Finite Group Databasebeta

← Group #13025885

Character table — Group #13025885

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244444444555588888888888888888810101010101010101010101010102020202020202020202020202020202032323232404040404040404040404040
order124424888851016161616202022442488102040404040808080808080808024444444448888888816161616161616161616161610204040244444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ31111111111111111111111-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111111-1-1-1-1111111111111111111-1iiii−i−i−i−i-1-1-1-1-1ii−i−i-1-1-1-1iiii−i−i−i−i1111-1-1ii−i−i-1-1ii−i−i
χ6111111111111111111-1-1-1-1111111111111111111-1−i−i−i−iiiii-1-1-1-1-1−i−iii-1-1-1-1−i−i−i−iiiii1111-1-1−i−iii-1-1−i−iii
χ7111111111111111111-1-1-1-1-1-1-1-111111111111111-1iiii−i−i−i−i-1-1-1-1-1ii−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-111−i−iii11−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-111111111111111-1−i−i−i−iiiii-1-1-1-1-1−i−iii-1-1-1-1−i−i−i−iiiii-1-1-1-111ii−i−i11ii−i−i
χ9111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ10111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ11111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ12111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ13111111111111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1ii−i−i1111−i−i−i−iiiii11-1-1-1-1ii−i−i11−i−iii
χ14111111111111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1−i−iii1111iiii−i−i−i−i11-1-1-1-1−i−iii11ii−i−i
χ15111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1ii−i−i1111−i−i−i−iiiii-1-11111−i−iii-1-1ii−i−i
χ16111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1−i−iii1111iiii−i−i−i−i-1-11111ii−i−i-1-1−i−iii
χ1711-1-1-1111-1-111ii−i−i-1-111-1-11-1i−i-1111-1-1iiii−i−i−i−i-111-1-111-1-1111-1-11-11-1ii−i−iii−i−iii−i−i1-1i−i1-11-11-1i−ii−ii−i
χ1811-1-1-1111-1-111ii−i−i-1-111-1-11-1i−i-1111-1-1iiii−i−i−i−i-1-1-111-1-111111-1-1-11-11ii−i−i−i−iii−i−iii1-1i−i1-1-11-11i−i−ii−ii
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χ2011-1-1-1111-1-111ii−i−i-1-111-1-1-11−ii-1111-1-1iiii−i−i−i−i-1-1-111-1-111111-1-1-11-11ii−i−i−i−iii−i−iii-11−ii-111-11-1−iii−ii−i
χ2111-1-1-1111-1-111ii−i−i-1-1-1-1111-1i−i-1111-1-1iiii−i−i−i−i1ii−i−i−i−iii-1-1-111i−i−ii−i−iii-1-11111-1-11-1i−i-11i−i−ii−ii-111-1
χ2211-1-1-1111-1-111ii−i−i-1-1-1-1111-1i−i-1111-1-1iiii−i−i−i−i1−i−iiiii−i−i-1-1-111−iii−i−i−iii11-1-1-1-1111-1i−i-11−iii−i−ii1-1-11
χ2311-1-1-1111-1-111ii−i−i-1-1-1-111-11−ii-1111-1-1iiii−i−i−i−i1ii−i−i−i−iii-1-1-111i−i−ii−i−iii-1-11111-1-1-11−ii1-1−iii−ii−i1-1-11
χ2411-1-1-1111-1-111ii−i−i-1-1-1-111-11−ii-1111-1-1iiii−i−i−i−i1−i−iiiii−i−i-1-1-111−iii−i−i−iii11-1-1-1-111-11−ii1-1i−i−iii−i-111-1
χ2511-1-1-1111-1-111−i−iii-1-111-1-11-1−ii-1111-1-1−i−i−i−iiiii-111-1-111-1-1111-1-11-11-1−i−iii−i−iii−i−iii1-1−ii1-11-11-1−ii−ii−ii
χ2611-1-1-1111-1-111−i−iii-1-111-1-11-1−ii-1111-1-1−i−i−i−iiiii-1-1-111-1-111111-1-1-11-11−i−iiiii−i−iii−i−i1-1−ii1-1-11-11−iii−ii−i
χ2711-1-1-1111-1-111−i−iii-1-111-1-1-11i−i-1111-1-1−i−i−i−iiiii-111-1-111-1-1111-1-11-11-1−i−iii−i−iii−i−iii-11i−i-11-11-11i−ii−ii−i
χ2811-1-1-1111-1-111−i−iii-1-111-1-1-11i−i-1111-1-1−i−i−i−iiiii-1-1-111-1-111111-1-1-11-11−i−iiiii−i−iii−i−i-11i−i-111-11-1i−i−ii−ii
χ2911-1-1-1111-1-111−i−iii-1-1-1-1111-1−ii-1111-1-1−i−i−i−iiiii1ii−i−i−i−iii-1-1-111i−i−iiii−i−i11-1-1-1-1111-1−ii-11i−i−iii−i1-1-11
χ3011-1-1-1111-1-111−i−iii-1-1-1-1111-1−ii-1111-1-1−i−i−i−iiiii1−i−iiiii−i−i-1-1-111−iii−iii−i−i-1-11111-1-11-1−ii-11−iii−ii−i-111-1
χ3111-1-1-1111-1-111−i−iii-1-1-1-111-11i−i-1111-1-1−i−i−i−iiiii1ii−i−i−i−iii-1-1-111i−i−iiii−i−i11-1-1-1-111-11i−i1-1−iii−i−ii-111-1
χ3211-1-1-1111-1-111−i−iii-1-1-1-111-11i−i-1111-1-1−i−i−i−iiiii1−i−iiiii−i−i-1-1-111−iii−iii−i−i-1-11111-1-1-11i−i1-1i−i−ii−ii1-1-11
χ33222222-2-2-2-2220000222222000022-2-2-2-2000000002222222222-2-2-2-2-2-2-2-20000000000000000000000000000
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χ36222222-2-2-2-222000022-2-2-2-2000022-2-2-2-200000000-2−2i−2i−2i−2i2i2i2i2i-222222i2i−2i−2i0000000000000000000000000000
χ372222-2-20000222−22−22222220000-2-2000022−2−222−2−2-22-22-22-22-2-2000000002−22−22−22−22−22−20000000000000000
χ382222-2-20000222−22−22222220000-2-2000022−2−222−2−2-2-22-22-22-22-2000000002−22−2−22−22−22−220000000000000000
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χ402222-2-20000222−22−222-2-2-2-20000-2-2000022−2−222−2−22−2i2i−2i2i2i−2i2i−2i200000000−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ412222-2-2000022−22−222222220000-2-20000−2−222−2−222-22-22-22-22-2-200000000−22−22−22−22−22−220000000000000000
χ422222-2-2000022−22−222222220000-2-20000−2−222−2−222-2-22-22-22-22-200000000−22−222−22−22−22−20000000000000000
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χ5122-2-22-2000022−i2i2i2−i2-2-2-2-22200002-20000−i2−i2i2i2i2i2−i2−i2-22i−2i−2i2i−2i2i2i−2i200000000i2−i2−i2i22−2−22−222−20000000000000000
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χ5322-2-2-22-2-222220000-2-222-2-20000-22-2-22200000000-222-2-222-2-22-2-222-22-220000000000000000000000000000
χ5422-2-2-22-2-222220000-2-222-2-20000-22-2-22200000000-2-2-222-2-2222-2-2222-22-20000000000000000000000000000
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χ5622-2-2-22-2-222220000-2-2-2-2220000-22-2-222000000002−2i−2i2i2i2i2i−2i−2i-222-2-22i−2i−2i2i0000000000000000000000000000
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χ798-88i−8i0042−424i2−4i2-220000−2i2i0000000000−22−i2i2ζ13−ζ29+ζ31−ζ47−ζ61−ζ63+ζ77+ζ79−ζ13+ζ29−ζ31+ζ47+ζ61+ζ63−ζ77−ζ79−ζ9−ζ11+ζ27−ζ41+ζ43+ζ57−ζ59+ζ73ζ9+ζ11−ζ27+ζ41−ζ43−ζ57+ζ59−ζ73−ζ9+ζ11−ζ27−ζ41−ζ43+ζ57+ζ59+ζ73ζ9−ζ11+ζ27+ζ41+ζ43−ζ57−ζ59−ζ73ζ13−ζ29−ζ31+ζ47−ζ61+ζ63+ζ77−ζ79−ζ13+ζ29+ζ31−ζ47+ζ61−ζ63−ζ77+ζ790000000000000000000000000000000000000000000000
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χ838-8−8i8i0042−42−4i24i2-2200002i−2i0000000000−22i2−i2−ζ9+ζ11−ζ27−ζ41−ζ43+ζ57+ζ59+ζ73ζ9−ζ11+ζ27+ζ41+ζ43−ζ57−ζ59−ζ73−ζ13+ζ29+ζ31−ζ47+ζ61−ζ63−ζ77+ζ79ζ13−ζ29−ζ31+ζ47−ζ61+ζ63+ζ77−ζ79ζ13−ζ29+ζ31−ζ47−ζ61−ζ63+ζ77+ζ79−ζ13+ζ29−ζ31+ζ47+ζ61+ζ63−ζ77−ζ79ζ9+ζ11−ζ27+ζ41−ζ43−ζ57+ζ59−ζ73−ζ9−ζ11+ζ27−ζ41+ζ43+ζ57−ζ59+ζ730000000000000000000000000000000000000000000000
χ848-8−8i8i0042−42−4i24i2-2200002i−2i0000000000−22i2−i2ζ9−ζ11+ζ27+ζ41+ζ43−ζ57−ζ59−ζ73−ζ9+ζ11−ζ27−ζ41−ζ43+ζ57+ζ59+ζ73ζ13−ζ29−ζ31+ζ47−ζ61+ζ63+ζ77−ζ79−ζ13+ζ29+ζ31−ζ47+ζ61−ζ63−ζ77+ζ79−ζ13+ζ29−ζ31+ζ47+ζ61+ζ63−ζ77−ζ79ζ13−ζ29+ζ31−ζ47−ζ61−ζ63+ζ77+ζ79−ζ9−ζ11+ζ27−ζ41+ζ43+ζ57−ζ59+ζ73ζ9+ζ11−ζ27+ζ41−ζ43−ζ57+ζ59−ζ730000000000000000000000000000000000000000000000
χ858-8−8i8i00−42424i2−4i2-2200002i−2i00000000002−2−i2i2ζ13−ζ29−ζ31+ζ47−ζ61+ζ63+ζ77−ζ79−ζ13+ζ29+ζ31−ζ47+ζ61−ζ63−ζ77+ζ79−ζ9+ζ11−ζ27−ζ41−ζ43+ζ57+ζ59+ζ73ζ9−ζ11+ζ27+ζ41+ζ43−ζ57−ζ59−ζ73ζ9+ζ11−ζ27+ζ41−ζ43−ζ57+ζ59−ζ73−ζ9−ζ11+ζ27−ζ41+ζ43+ζ57−ζ59+ζ73−ζ13+ζ29−ζ31+ζ47+ζ61+ζ63−ζ77−ζ79ζ13−ζ29+ζ31−ζ47−ζ61−ζ63+ζ77+ζ790000000000000000000000000000000000000000000000
χ868-8−8i8i00−42424i2−4i2-2200002i−2i00000000002−2−i2i2−ζ13+ζ29+ζ31−ζ47+ζ61−ζ63−ζ77+ζ79ζ13−ζ29−ζ31+ζ47−ζ61+ζ63+ζ77−ζ79ζ9−ζ11+ζ27+ζ41+ζ43−ζ57−ζ59−ζ73−ζ9+ζ11−ζ27−ζ41−ζ43+ζ57+ζ59+ζ73−ζ9−ζ11+ζ27−ζ41+ζ43+ζ57−ζ59+ζ73ζ9+ζ11−ζ27+ζ41−ζ43−ζ57+ζ59−ζ73ζ13−ζ29+ζ31−ζ47−ζ61−ζ63+ζ77+ζ79−ζ13+ζ29−ζ31+ζ47+ζ61+ζ63−ζ77−ζ790000000000000000000000000000000000000000000000

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