Finite Group Databasebeta

← Group #14313769

Character table — Group #14313769

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1122244444466888888888888121212121216161616161616202024242424242424404040404040404040606080808080120120120120120
order122364561010104441215202020202020303030210101010126060606060604442020202020204888812121212222424242448888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1
χ31111111111111111111111111111111111111-1-11111111-1ii−i−i-1-1-1-1-1-1ii−i−i-1ii−i−i
χ41111111111111111111111111111111111111-1-11111111-1−i−iii-1-1-1-1-1-1−i−iii-1−i−iii
χ51111111111111-11111-1-1-1-111111111-111-1-1-1-111-111-1-1-1-1-11-11-1-1-111111-11-1-11-11-1
χ61111111111111-11111-1-1-1-111111111-111-1-1-1-111-111-1-1-1-1-1-11-11-1-11111-11-11-1-11-11
χ71111111111111-11111-1-1-1-111111111-111-1-1-1-1-1-1-111-1-1-1-11i−i−ii11-1-1-1-1i−i−ii1i−i−ii
χ81111111111111-11111-1-1-1-111111111-111-1-1-1-1-1-1-111-1-1-1-11−iii−i11-1-1-1-1−iii−i1−iii−i
χ911111111111-1-1111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1
χ1011111111111-1-1111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-11111
χ1111111111111-1-1111111111111-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-111ii−i−i1−i−iii
χ1211111111111-1-1111111111111-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-111−i−iii1ii−i−i
χ1311111111111-1-1-11111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1111-1-11111-11-11-1-1-111-1-11-11-11-11-11
χ1411111111111-1-1-11111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1111-1-11111-1-11-11-1-111-1-1-11-1111-11-1
χ1511111111111-1-1-11111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-11-1-111111i−i−ii11-1-111i−i−ii-1−iii−i
χ1611111111111-1-1-11111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-11-1-111111−iii−i11-1-111−iii−i-1i−i−ii
χ1722222-222222220-22-2-20000222-2-2-2-2-20-2-200002-2022000000000002-22-2000000000
χ1822222-222222220-22-2-20000222-2-2-2-2-20-2-20000-2202200000000000-22-22000000000
χ1922222-222222-2-20-22-2-20000222222220-2-200002-20-2-2000000000002-2-22000000000
χ2022222-222222-2-20-22-2-20000222222220-2-20000-220-2-200000000000-222-2000000000
χ21222-1-122-1222002-1-1222222-1-1-100000-1-1-1-1-1-1-122000000022222-1-1-1-100-1-1-1-100000
χ22222-1-122-1222002-1-1222222-1-1-100000-1-1-1-1-1-1-12200000002-2-2-2-2-1-1-1-100111100000
χ23222-1-122-1222002-1-1222222-1-1-100000-1-1-1-1-1-1-1-2-20000000-22i2i−2i−2i111100−i−iii00000
χ24222-1-122-1222002-1-1222222-1-1-100000-1-1-1-1-1-1-1-2-20000000-2−2i−2i2i2i111100ii−i−i00000
χ25222-1-122-122200-2-1-122-2-2-2-2-1-1-1000001-1-11111220000000-22-22-211-1-100-11-1100000
χ26222-1-122-122200-2-1-122-2-2-2-2-1-1-1000001-1-11111220000000-2-22-2211-1-1001-11-100000
χ27222-1-122-122200-2-1-122-2-2-2-2-1-1-1000001-1-11111-2-2000000022i−2i−2i2i-1-11100−iii−i00000
χ28222-1-122-122200-2-1-122-2-2-2-2-1-1-1000001-1-11111-2-200000002−2i2i2i−2i-1-11100i−i−ii00000
χ29444444-14-1-1-14444-1-1-1-1-1-1-1-1-1-14-1-1-1-14-1-1-1-1-1-1004-1-1-1-1-1-100000000000000000000
χ30444444-14-1-1-144-44-1-1-11111-1-1-14-1-1-1-1-4-1-1111100-4-1-1111100000000000000000000
χ31444444-14-1-1-1-4-444-1-1-1-1-1-1-1-1-1-1-411114-1-1-1-1-1-100-411111100000000000000000000
χ32444444-14-1-1-1-4-4-44-1-1-11111-1-1-1-41111-4-1-1111100411-1-1-1-100000000000000000000
χ3344444-4-14-1-1-1440-4-111−5−555-1-1-1-41111011−5−555000-1-1−5−55500000000000000000000
χ3444444-4-14-1-1-1440-4-11155−5−5-1-1-1-4111101155−5−5000-1-155−5−500000000000000000000
χ3544444-4-14-1-1-1-4-40-4-111−5−555-1-1-14-1-1-1-1011−5−5550001155−5−500000000000000000000
χ3644444-4-14-1-1-1-4-40-4-11155−5−5-1-1-14-1-1-1-101155−5−500011−5−55500000000000000000000
χ37444-2-2-44-24440002-2-4-40000-2-2-20000002200004-400000000000000-2200000000000
χ38444-2-2-44-24440002-2-4-40000-2-2-2000000220000-44000000000000002-200000000000
χ3944-44404-4-4-444-4004000000-4-440000000000000004-4000000000000000000000000
χ4044-44404-4-4-44-44004000000-4-44000000000000000-44000000000000000000000000
χ4144-4440-1-411-14-400-1−55ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ5811-10−5−5550−55ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58000-11ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ5800000000000000000000
χ4244-4440-1-411-14-400-1−55−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ5811-10−5−5550−55−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58000-11−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ5800000000000000000000
χ4344-4440-1-411-14-400-15−5ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ5811-1055−5−505−5ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58000-11ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ5800000000000000000000
χ4444-4440-1-411-14-400-15−5−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ5811-1055−5−505−5−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58000-11−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ5800000000000000000000
χ4544-4440-1-411-1-4400-1−55ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ5811-1055−5−50−55ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ580001-1−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ5800000000000000000000
χ4644-4440-1-411-1-4400-1−55−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ5811-1055−5−50−55−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ580001-1ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ5800000000000000000000
χ4744-4440-1-411-1-4400-15−5ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ5811-10−5−55505−5ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ580001-1−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ5800000000000000000000
χ4844-4440-1-411-1-4400-15−5−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ5811-10−5−55505−5−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ580001-1ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ5800000000000000000000
χ49888-4-48-2-4-2-2-2008-41-2-2-2-2-2-211100000-411111100000000000000000000000000000
χ50888-4-48-2-4-2-2-200-8-41-2-2222211100000411-1-1-1-100000000000000000000000000000
χ51888-4-4-8-2-4-2-2-20004122−25−252525111000000-1-155−5−500000000000000000000000000000
χ52888-4-4-8-2-4-2-2-200041222525−25−25111000000-1-1−5−55500000000000000000000000000000
χ5388-8-4-4084-8-880000-400000044-400000000000000000000000000000000000000000
χ5488-8-4-40-2422-200001−25252ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ58-1-110000005−5−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ5800000000000000000000000000000
χ5588-8-4-40-2422-200001−2525−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58-1-110000005−5ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ5800000000000000000000000000000
χ5688-8-4-40-2422-20000125−252ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58-1-11000000−55−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ5800000000000000000000000000000
χ5788-8-4-40-2422-20000125−25−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ58-1-11000000−55ζ2+ζ14+ζ22−ζ26+ζ34−ζ38−ζ46−ζ58−ζ2−ζ14−ζ22+ζ26−ζ34+ζ38+ζ46+ζ58−ζ2+ζ14−ζ22−ζ26+ζ34+ζ38−ζ46+ζ58ζ2−ζ14+ζ22+ζ26−ζ34−ζ38+ζ46−ζ5800000000000000000000000000000
χ588-808-808000-80000800000000-800000000000000000000000000000000000000000
χ598-808-80-20−252520000-2000000−2525202ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ58000000000000000000000000000000000000
χ608-808-80-20−252520000-2000000−252520−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58000000000000000000000000000000000000
χ618-808-80-2025−2520000-200000025−25202ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ58−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58000000000000000000000000000000000000
χ628-808-80-2025−2520000-200000025−2520−2ζ2−2ζ14−2ζ22+2ζ26−2ζ34+2ζ38+2ζ46+2ζ582ζ2+2ζ14+2ζ22−2ζ26+2ζ34−2ζ38−2ζ46−2ζ582ζ2−2ζ14+2ζ22+2ζ26−2ζ34−2ζ38+2ζ46−2ζ58−2ζ2+2ζ14−2ζ22−2ζ26+2ζ34+2ζ38−2ζ46+2ζ58000000000000000000000000000000000000
χ638-80-4408000-80000-400000000400000000000000000000000000−2i32i30000000000000
χ648-80-4408000-80000-4000000004000000000000000000000000002i3−2i30000000000000
χ6516-160-880-40−454540000200000025−25-200000000000000000000000000000000000000000
χ6616-160-880-4045−45400002000000−2525-200000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.