Finite Group Databasebeta

← Group #12013475

Character table — Group #12013475

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101
size11112222222222222222444444444444444444488888888888888888888888888888810101010161616161616161620202020202032323232324040404040404040160
order122244445588881010101010104882020202020202020404040404040404044441616161620204040404080808080808080808080808080808080888820202020202020208888882101010108888161616162
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-11111-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1
χ6111111111111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ7111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11
χ8111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1
χ92222222222-2-2-2-22222222-2-222222222-2-2-2-2-2-2-2-20000000022-2-2-2-2000000000000000022220000000022-2-2-2-200000000000000
χ102222222222-2-2-2-22222222-2-222222222-2-2-2-2-2-2-2-20000000022-2-2-2-20000000000000000-2-2-2-200000000-2-2222200000000000000
χ1122222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52222−1+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+52−1−52−1−5222222222−1+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+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−520000−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000002−1+52−1+52−1−52−1−52000000000
χ1222222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52222−1+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+52−1−52−1−522222-2-2-2-2−1+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+520000−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000-21−521−521+521+52000000000
χ1322222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52222−1+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+52−1−52−1−52-2-2-2-22222−1+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+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−5200001−521−521−521−521+521+521+521+52000000-21−521−521+521+52000000000
χ1422222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52222−1+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+52−1−52−1−52-2-2-2-2-2-2-2-2−1+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+5200001−521−521−521−521+521+521+521+520000002−1+52−1+52−1−52−1−52000000000
χ1522222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1+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+5222222222−1−52−1+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+520000−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000002−1−52−1−52−1+52−1+52000000000
χ1622222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1+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+522222-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521+521+521+521+521−521−521−521−521−521−521−521−520000−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000000-21+521+521−521−52000000000
χ1722222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1+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+52-2-2-2-22222−1−52−1+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+5200001+521+521+521+521−521−521−521−52000000-21+521+521−521−52000000000
χ1822222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1+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+52-2-2-2-2-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521+521+521+521+521−521−521−521−521−521−521−521−5200001+521+521+521+521−521−521−521−520000002−1−52−1−52−1+52−1+52000000000
χ19222222-2-2222222222222-2-2-2-2-2-2-222222222222222-2-20000-2-2-2-2-2-20000000000000000000022-2-222-2-200000000000000000000
χ20222222-2-2222222222222-2-2-2-2-2-2-2222222222222-2-2220000-2-2-2-2-2-200000000000000000000-2-222-2-22200000000000000000000
χ21222222-2-222-2-2-2-2222222-222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000000000000002i2i−2i−2i00000
χ22222222-2-222-2-2-2-2222222-222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-22222000000000000000000000000000000000000000−2i−2i2i2i00000
χ23222222-2-2−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-200001−521+521−521−521+521+52ζ24−ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ720000−1+52−1+521−521−52−1−52−1−521+521+520000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72000000000
χ24222222-2-2−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-200001−521+521−521−521+521+52−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ56ζ8−ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ720000−1+52−1+521−521−52−1−52−1−521+521+520000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72000000000
χ25222222-2-2−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-22200001−521+521−521−521+521+52ζ24−ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ7200001−521−52−1+52−1+521+521+52−1−52−1−520000000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72000000000
χ26222222-2-2−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−52-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-22200001−521+521−521−521+521+52−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ56ζ8−ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ7200001−521−52−1+52−1+521+521+52−1−52−1−520000000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72000000000
χ27222222-2-2−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-200001+521−521+521+521−521−52−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ72−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ560000−1−52−1−521+521+52−1+52−1+521−521−520000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56000000000
χ28222222-2-2−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-200001+521−521+521+521−521−52ζ8−ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72ζ24−ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ560000−1−52−1−521+521+52−1+52−1+521−521−520000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56000000000
χ29222222-2-2−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-22200001+521−521+521+521−521−52−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ72−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ5600001+521+52−1−52−1−521−521−52−1+52−1+520000000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56000000000
χ30222222-2-2−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+52-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-22200001+521−521+521+521−521−52ζ8−ζ72ζ8−ζ72ζ8−ζ72ζ8−ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72−ζ8+ζ72ζ24−ζ56ζ24−ζ56ζ24−ζ56ζ24−ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ56−ζ24+ζ5600001+521+52−1−52−1−521−521−52−1+52−1+520000000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56000000000
χ312222-2-222220000222222-2002222-2-2-2-200000000000022−2−2-2-2000022−2−222−2−222−2−222−2−2222200000000-2-2000000000000022−2−20
χ322222-2-222220000222222-2002222-2-2-2-200000000000022−2−2-2-2000022−2−222−2−222−2−222−2−2-2-2-2-200000000220000000000000−2−2220
χ332222-2-222220000222222-2002222-2-2-2-2000000000000−2−222-2-20000−2−222−2−222−2−222−2−222222200000000-2-20000000000000−2−2220
χ342222-2-222220000222222-2002222-2-2-2-2000000000000−2−222-2-20000−2−222−2−222−2−222−2−222-2-2-2-20000000022000000000000022−2−20
χ3522-2-2002-2222−22−222-2-2-2-202−22-22-200002−22−22−22−20000−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+ζ77002−22−2−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+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+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+ζ79−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ7722-2-2000000000022−2−2000000000−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+ζ770
χ3622-2-2002-2222−22−222-2-2-2-202−22-22-200002−22−22−22−20000−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+ζ77002−22−2−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+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+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+ζ79−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77-2-2220000000000−2−222000000000ζ9+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−ζ770
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χ944-4-44000044−222222−22-4-4-44-4400000000000−2222−222222−2222−2200000000000000000000000000000022−22−22220000000000-222-200000000000000
χ954-4-44000044−222222−22-4-4-44-4400000000000−2222−222222−2222−22000000000000000000000000000000−222222−2200000000002-2-2200000000000000
χ968-88-8-8800−2+25−2−2500002−252+25−2+252−25−2−252+2500000002−25−2+252+25−2−250000000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-8800−2−25−2+2500002+252−25−2−252+25−2+252−2500000002+25−2−252−25−2+250000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-880000−2+25−2−2542−42−42422−252+252−25−2+252+25−2−2500000000000−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26+2ζ46−2ζ742ζ42+2ζ58−2ζ62−2ζ78−2ζ42−2ζ58+2ζ62+2ζ782ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26−2ζ46+2ζ74−2ζ42−2ζ58+2ζ62+2ζ782ζ42+2ζ58−2ζ62−2ζ7800000000000000000000000000000000000000000000000000000000000000
χ998-8-880000−2+25−2−25−424242−422−252+252−25−2+252+25−2−25000000000002ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26−2ζ46+2ζ74−2ζ42−2ζ58+2ζ62+2ζ782ζ42+2ζ58−2ζ62−2ζ78−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26+2ζ46−2ζ742ζ42+2ζ58−2ζ62−2ζ78−2ζ42−2ζ58+2ζ62+2ζ7800000000000000000000000000000000000000000000000000000000000000
χ1008-8-880000−2−25−2+2542−42−42422+252−252+25−2−252−25−2+25000000000002ζ42+2ζ58−2ζ62−2ζ78−2ζ42−2ζ58+2ζ62+2ζ78−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26+2ζ46−2ζ74−2ζ42−2ζ58+2ζ62+2ζ782ζ42+2ζ58−2ζ62−2ζ782ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26−2ζ46+2ζ7400000000000000000000000000000000000000000000000000000000000000
χ1018-8-880000−2−25−2+25−424242−422+252−252+25−2−252−25−2+2500000000000−2ζ42−2ζ58+2ζ62+2ζ782ζ42+2ζ58−2ζ62−2ζ782ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26−2ζ46+2ζ742ζ42+2ζ58−2ζ62−2ζ78−2ζ42−2ζ58+2ζ62+2ζ78−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26+2ζ46−2ζ7400000000000000000000000000000000000000000000000000000000000000

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