Finite Group Databasebeta

← Group #13027166

Character table — Group #13027166

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444445555888888888888881010101010101616202020202020202020202020202020202020202032323232808080808080
order122244888851010101616161644442020404040408080808080808080228888244444888816161616161616161616161610102020448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−i1111-1-1i−ii−i
χ6111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii1111-1-1−ii−ii
χ7111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-111−ii−ii
χ8111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1-1-1−i−i−i−iiiii-1-1-1-111i−ii−i
χ911111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1
χ1011111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11-1-111
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-111-1-1
χ1311111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1ii−i−iii−i−i1111−i−i−i−iiiii11-1-11-1i−i−ii
χ1411111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1−i−iii−i−iii1111iiii−i−i−i−i11-1-11-1−iii−i
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11ii−i−iii−i−i1111−i−i−i−iiiii-1-111-11−iii−i
χ1611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i−iii−i−iii1111iiii−i−i−i−i-1-111-11i−i−ii
χ17222222-2-2-2-222220000222222-2-2-2-20000000022-2-2-2-2002222-2-2-2-20000000000000000000000
χ18222222-2-2-2-222220000222222-2-2-2-20000000022-2-2-2-200-2-2-2-222220000000000000000000000
χ19222222-2-2-2-222220000-2-2-2-222-2-2-2-200000000-2-22222002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ20222222-2-2-2-222220000-2-2-2-222-2-2-2-200000000-2-2222200−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ212222-2-20000222222−2−22222-2-200002222−2−2−2−2-2-200000000002-22-222−2−222−2−222−2−20000000000
χ222222-2-20000222222−2−22222-2-200002222−2−2−2−2-2-20000000000-22-2222−2−2−2−222−2−2220000000000
χ232222-2-20000222222−2−2-2-2-2-2-2-200002222−2−2−2−22200000000002i−2i−2i2i−2−222i2i2−i2−i2−i2−i2i2i20000000000
χ242222-2-20000222222−2−2-2-2-2-2-2-200002222−2−2−2−2220000000000−2i2i2i−2i−2−222−i2−i2i2i2i2i2−i2−i20000000000
χ252222-2-200002222−2−2222222-2-20000−2−2−2−22222-2-200000000002-22-2−2−222−2−222−2−2220000000000
χ262222-2-200002222−2−2222222-2-20000−2−2−2−22222-2-20000000000-22-22−2−22222−2−222−2−20000000000
χ272222-2-200002222−2−222-2-2-2-2-2-20000−2−2−2−222222200000000002i−2i−2i2i22−2−2−i2−i2i2i2i2i2−i2−i20000000000
χ282222-2-200002222−2−222-2-2-2-2-2-20000−2−2−2−22222220000000000−2i2i2i−2i22−2−2i2i2−i2−i2−i2−i2i2i20000000000
χ292-2-222-200002-22-2i2−i2i2−i222-2-22-20000i2i2−i2−i2i2i2−i2−i2-220000002-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ302-2-222-200002-22-2i2−i2i2−i222-2-22-20000i2i2−i2−i2i2i2−i2−i2-22000000-22-220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000
χ312-2-222-200002-22-2i2−i2i2−i2-2-2222-20000i2i2−i2−i2i2i2−i2−i22-20000002i−2i−2i2i0000−i2i2−i2i2−22−222−22−20000000000
χ322-2-222-200002-22-2i2−i2i2−i2-2-2222-20000i2i2−i2−i2i2i2−i2−i22-2000000−2i2i2i−2i0000−i2i2−i2i22−22−2−22−220000000000
χ332-2-222-200002-22-2−i2i2−i2i222-2-22-20000−i2−i2i2i2−i2−i2i2i2-220000002-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ342-2-222-200002-22-2−i2i2−i2i222-2-22-20000−i2−i2i2i2−i2−i2i2i2-22000000-22-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000
χ352-2-222-200002-22-2−i2i2−i2i2-2-2222-20000−i2−i2i2i2−i2−i2i2i22-20000002i−2i−2i2i0000i2−i2i2−i22−22−2−22−220000000000
χ362-2-222-200002-22-2−i2i2−i2i2-2-2222-20000−i2−i2i2i2−i2−i2i2i22-2000000−2i2i2i−2i0000i2−i2i2−i2−22−222−22−20000000000
χ372-2-22-2222-2-22-22-22i−2i−2i2i22-2-2-2222-2-22i2i−2i−2i−2i−2i2i2i2-2-2-22200000000002i−2i−2i2i000000000000000000
χ382-2-22-2222-2-22-22-22i−2i−2i2i-2-222-2222-2-22i2i−2i−2i−2i−2i2i2i-2222-2-20000000000−2i2i2i−2i000000000000000000
χ392-2-22-2222-2-22-22-2−2i2i2i−2i22-2-2-2222-2-2−2i−2i2i2i2i2i−2i−2i2-2-2-2220000000000−2i2i2i−2i000000000000000000
χ402-2-22-2222-2-22-22-2−2i2i2i−2i-2-222-2222-2-2−2i−2i2i2i2i2i−2i−2i-2222-2-200000000002i−2i−2i2i000000000000000000
χ412-2-22-22-2-2222-22-2000022-2-2-22-2-222000000002-222-2-2000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ422-2-22-22-2-2222-22-2000022-2-2-22-2-222000000002-222-2-200000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ432-2-22-22-2-2222-22-20000-2-222-22-2-22200000000-22-2-222000000000000002-2-22-222-20000000000
χ442-2-22-22-2-2222-22-20000-2-222-22-2-22200000000-22-2-22200000000000000-222-22-2-220000000000
χ454444444444-1-1-1-144440000-1-1-1-1-1-1-1-1-1-1-1-1-1-10000004400000000000000000000-1-1-1-1000000
χ464444444444-1-1-1-144440000-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-4-4000000000000000000001111000000
χ474444444444-1-1-1-1-4-4-4-40000-1-1-1-1-1-1111111110000004-400000000000000000000-1-111000000
χ484444444444-1-1-1-1-4-4-4-40000-1-1-1-1-1-111111111000000-440000000000000000000011-1-1000000
χ4944-4-40022−2222−224-4-4400004i−4i4i−4i0022−2222−2200000000002i2−2i22i2−2i200000000000000000000000000000000
χ5044-4-40022−2222−224-4-440000−4i4i−4i4i0022−2222−220000000000−2i22i2−2i22i200000000000000000000000000000000
χ5144-4-400−2222−22224-4-4400004i−4i4i−4i00−2222−22220000000000−2i22i2−2i22i200000000000000000000000000000000
χ5244-4-400−2222−22224-4-440000−4i4i−4i4i00−2222−222200000000002i2−2i22i2−2i200000000000000000000000000000000
χ534-44-40022−22−222244-4-400004i−4i−4i4i0022−22−22220000000000−2i22i22i2−2i200000000000000000000000000000000
χ544-44-40022−22−222244-4-40000−4i4i4i−4i0022−22−222200000000002i2−2i2−2i22i200000000000000000000000000000000
χ554-44-400−222222−2244-4-400004i−4i−4i4i00−222222−2200000000002i2−2i2−2i22i200000000000000000000000000000000
χ564-44-400−222222−2244-4-40000−4i4i4i−4i00−222222−220000000000−2i22i22i2−2i200000000000000000000000000000000
χ574-4-44-4444-4-4-11-114i−4i−4i4i00001-1-1-111−i−iiiii−i−i00000000000000000000000000005−5i5−i5000000
χ584-4-44-4444-4-4-11-114i−4i−4i4i00001-1-1-111−i−iiiii−i−i0000000000000000000000000000−55−i5i5000000
χ594-4-44-4444-4-4-11-11−4i4i4i−4i00001-1-1-111ii−i−i−i−iii00000000000000000000000000005−5−i5i5000000
χ604-4-44-4444-4-4-11-11−4i4i4i−4i00001-1-1-111ii−i−i−i−iii0000000000000000000000000000−55i5−i5000000
χ61888888-8-8-8-8-2-2-2-200000000-2-222220000000000000000000000000000000000000000000000
χ628888-8-80000-2-2-2-24242−42−420000220000−2−2−2−2222200000000000000000000000000000000000000
χ638888-8-80000-2-2-2-2−42−42424200002200002222−2−2−2−200000000000000000000000000000000000000
χ6488-8-80042−4242−42-222-20000000000−22−22ζ11+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−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−ζ7900000000000000000000000000000000000000
χ6588-8-80042−4242−42-222-20000000000−22−22−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+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+ζ7900000000000000000000000000000000000000
χ6688-8-800−4242−4242-222-200000000002−22−2−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−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+ζ7700000000000000000000000000000000000000
χ6788-8-800−4242−4242-222-200000000002−22−2ζ9−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+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−ζ7700000000000000000000000000000000000000
χ688-88-80042−42−4242-2-2220000000000−222−2−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−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+ζ7700000000000000000000000000000000000000
χ698-88-80042−42−4242-2-2220000000000−222−2ζ9+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+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−ζ7700000000000000000000000000000000000000
χ708-88-800−424242−42-2-22200000000002−2−22ζ11−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−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−ζ7900000000000000000000000000000000000000
χ718-88-800−424242−42-2-22200000000002−2−22−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+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+ζ7900000000000000000000000000000000000000
χ728-8-888-80000-22-224i2−4i24i2−4i20000-220000−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000000000
χ738-8-888-80000-22-22−4i24i2−4i24i20000-220000i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000000000
χ748-8-88-88-8-888-22-22000000002-222-2-20000000000000000000000000000000000000000000000

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