i2−i200000i2−i2−i2i20000
χ2922-2-2-220022-22-2-2020-20-2000022-22-222-2-2002200-2-22-2000000000000020-2000000000
χ3022-2-2-220022-22-2-2020-20-200002-22-22-2-222002200-2-22-20000000000000-202000000000
χ3122-2-2-220022-22-2-20-2020-2000022-22-222-2-200-2-200222-20000000000000-202000000000
χ3222-2-2-220022-22-2-20-2020-200002-22-22-2-22200-2-200222-2000000000000020-2000000000
χ3322-2-2-22002-222-2-220-200-2000022-22-2-2-2222200-2-200-22000000000000-2020000000000
χ3422-2-2-22002-222-2-220-200-200002-22-2222-2-22200-2-200-2200000000000020-20000000000
χ3522-2-2-22002-222-2-2-20200-2000022-22-2-2-222-2-2002200-2200000000000020-20000000000
χ3622-2-2-22002-222-2-2-20200-200002-22-2222-2-2-2-2002200-22000000000000-2020000000000
χ3744444444-144-1-1-144444-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ3844444444-144-1-1-1-4-4-4-44-1-1-1-1-1-10000000011111111-1-1-1-100000000000000000000000
χ3944444444-1-4-4-1-1-10000-4-1-1-1-1-1-1000000005−55−55−55−5111100000000000000000000000
χ4044444444-1-4-4-1-1-10000-4-1-1-1-1-1-100000000−55−55−55−55111100000000000000000000000
χ41444444-4-4-144-1-1-14-44-4-4-11111-100000000-1-111-1-111-1-11100000000000000000000000
χ42444444-4-4-144-1-1-1-44-44-4-11111-10000000011-1-111-1-1-1-11100000000000000000000000
χ43444444-4-4-1-4-4-1-1-100004-11111-1000000005−5−555−5−5511-1-100000000000000000000000
χ44444444-4-4-1-4-4-1-1-100004-11111-100000000−555−5−555−511-1-100000000000000000000000
χ454444-4-40040044400000-40000-44-4-44000000000000000000000000000000000000000
χ464444-4-40040044400000-40000-4-444-4000000000000000000000000000000000000000
χ4744-4-4-4400-14-4-111040-4015−55−5-1000000005−5-1-1−5511-115−500000000000000000000000
χ4844-4-4-4400-14-4-111040-401−55−55-100000000−55-1-15−511-11−5500000000000000000000000
χ4944-4-4-4400-14-4-1110-404015−55−5-100000000−55115−5-1-1-115−500000000000000000000000
χ5044-4-4-4400-14-4-1110-40401−55−55-1000000005−511−55-1-1-11−5500000000000000000000000
χ5144-4-4-4400-1-44-11140-40015−55−5-100000000-1-15−511−551-1−5500000000000000000000000
χ5244-4-4-4400-1-44-11140-4001−55−55-100000000-1-1−55115−51-15−500000000000000000000000
χ5344-4-4-4400-1-44-111-4040015−55−5-10000000011−55-1-15−51-1−5500000000000000000000000
χ5444-4-4-4400-1-44-111-404001−55−55-100000000115−5-1-1−551-15−500000000000000000000000
χ554-44i−4i0000400-44i−4i00000000000000022−222i2−2i2000000000000002ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ77−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ73−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ59−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ790000000000000
χ564-44i−4i0000400-44i−4i00000000000000022−222i2−2i200000000000000−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ772ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ732ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ592ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ790000000000000
χ574-44i−4i0000400-44i−4i000000000000000−2222−2i22i200000000000000−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ73−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ772ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ79−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ590000000000000
χ584-44i−4i0000400-44i−4i000000000000000−2222−2i22i2000000000000002ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ732ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ77−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ792ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ590000000000000
χ594-4−4i4i0000400-4−4i4i00000000000000022−22−2i22i200000000000000−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ592ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ792ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ772ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ730000000000000
χ604-4−4i4i0000400-4−4i4i00000000000000022−22−2i22i2000000000000002ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ59−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ79−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ77−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ730000000000000
χ614-4−4i4i0000400-4−4i4i000000000000000−22222i2−2i200000000000000−2ζ31−2ζ47−2ζ63−2ζ792ζ31+2ζ47+2ζ63+2ζ79−2ζ11−2ζ27−2ζ43−2ζ592ζ11+2ζ27+2ζ43+2ζ592ζ9+2ζ41+2ζ57+2ζ73−2ζ9−2ζ41−2ζ57−2ζ73−2ζ13−2ζ29−2ζ61−2ζ772ζ13+2ζ29+2ζ61+2ζ770000000000000
χ624-4−4i4i0000400-4−4i4i000000000000000−22222i2−2i2000000000000002ζ31+2ζ47+2ζ63+2ζ79−2ζ31−2ζ47−2ζ63−2ζ792ζ11+2ζ27+2ζ43+2ζ59−2ζ11−2ζ27−2ζ43−2ζ59−2ζ9−2ζ41−2ζ57−2ζ732ζ9+2ζ41+2ζ57+2ζ732ζ13+2ζ29+2ζ61+2ζ77−2ζ13−2ζ29−2ζ61−2ζ770000000000000
χ638888-8-800-200-2-2-200000225−25−252520000000000000000000000000000000000000000000
χ648888-8-800-200-2-2-2000002−252525−2520000000000000000000000000000000000000000000
χ6588-8-88-88-8-200-22200000-2-2-22220000000000000000000000000000000000000000000
χ6688-8-88-8-88-200-22200000-222-2-220000000000000000000000000000000000000000000
χ6716-1616i−16i0000-4004−4i4i000000000000000000000000000000000000000000000000000000
χ6816-16−16i16i0000-40044i−4i000000000000000000000000000000000000000000000000000000

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