Finite Group Databasebeta

← Group #13027200

Character table — Group #13027200

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444444445555888888888888881010101010101616202020202020202020202020202020202020202032323232808080808080
order122244888851010101616161622222020404040408080808080808080448888444444888816161616161616161616161620202020444444
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
χ5111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111i−ii−iii−i−i-1-1-1-1iiii−i−i−i−i1111-1-1ii−i−i
χ6111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111−ii−ii−i−iii-1-1-1-1−i−i−i−iiiii1111-1-1−i−iii
χ7111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1i−ii−iii−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-111−i−iii
χ8111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii-1-1-1-1−i−i−i−iiiii-1-1-1-111ii−i−i
χ911111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-11-1
χ1011111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-11-11
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-11
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1i−ii−iii−i−i1111−i−i−i−iiiii11-1-1-11i−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−ii−ii−i−iii1111iiii−i−i−i−i11-1-1-11−iii−i
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11i−ii−iii−i−i1111−i−i−i−iiiii-1-1111-1−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−ii−ii−i−iii1111iiii−i−i−i−i-1-1111-1i−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
χ19222222-2-2-2-222220000-2-2-2-222-2-2-2-200000000-2-22222002i−2i2i−2i−2i−2i2i2i0000000000000000000000
χ20222222-2-2-2-222220000-2-2-2-222-2-2-2-200000000-2-2222200−2i2i−2i2i2i2i−2i−2i0000000000000000000000
χ212222-2-20000222222−2−22222-2-200002222−2−2−2−2-2-200000022-2-2000022−2−222−2−222−2−20000000000
χ222222-2-20000222222−2−22222-2-200002222−2−2−2−2-2-2000000-2-222000022−2−2−2−222−2−2220000000000
χ232222-2-20000222222−2−2-2-2-2-2-2-200002222−2−2−2−2220000002i−2i−2i2i0000−2−222i2i2−i2−i2−i2−i2i2i20000000000
χ242222-2-20000222222−2−2-2-2-2-2-2-200002222−2−2−2−222000000−2i2i2i−2i0000−2−222−i2−i2i2i2i2i2−i2−i20000000000
χ252222-2-200002222−2−2222222-2-20000−2−2−2−22222-2-200000022-2-20000−2−222−2−222−2−2220000000000
χ262222-2-200002222−2−2222222-2-20000−2−2−2−22222-2-2000000-2-2220000−2−22222−2−222−2−20000000000
χ272222-2-200002222−2−222-2-2-2-2-2-20000−2−2−2−22222220000002i−2i−2i2i000022−2−2−i2−i2i2i2i2i2−i2−i20000000000
χ282222-2-200002222−2−222-2-2-2-2-2-20000−2−2−2−2222222000000−2i2i2i−2i000022−2−2i2i2−i2−i2−i2−i2i2i20000000000
χ2922-2-22-2000022-2-22−22−222-2-22-2000022−2−222−2−2-2200000000002-22-22−22−22−22−22−22−20000000000
χ3022-2-22-2000022-2-22−22−222-2-22-2000022−2−222−2−2-220000000000-22-222−22−2−22−22−22−220000000000
χ3122-2-22-2000022-2-22−22−2-2-2222-2000022−2−222−2−22-200000000002i−2i−2i2i−22−22i2−i2i2−i2−i2i2−i2i20000000000
χ3222-2-22-2000022-2-22−22−2-2-2222-2000022−2−222−2−22-20000000000−2i2i2i−2i−22−22−i2i2−i2i2i2−i2i2−i20000000000
χ3322-2-22-2000022-2-2−22−2222-2-22-20000−2−222−2−222-2200000000002-22-2−22−22−22−22−22−220000000000
χ3422-2-22-2000022-2-2−22−2222-2-22-20000−2−222−2−222-220000000000-22-22−22−222−22−22−22−20000000000
χ3522-2-22-2000022-2-2−22−22-2-2222-20000−2−222−2−2222-200000000002i−2i−2i2i2−22−2−i2i2−i2i2i2−i2i2−i20000000000
χ3622-2-22-2000022-2-2−22−22-2-2222-20000−2−222−2−2222-20000000000−2i2i2i−2i2−22−2i2−i2i2−i2−i2i2−i2i20000000000
χ3722-2-2-2222-2-222-2-2000022-2-2-2222-2-2000000002-2-2-222000000000000002-2-222-2-220000000000
χ3822-2-2-2222-2-222-2-2000022-2-2-2222-2-2000000002-2-2-22200000000000000-222-2-222-20000000000
χ3922-2-2-2222-2-222-2-20000-2-222-2222-2-200000000-2222-2-2000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ4022-2-2-2222-2-222-2-20000-2-222-2222-2-200000000-2222-2-200000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ4122-2-2-22-2-22222-2-22-2-2222-2-2-22-2-22222-2-2-2-2222-222-2-200000000002-2-22000000000000000000
χ4222-2-2-22-2-22222-2-22-2-22-2-222-22-2-22222-2-2-2-222-22-2-2220000000000-222-2000000000000000000
χ4322-2-2-22-2-22222-2-2-222-222-2-2-22-2-222-2-22222-2-22-222-2-20000000000-222-2000000000000000000
χ4422-2-2-22-2-22222-2-2-222-2-2-222-22-2-222-2-22222-2-2-22-2-22200000000002-2-22000000000000000000
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
χ4944-4-4-44-4-444-1-1114-4-4400001-111-1-1-1-11111-1-10000000000000000000000000000i5−i5i5−i5000000
χ5044-4-4-44-4-444-1-1114-4-4400001-111-1-1-1-11111-1-10000000000000000000000000000−i5i5−i5i5000000
χ5144-4-4-44-4-444-1-111-444-400001-111-1-111-1-1-1-1110000000000000000000000000000i5−i5−i5i5000000
χ5244-4-4-44-4-444-1-111-444-400001-111-1-111-1-1-1-1110000000000000000000000000000−i5i5i5−i5000000
χ534-44-40022−2222−224-44-400004-44-40022−2222−22000000000022−2222−2200000000000000000000000000000000
χ544-44-40022−2222−224-44-40000-44-440022−2222−220000000000−2222−222200000000000000000000000000000000
χ554-44-400−2222−22224-44-400004-44-400−2222−22220000000000−2222−222200000000000000000000000000000000
χ564-44-400−2222−22224-44-40000-44-4400−2222−2222000000000022−2222−2200000000000000000000000000000000
χ574-4-440022−22−22224-4-4400004-4-440022−22−22220000000000−222222−2200000000000000000000000000000000
χ584-4-440022−22−22224-4-440000-444-40022−22−2222000000000022−22−222200000000000000000000000000000000
χ594-4-4400−222222−224-4-4400004-4-4400−222222−22000000000022−22−222200000000000000000000000000000000
χ604-4-4400−222222−224-4-440000-444-400−222222−220000000000−222222−2200000000000000000000000000000000
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
χ6488-8-88-80000-2-22242−4242−420000-220000−2−222−2−22200000000000000000000000000000000000000
χ6588-8-88-80000-2-222−4242−42420000-22000022−2−222−2−200000000000000000000000000000000000000
χ6688-8-8-8888-8-8-2-222000000002-2-2-2220000000000000000000000000000000000000000000000
χ678-88-80042−4242−42-22-220000000000−22−22ζ11−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
χ688-88-80042−4242−42-22-220000000000−22−22−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
χ698-88-800−4242−4242-22-2200000000002−22−2−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
χ708-88-800−4242−4242-22-2200000000002−22−2ζ9+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
χ718-8-880042−42−4242-222-20000000000−222−2−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−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
χ728-8-880042−42−4242-222-20000000000−222−2ζ9+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+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
χ738-8-8800−424242−42-222-200000000002−2−22ζ11−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−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
χ748-8-8800−424242−42-222-200000000002−2−22−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+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

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