Finite Group Databasebeta

← Group #11986867

Character table — Group #11986867

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size112222222222222444444444444444444488888888888888888888888888832323232323232323232404040404040404080808080
order122445588101010101010248161616162020202040404040404040408101016162020404040408080808080808080808080808080808024101010102020202032323232323232324444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-11-1-1-1-1111111111111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1iiii−i−i−i−iii−i−i
χ6111111111111111-1-11-1-1-1-1111111111111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1−i−i−i−iiiii−i−iii
χ7111111111111111-1-11-1-1-1-1111111111111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111iiii−i−i−i−i−i−iii
χ8111111111111111-1-11-1-1-1-1111111111111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111−i−i−i−iiiiiii−i−i
χ9222222222222222222-2-2-2-2222222222222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000
χ10222222222222222-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000
χ112222222-2-222222222-200002222-2-2-2-2-2-2-2-2-2220022-2-2-2-20000000000000000000000000022−2−222−2−20000
χ122222222-2-222222222-200002222-2-2-2-2-2-2-2-2-2220022-2-2-2-200000000000000000000000000−2−222−2−2220000
χ132222222-2-2222222-2-2-200002222-2-2-2-2-2-2-2-22-2-200-2-2222200000000000000000000000000i2i2−i2−i2−i2−i2i2i20000
χ142222222-2-2222222-2-2-200002222-2-2-2-2-2-2-2-22-2-200-2-2222200000000000000000000000000−i2−i2i2i2i2i2−i2−i20000
χ1522222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−522222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000
χ1622222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−522222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+52000000000000
χ1722222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72000000000000
χ1822222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72000000000000
χ1922222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52-2-222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-21−521+52-2-21−521+521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72000000000000
χ2022222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52-2-222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-21−521+52-2-21−521+521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72000000000000
χ2122222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52-2-22-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-21−521+52221−521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+522-2−1+52−1+52−1−52−1−521−521−521+521+52000000000000
χ2222222−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52-2-22-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-21−521+52221−521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-221−521−521+521+52−1+52−1+52−1−52−1−52000000000000
χ2322222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+522222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000
χ2422222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+522222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−521+521+521−521−52000000000000
χ2522222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56000000000000
χ2622222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56000000000000
χ2722222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52-2-222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-21+521−52-2-21+521−521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56000000000000
χ2822222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52-2-222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-21+521−52-2-21+521−521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56000000000000
χ2922222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52-2-22-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-21+521−52221+521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−522-2−1−52−1−52−1+52−1+521+521+521−521−52000000000000
χ3022222−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52-2-22-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-21+521−52221+521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-221+521+521−521−52−1−52−1−52−1+52−1+52000000000000
χ31222-2-222002222222-2022−2−2-2-2-2-2000000000222−2-2-2000022−2−222−2−222−2−222−2−20000000000ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ770000
χ32222-2-222002222222-2022−2−2-2-2-2-2000000000222−2-2-2000022−2−222−2−222−2−222−2−20000000000−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ770000
χ33222-2-222002222222-20−2−222-2-2-2-200000000022−22-2-20000−2−222−2−222−2−222−2−2220000000000−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ790000
χ34222-2-222002222222-20−2−222-2-2-2-200000000022−22-2-20000−2−222−2−222−2−222−2−2220000000000ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ79ζ11−ζ13+ζ27−ζ29+ζ43+ζ59−ζ61−ζ77−ζ11+ζ13−ζ27+ζ29−ζ43−ζ59+ζ61+ζ77ζ9−ζ31+ζ41−ζ47+ζ57−ζ63+ζ73−ζ79−ζ9+ζ31−ζ41+ζ47−ζ57+ζ63−ζ73+ζ790000
χ35222-2-22200222222-22022−2−2-2-2-2-2000000000-2-2−22220000−2−222−2−22222−2−222−2−20000000000−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ770000
χ36222-2-22200222222-22022−2−2-2-2-2-2000000000-2-2−22220000−2−222−2−22222−2−222−2−20000000000ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ770000
χ37222-2-22200222222-220−2−222-2-2-2-2000000000-2-22−222000022−2−222−2−2−2−222−2−2220000000000−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ790000
χ38222-2-22200222222-220−2−222-2-2-2-2000000000-2-22−222000022−2−222−2−2−2−222−2−2220000000000ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ790000
χ3922-2-2222-2-222-2-2-2-20022i−2i2i−2i-2-2222222-2-2-2-200000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000001+i−1−i1−i−1+i
χ4022-2-2222-2-222-2-2-2-20022i−2i2i−2i-2-2222222-2-2-2-200000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000−1−i1+i−1+i1−i
χ4122-2-2222-2-222-2-2-2-2002−2i2i−2i2i-2-2222222-2-2-2-20000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000001−i−1+i1+i−1−i
χ4222-2-2222-2-222-2-2-2-2002−2i2i−2i2i-2-2222222-2-2-2-20000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000−1+i1−i−1−i1+i
χ4344444−1+5−1−5-4-4−1+5−1−5−1+5−1+5−1−5−1−544-40000−1+5−1−5−1+5−1−51−51−51+51+51−51−51+51+5-4−1+5−1−500−1+5−1−51−51−51+51+500000000000000000000000000000000000000
χ4444444−1+5−1−5-4-4−1+5−1−5−1+5−1+5−1−5−1−5-4-4-40000−1+5−1−5−1+5−1−51−51−51+51+51−51−51+51+541−51+5001−51+5−1+5−1+5−1−5−1−500000000000000000000000000000000000000
χ4544444−1−5−1+5-4-4−1−5−1+5−1−5−1−5−1+5−1+544-40000−1−5−1+5−1−5−1+51+51+51−51−51+51+51−51−5-4−1−5−1+500−1−5−1+51+51+51−51−500000000000000000000000000000000000000
χ4644444−1−5−1+5-4-4−1−5−1+5−1−5−1−5−1+5−1+5-4-4-40000−1−5−1+5−1−5−1+51+51+51−51−51+51+51−51−541+51−5001+51−5−1−5−1−5−1+5−1+500000000000000000000000000000000000000
χ47444-4-4−1+5−1−500−1+5−1−5−1+5−1+5−1−5−1−54-402222−22−221−51+51−51+5000000000−1+5−1−522−221−51+50000−ζ14+ζ26−ζ46+ζ74−ζ14+ζ26−ζ46+ζ74ζ14−ζ26+ζ46−ζ74ζ14−ζ26+ζ46−ζ74ζ42+ζ58−ζ62−ζ78ζ42+ζ58−ζ62−ζ78−ζ42−ζ58+ζ62+ζ78−ζ42−ζ58+ζ62+ζ78−ζ14+ζ26−ζ46+ζ74−ζ14+ζ26−ζ46+ζ74ζ14−ζ26+ζ46−ζ74ζ14−ζ26+ζ46−ζ74ζ42+ζ58−ζ62−ζ78ζ42+ζ58−ζ62−ζ78−ζ42−ζ58+ζ62+ζ78−ζ42−ζ58+ζ62+ζ780000000000000000000000
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Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.