Finite Group Databasebeta

← Group #13026739

Character table — Group #13026739

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444448888888888888888881010101016202020202020323232324040404040404040404040404040808080
order1222445881010104416162020404040408080808080808080224444444882020202044444488161616161616488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-1
χ3111111111111111111111111111111-1-1-1-11ii−i−i-1-11111-1-1ii−i−ii−i-1-1ii−i−i-1i−i
χ4111111111111111111111111111111-1-1-1-11−i−iii-1-11111-1-1−i−iii−ii-1-1−i−iii-1−ii
χ511111111111111-1-1111111-1-1-1-1-1-1-1-11111-1111111-1-11111111111-1-1-1-1-1-1-1-1-1
χ611111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-111
χ711111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-111-1-1ii−i−ii−i11−i−iii1−ii
χ811111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-111-1-1−i−iii−ii11ii−i−i1i−i
χ9111111111111-1-111111111111111111111-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1
χ10111111111111-1-111111111111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-111
χ11111111111111-1-11111111111111111-1-1-1-1-1ii−i−i-1-1-1-1-1-111−i−iiii−i-1-1ii−i−i1−ii
χ12111111111111-1-11111111111111111-1-1-1-1-1−i−iii-1-1-1-1-1-111ii−i−i−ii-1-1−i−iii1i−i
χ13111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111
χ14111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1
χ15111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11ii−i−i-1-111-1-111−i−iiii−i11−i−iii-1i−i
χ16111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11−i−iii-1-111-1-111ii−i−i−ii11ii−i−i-1−ii
χ172222222-2-2222000022-2-2-2-200000000222202222-2-20000000000-2-2000000000
χ182222222-2-2222000022-2-2-2-20000000022220-2-2-2-2-2-2000000000022000000000
χ192222222-2-2222000022-2-2-2-200000000-2-2-2-202i2i−2i−2i220000000000−2i2i000000000
χ202222222-2-2222000022-2-2-2-200000000-2-2-2-20−2i−2i2i2i2200000000002i−2i000000000
χ212-2-222-2200-2-2200i2−i22-20000i2i2i2i2−i2−i2−i2−i22-2-2202i−2i2i−2i00000000000000i2−i22−22−2000
χ222-2-222-2200-2-2200i2−i22-20000i2i2i2i2−i2−i2−i2−i22-2-220−2i2i−2i2i00000000000000i2−i2−22−22000
χ232-2-222-2200-2-2200i2−i22-20000i2i2i2i2−i2−i2−i2−i2-222-202-2-2200000000000000−i2i2−i2i2i2−i2000
χ242-2-222-2200-2-2200i2−i22-20000i2i2i2i2−i2−i2−i2−i2-222-20-222-200000000000000−i2i2i2−i2−i2i2000
χ252-2-222-2200-2-2200−i2i22-20000−i2−i2−i2−i2i2i2i2i22-2-2202i−2i2i−2i00000000000000−i2i2−22−22000
χ262-2-222-2200-2-2200−i2i22-20000−i2−i2−i2−i2i2i2i2i22-2-220−2i2i−2i2i00000000000000−i2i22−22−2000
χ272-2-222-2200-2-2200−i2i22-20000−i2−i2−i2−i2i2i2i2i2-222-202-2-2200000000000000i2−i2i2−i2−i2i2000
χ282-2-222-2200-2-2200−i2i22-20000−i2−i2−i2−i2i2i2i2i2-222-20-222-200000000000000i2−i2−i2i2i2−i2000
χ292-2-22-2222-2-2-222-200-2222-2-2000000002-22-2000002-2002-22-2000000000000000
χ302-2-22-2222-2-2-222-200-2222-2-200000000-22-2200000-22002-2-22000000000000000
χ312-2-22-2222-2-2-22-2200-2222-2-2000000002-22-2000002-200-22-22000000000000000
χ322-2-22-2222-2-2-22-2200-2222-2-200000000-22-2200000-2200-222-2000000000000000
χ332-2-22-222-22-2-220000-22-2-222000000002-22-200000-220000002i−2i2i−2i00000000000
χ342-2-22-222-22-2-220000-22-2-222000000002-22-200000-22000000−2i2i−2i2i00000000000
χ352-2-22-222-22-2-220000-22-2-22200000000-22-22000002-20000002-2-2200000000000
χ362-2-22-222-22-2-220000-22-2-22200000000-22-22000002-2000000-222-200000000000
χ37444444-144-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-100004000000-1-1-1-100000000000000000
χ38444444-144-1-1-144-4-4-1-1-1-1-1-1111111110000-400000011-1-100000000000000000
χ39444444-144-1-1-1-4-444-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4000000111100000000000000000
χ40444444-144-1-1-1-4-4-4-4-1-1-1-1-1-11111111100004000000-1-11100000000000000000
χ414444-4-44004440000-4-400000000000044-4-40000000000000000000000000000
χ424444-4-44004440000-4-4000000000000-4-4440000000000000000000000000000
χ434-4-44-44-14-411-14-4001-1-1-111i5i5−i5−i5i5i5−i5−i500000000000i5−i5-1100000000000000000
χ444-4-44-44-14-411-14-4001-1-1-111−i5−i5i5i5−i5−i5i5i500000000000−i5i5-1100000000000000000
χ454-4-44-44-14-411-1-44001-1-1-111i5i5−i5−i5i5i5−i5−i500000000000−i5i51-100000000000000000
χ464-4-44-44-14-411-1-44001-1-1-111−i5−i5i5i5−i5−i5i5i500000000000i5−i51-100000000000000000
χ47888888-2-8-8-2-2-20000-2-222220000000000000000000000000000000000000000
χ488888-8-8-200-2-2-200002200001010−10−10−10−10101000000000000000000000000000000000
χ498888-8-8-200-2-2-20000220000−10−1010101010−10−1000000000000000000000000000000000
χ5088-8-800800-88-800000000000000000000000000000000000000000000000000
χ5188-8-800-2002-2200000010−1010−10ζ11−ζ29−ζ47−ζ57−ζ59+ζ61+ζ63+ζ73−ζ11+ζ29+ζ47+ζ57+ζ59−ζ61−ζ63−ζ73ζ9+ζ13−ζ27−ζ31−ζ41+ζ43−ζ77+ζ79−ζ9−ζ13+ζ27+ζ31+ζ41−ζ43+ζ77−ζ79ζ9+ζ13−ζ27−ζ31−ζ41+ζ43−ζ77+ζ79−ζ9−ζ13+ζ27+ζ31+ζ41−ζ43+ζ77−ζ79ζ11−ζ29−ζ47−ζ57−ζ59+ζ61+ζ63+ζ73−ζ11+ζ29+ζ47+ζ57+ζ59−ζ61−ζ63−ζ7300000000000000000000000000000000
χ5288-8-800-2002-2200000010−1010−10−ζ11+ζ29+ζ47+ζ57+ζ59−ζ61−ζ63−ζ73ζ11−ζ29−ζ47−ζ57−ζ59+ζ61+ζ63+ζ73−ζ9−ζ13+ζ27+ζ31+ζ41−ζ43+ζ77−ζ79ζ9+ζ13−ζ27−ζ31−ζ41+ζ43−ζ77+ζ79−ζ9−ζ13+ζ27+ζ31+ζ41−ζ43+ζ77−ζ79ζ9+ζ13−ζ27−ζ31−ζ41+ζ43−ζ77+ζ79−ζ11+ζ29+ζ47+ζ57+ζ59−ζ61−ζ63−ζ73ζ11−ζ29−ζ47−ζ57−ζ59+ζ61+ζ63+ζ7300000000000000000000000000000000
χ5388-8-800-2002-22000000−1010−1010ζ9+ζ13−ζ27−ζ31−ζ41+ζ43−ζ77+ζ79−ζ9−ζ13+ζ27+ζ31+ζ41−ζ43+ζ77−ζ79−ζ11+ζ29+ζ47+ζ57+ζ59−ζ61−ζ63−ζ73ζ11−ζ29−ζ47−ζ57−ζ59+ζ61+ζ63+ζ73−ζ11+ζ29+ζ47+ζ57+ζ59−ζ61−ζ63−ζ73ζ11−ζ29−ζ47−ζ57−ζ59+ζ61+ζ63+ζ73ζ9+ζ13−ζ27−ζ31−ζ41+ζ43−ζ77+ζ79−ζ9−ζ13+ζ27+ζ31+ζ41−ζ43+ζ77−ζ7900000000000000000000000000000000
χ5488-8-800-2002-22000000−1010−1010−ζ9−ζ13+ζ27+ζ31+ζ41−ζ43+ζ77−ζ79ζ9+ζ13−ζ27−ζ31−ζ41+ζ43−ζ77+ζ79ζ11−ζ29−ζ47−ζ57−ζ59+ζ61+ζ63+ζ73−ζ11+ζ29+ζ47+ζ57+ζ59−ζ61−ζ63−ζ73ζ11−ζ29−ζ47−ζ57−ζ59+ζ61+ζ63+ζ73−ζ11+ζ29+ζ47+ζ57+ζ59−ζ61−ζ63−ζ73−ζ9−ζ13+ζ27+ζ31+ζ41−ζ43+ζ77−ζ79ζ9+ζ13−ζ27−ζ31−ζ41+ζ43−ζ77+ζ7900000000000000000000000000000000
χ558-88-8008008-8-800000000000000000000000000000000000000000000000000
χ568-88-800-200-22200000010−10−1010ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ7900000000000000000000000000000000
χ578-88-800-200-22200000010−10−1010−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ7900000000000000000000000000000000
χ588-88-800-200-222000000−101010−10ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ7300000000000000000000000000000000
χ598-88-800-200-222000000−101010−10−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ7300000000000000000000000000000000
χ608-8-888-8-20022-2004i2−4i2-220000−i2−i2−i2−i2i2i2i2i200000000000000000000000000000000
χ618-8-888-8-20022-200−4i24i2-220000i2i2i2i2−i2−i2−i2−i200000000000000000000000000000000
χ628-8-88-88-2-8822-200002-222-2-20000000000000000000000000000000000000000

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