Finite Group Databasebeta

← Group #13026889

Character table — Group #13026889

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122222444448888888888888888881010101016202020202020323232324040404040404040404040404040808080
order1224488581010104416162020404040408080808080808080224448888882020202022448888161616161616488
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-11-1-1
χ3111111111111111111111111111111-1-1-1-11-1ii−i−i-11111-1-1i−iii−i−i-1-1ii−i−i-1i−i
χ4111111111111111111111111111111-1-1-1-11-1−i−iii-11111-1-1−ii−i−iii-1-1−i−iii-1−ii
χ511111111111111-1-1111111-1-1-1-1-1-1-1-11111-111111111-1-111111111-1-1-1-1-1-1-1-1-1
χ611111111111111-1-1111111-1-1-1-1-1-1-1-11111-11-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111-111
χ711111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-111-1-1-1-1i−iii−i−i11−i−iii1−ii
χ811111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-111-1-1-1-1−ii−i−iii11ii−i−i1i−i
χ9111111111111-1-111111111111111111111-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1
χ10111111111111-1-111111111111111111111-11-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-111
χ11111111111111-1-11111111111111111-1-1-1-1-1-1ii−i−i-1-1-1-1-111i−i−i−iii-1-1ii−i−i1−ii
χ12111111111111-1-11111111111111111-1-1-1-1-1-1−i−iii-1-1-1-1-111−iiii−i−i-1-1−i−iii1i−i
χ13111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111
χ14111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-1-1-11111-1-111111-1-1
χ15111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1ii−i−i-1-1-11111i−i−i−iii11−i−iii-1i−i
χ16111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1−i−iii-1-1-11111−iiii−i−i11ii−i−i-1−ii
χ1722222-2-22-2222000022-2-2-2-20000000022220-22222-2000000-2-20000000000000
χ1822222-2-22-2222000022-2-2-2-20000000022220-2-2-2-2-2-2000000220000000000000
χ1922222-2-22-2222000022-2-2-2-200000000-2-2-2-2022i2i−2i−2i2000000−2i2i0000000000000
χ2022222-2-22-2222000022-2-2-2-200000000-2-2-2-202−2i−2i2i2i20000002i−2i0000000000000
χ21222-2-20020222002−2-2-200002222−2−2−2−222-2-2002i−2i2i−2i00000000000002−2i2−i2i2−i2000
χ22222-2-20020222002−2-2-200002222−2−2−2−222-2-200−2i2i−2i2i00000000000002−2−i2i2−i2i2000
χ23222-2-20020222002−2-2-200002222−2−2−2−2-2-222002-2-220000000000000−222−2−22000
χ24222-2-20020222002−2-2-200002222−2−2−2−2-2-22200-222-20000000000000−22−222−2000
χ25222-2-2002022200−22-2-20000−2−2−2−2222222-2-2002i−2i2i−2i0000000000000−22−i2i2−i2i2000
χ26222-2-2002022200−22-2-20000−2−2−2−2222222-2-200−2i2i−2i2i0000000000000−22i2−i2i2−i2000
χ27222-2-2002022200−22-2-20000−2−2−2−22222-2-222002-2-2200000000000002−2−222−2000
χ28222-2-2002022200−22-2-20000−2−2−2−22222-2-22200-222-200000000000002−22−2−22000
χ2922-2-22222-2-2-222-200-22-2-222000000002-22-20-2000022-2002-2000000000000000
χ3022-2-22222-2-2-222-200-22-2-22200000000-22-22020000-22-200-22000000000000000
χ3122-2-22222-2-2-22-2200-22-2-222000000002-22-20-200002-2200-22000000000000000
χ3222-2-22222-2-2-22-2200-22-2-22200000000-22-22020000-2-22002-2000000000000000
χ3322-2-22-2-222-2-220000-2222-2-2000000002-22-2020000-2000000002i−2i2i−2i000000000
χ3422-2-22-2-222-2-220000-2222-2-2000000002-22-2020000-200000000−2i2i−2i2i000000000
χ3522-2-22-2-222-2-220000-2222-2-200000000-22-220-200002000000002-2-22000000000
χ3622-2-22-2-222-2-220000-2222-2-200000000-22-220-20000200000000-222-2000000000
χ374444444-14-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-100004000000-1-1-1-100000000000000000
χ384444444-14-1-1-144-4-4-1-1-1-1-1-1111111110000-4000000-1-11100000000000000000
χ394444444-14-1-1-1-4-444-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4000000111100000000000000000
χ404444444-14-1-1-1-4-4-4-4-1-1-1-1-1-1111111110000400000011-1-100000000000000000
χ4144-44-40040-4-4400004-40000000000004-4-440000000000000000000000000000
χ4244-44-40040-4-4400004-4000000000000-444-40000000000000000000000000000
χ4344-4-4444-1-411-14-4001-111-1-155−5−555−5−500000000000-115−500000000000000000
χ4444-4-4444-1-411-14-4001-111-1-1−5−555−5−55500000000000-11−5500000000000000000
χ4544-4-4444-1-411-1-44001-111-1-155−5−555−5−5000000000001-1−5500000000000000000
χ4644-4-4444-1-411-1-44001-111-1-1−5−555−5−555000000000001-15−500000000000000000
χ4788888-8-8-2-8-2-2-20000-2-222220000000000000000000000000000000000000000
χ48888-8-800-20-2-2-20042−42220000−2−2−2−2222200000000000000000000000000000000
χ49888-8-800-20-2-2-200−42422200002222−2−2−2−200000000000000000000000000000000
χ5088-88-800-2022-20000-2200001010−10−10−10−10101000000000000000000000000000000000
χ5188-88-800-2022-20000-220000−10−1010101010−10−1000000000000000000000000000000000
χ5288-8-88-8-8-2822-200002-2-2-2220000000000000000000000000000000000000000
χ538-800042−428000-80000000042−420000000000000000000000000000000000000000
χ548-800042−42-2025−25200000010−10−22ζ11+ζ13+ζ27+ζ29−ζ43−ζ59−ζ61−ζ77−ζ11−ζ13−ζ27−ζ29+ζ43+ζ59+ζ61+ζ77−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+ζ79ζ9+ζ31−ζ41−ζ47+ζ57+ζ63−ζ73−ζ79−ζ9−ζ31+ζ41+ζ47−ζ57−ζ63+ζ73+ζ7900000000000000000000000000000000
χ558-800042−42-2025−25200000010−10−22−ζ11−ζ13−ζ27−ζ29+ζ43+ζ59+ζ61+ζ77ζ11+ζ13+ζ27+ζ29−ζ43−ζ59−ζ61−ζ77ζ11−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−ζ9−ζ31+ζ41+ζ47−ζ57−ζ63+ζ73+ζ79ζ9+ζ31−ζ41−ζ47+ζ57+ζ63−ζ73−ζ7900000000000000000000000000000000
χ568-800042−42-20−25252000000−1010−22−ζ11+ζ13+ζ27−ζ29−ζ43+ζ59+ζ61−ζ77ζ11−ζ13−ζ27+ζ29+ζ43−ζ59−ζ61+ζ77−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−ζ79ζ9+ζ31−ζ41+ζ47−ζ57−ζ63+ζ73−ζ79−ζ9−ζ31+ζ41−ζ47+ζ57+ζ63−ζ73+ζ7900000000000000000000000000000000
χ578-800042−42-20−25252000000−1010−22ζ11−ζ13−ζ27+ζ29+ζ43−ζ59−ζ61+ζ77−ζ11+ζ13+ζ27−ζ29−ζ43+ζ59+ζ61−ζ77ζ11+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+ζ79−ζ9−ζ31+ζ41−ζ47+ζ57+ζ63−ζ73+ζ79ζ9+ζ31−ζ41+ζ47−ζ57−ζ63+ζ73−ζ7900000000000000000000000000000000
χ588-8000−42428000-800000000−42420000000000000000000000000000000000000000
χ598-8000−4242-2025−252000000−10102−2ζ9+ζ31−ζ41+ζ47−ζ57−ζ63+ζ73−ζ79−ζ9−ζ31+ζ41−ζ47+ζ57+ζ63−ζ73+ζ79−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−ζ11+ζ13+ζ27−ζ29−ζ43+ζ59+ζ61−ζ77ζ11−ζ13−ζ27+ζ29+ζ43−ζ59−ζ61+ζ7700000000000000000000000000000000
χ608-8000−4242-2025−252000000−10102−2−ζ9−ζ31+ζ41−ζ47+ζ57+ζ63−ζ73+ζ79ζ9+ζ31−ζ41+ζ47−ζ57−ζ63+ζ73−ζ79ζ9+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+ζ77ζ11−ζ13−ζ27+ζ29+ζ43−ζ59−ζ61+ζ77−ζ11+ζ13+ζ27−ζ29−ζ43+ζ59+ζ61−ζ7700000000000000000000000000000000
χ618-8000−4242-20−2525200000010−102−2ζ9+ζ31−ζ41−ζ47+ζ57+ζ63−ζ73−ζ79−ζ9−ζ31+ζ41+ζ47−ζ57−ζ63+ζ73+ζ79ζ9+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+ζ77ζ11+ζ13+ζ27+ζ29−ζ43−ζ59−ζ61−ζ77−ζ11−ζ13−ζ27−ζ29+ζ43+ζ59+ζ61+ζ7700000000000000000000000000000000
χ628-8000−4242-20−2525200000010−102−2−ζ9−ζ31+ζ41+ζ47−ζ57−ζ63+ζ73+ζ79ζ9+ζ31−ζ41−ζ47+ζ57+ζ63−ζ73−ζ79−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−ζ11−ζ13−ζ27−ζ29+ζ43+ζ59+ζ61+ζ77ζ11+ζ13+ζ27+ζ29−ζ43−ζ59−ζ61−ζ7700000000000000000000000000000000

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