Finite Group Databasebeta

← Group #14285329

Character table — Group #14285329

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222444446688888888888810101010121212121216161616161616202020202424242424242440404040404040404040404040606080120120120120120
order12223666451010104441215202020202020303030444442020202012606060606060121212122101010102020488882424242424242424241228888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111111-1i−ii−iiiii−i−i−i−i-1-1-1-1i−ii−i
χ4111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111111-1−ii−ii−i−i−i−iiiii-1-1-1-1−ii−ii
χ5111111111111111-11111-1-1-1-1111111111111-111-1-1-1-11111-1-1-1-1-111-111-1-111-1-111-1-111-1-111-1-1
χ6111111111111111-11111-1-1-1-1111111111111-111-1-1-1-11111-1-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-111
χ7111111111111111-11111-1-1-1-1111-1-1-1-111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1111i−i−iiii−i−i−i−iii-1-111i−i−ii
χ8111111111111111-11111-1-1-1-1111-1-1-1-111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1111−iii−i−i−iiiii−i−i-1-111−iii−i
χ91111111111111-1-11111111111111111-1-1-1-1-111111111111-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1
χ101111111111111-1-11111111111111111-1-1-1-1-111111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111
χ111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iiiii−i−i−i−i11-11−ii−ii
χ121111111111111-1-1111111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−i−i−i−iiiii11-11i−ii−i
χ131111111111111-1-1-11111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1111111111-1-1-111-1-111-1-111-1-1-1-1-11-1-111
χ141111111111111-1-1-11111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-111-1-111-1-111-1-1-1111-1-1
χ151111111111111-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-11i−i−iiii−i−i−i−iii111-1−iii−i
χ161111111111111-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-11−iii−i−i−iiiii−i−i111-1i−i−ii
χ1722222222-22222220-22-2-200002222-2-22-222220-2-200002-22-200000-2-20000000000000-22000000
χ1822222222-22222220-22-2-20000222-222-2-222220-2-20000-22-2200000-2-200000000000002-2000000
χ1922222222-22222-2-20-22-2-200002222-2-222-2-2-2-20-2-200002-22-2000002200000000000002-2000000
χ2022222222-22222-2-20-22-2-20000222-222-22-2-2-2-20-2-20000-22-2200000220000000000000-22000000
χ212222-1-1-1-122222002-1-1222222-1-1-1222200000-1-1-1-1-1-1-1-1-1-1-1000000022222-1-1-1-1-1-1-1-100-100000
χ222222-1-1-1-122222002-1-1222222-1-1-1222200000-1-1-1-1-1-1-1-1-1-1-100000002-2-2-2-21111111100-100000
χ232222-1-1-1-122222002-1-1222222-1-1-1-2-2-2-200000-1-1-1-1-1-1-111110000000-22i−2i2i−2i−i−i−i−iiiii00100000
χ242222-1-1-1-122222002-1-1222222-1-1-1-2-2-2-200000-1-1-1-1-1-1-111110000000-2−2i2i−2i2iiiii−i−i−i−i00100000
χ252222-1-1-1-12222200-2-1-122-2-2-2-2-1-1-12222000001-1-11111-1-1-1-10000000-222-2-2-1-111-1-11100100000
χ262222-1-1-1-12222200-2-1-122-2-2-2-2-1-1-12222000001-1-11111-1-1-1-10000000-2-2-22211-1-111-1-100100000
χ272222-1-1-1-12222200-2-1-122-2-2-2-2-1-1-1-2-2-2-2000001-1-111111111000000022i−2i−2i2i−i−iiiii−i−i00-100000
χ282222-1-1-1-12222200-2-1-122-2-2-2-2-1-1-1-2-2-2-2000001-1-11111111100000002−2i2i2i−2iii−i−i−i−iii00-100000
χ29444444444-1-1-1-14444-1-1-1-1-1-1-1-1-1-100004-1-1-1-14-1-1-1-1-1-100004-1-1-1-1-1-1000000000000000000000
χ30444444444-1-1-1-144-44-1-1-11111-1-1-100004-1-1-1-1-4-1-111110000-41111-1-1000000000000000000000
χ31444444444-1-1-1-1-4-444-1-1-1-1-1-1-1-1-1-10000-411114-1-1-1-1-1-10000-4111111000000000000000000000
χ32444444444-1-1-1-1-4-4-44-1-1-11111-1-1-10000-41111-4-1-1111100004-1-1-1-111000000000000000000000
χ3344444444-4-1-1-1-1440-4-111−5−555-1-1-10000-4-1-1-1-1011−5−55500000−5−55511000000000000000000000
χ3444444444-4-1-1-1-1440-4-11155−5−5-1-1-10000-4-1-1-1-101155−5−50000055−5−511000000000000000000000
χ3544444444-4-1-1-1-1-4-40-4-111−5−555-1-1-1000041111011−5−5550000055−5−5-1-1000000000000000000000
χ3644444444-4-1-1-1-1-4-40-4-11155−5−5-1-1-100004111101155−5−500000−5−555-1-1000000000000000000000
χ374444-2-2-2-2-444440002-2-4-40000-2-2-24-4-44000000220000-22-220000000000000000000000000000
χ384444-2-2-2-2-444440002-2-4-40000-2-2-2-444-40000002200002-22-20000000000000000000000000000
χ3944-4-44-44-404-44-4000040000004-4-4400-400000000000040-400000000000000000000000000000
χ4044-4-44-44-404-44-4000040000004-4-4-4004000000000000-40400000000000000000000000000000
χ4144-4-4-22-2204-44-40000-2000000-222400-4000000000000-2020000000000000−i6i600−i6i60000000000
χ4244-4-4-22-2204-44-40000-2000000-222400-4000000000000-2020000000000000i6−i600i6−i60000000000
χ4344-4-4-22-2204-44-40000-2000000-222-400400000000000020-200000000000006−600−660000000000
χ4444-4-4-22-2204-44-40000-2000000-222-400400000000000020-20000000000000−66006−60000000000
χ454-44-444-4-4044-4-44i−4i004000000-44-4000004i4i−4i−4i000000000000000000000000000000000000000
χ464-44-444-4-4044-4-4−4i4i004000000-44-400000−4i−4i4i4i000000000000000000000000000000000000000
χ474-44-444-4-40-1-1114i−4i00-1−55ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ1181-1100000−i−iii0−55ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ11800000ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−i5i5000000000000000000000
χ484-44-444-4-40-1-1114i−4i00-1−55−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ1181-1100000−i−iii0−55−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ11800000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−i5i5000000000000000000000
χ494-44-444-4-40-1-1114i−4i00-15−5ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ1181-1100000−i−iii05−5ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ11800000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116i5−i5000000000000000000000
χ504-44-444-4-40-1-1114i−4i00-15−5−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ1181-1100000−i−iii05−5−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ11800000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116i5−i5000000000000000000000
χ514-44-444-4-40-1-111−4i4i00-1−55ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ1181-1100000ii−i−i0−55ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ11800000−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116i5−i5000000000000000000000
χ524-44-444-4-40-1-111−4i4i00-1−55−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ1181-1100000ii−i−i0−55−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ11800000ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116i5−i5000000000000000000000
χ534-44-444-4-40-1-111−4i4i00-15−5ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ1181-1100000ii−i−i05−5ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ11800000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116−i5i5000000000000000000000
χ544-44-444-4-40-1-111−4i4i00-15−5−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ1181-1100000ii−i−i05−5−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ11800000ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−i5i5000000000000000000000
χ554-4-444-4-4404-4-4400004000000-4-4404-400000000000000-4040000000000000000000000000000
χ564-4-444-4-4404-4-4400004000000-4-440-440000000000000040-40000000000000000000000000000
χ574-4-44-222-204-4-440000-200000022-204-40000000000000020-200000000000000−i6i600−i6i600000000
χ584-4-44-222-204-4-440000-200000022-204-40000000000000020-200000000000000i6−i600i6−i600000000
χ594-4-44-222-204-4-440000-200000022-20-4400000000000000-202000000000000006−600−6600000000
χ604-4-44-222-204-4-440000-200000022-20-4400000000000000-20200000000000000−66006−600000000
χ618888-4-4-4-48-2-2-2-2008-41-2-2-2-2-2-2111000000000-411111100000000000000000000000000000000
χ628888-4-4-4-48-2-2-2-200-8-41-2-22222111000000000411-1-1-1-100000000000000000000000000000000
χ638888-4-4-4-4-8-2-2-2-20004122−25−2525251110000000000-1-155−5−500000000000000000000000000000000
χ648888-4-4-4-4-8-2-2-2-200041222525−25−251110000000000-1-1−5−55500000000000000000000000000000000
χ6588-8-88-88-80-22-220000-2000000-22200000−2i52i5−2i52i5000000000000000000000000000000000000000
χ6688-8-88-88-80-22-220000-2000000-222000002i5−2i52i5−2i5000000000000000000000000000000000000000
χ678-88-8-4-444088-8-80000-40000004-44000000000000000000000000000000000000000000000000
χ688-88-8-4-4440-2-22200001−25252ζ14+2ζ22−2ζ38−2ζ46+2ζ62−2ζ86+2ζ94−2ζ118−2ζ14−2ζ22+2ζ38+2ζ46−2ζ62+2ζ86−2ζ94+2ζ1182ζ14−2ζ22+2ζ38−2ζ46−2ζ62−2ζ86+2ζ94+2ζ118−2ζ14+2ζ22−2ζ38+2ζ46+2ζ62+2ζ86−2ζ94−2ζ118-11-100000000005−5−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ11800000000000000000000000000000000
χ698-88-8-4-4440-2-22200001−2525−2ζ14−2ζ22+2ζ38+2ζ46−2ζ62+2ζ86−2ζ94+2ζ1182ζ14+2ζ22−2ζ38−2ζ46+2ζ62−2ζ86+2ζ94−2ζ118−2ζ14+2ζ22−2ζ38+2ζ46+2ζ62+2ζ86−2ζ94−2ζ1182ζ14−2ζ22+2ζ38−2ζ46−2ζ62−2ζ86+2ζ94+2ζ118-11-100000000005−5ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ11800000000000000000000000000000000
χ708-88-8-4-4440-2-2220000125−252ζ14−2ζ22+2ζ38−2ζ46−2ζ62−2ζ86+2ζ94+2ζ118−2ζ14+2ζ22−2ζ38+2ζ46+2ζ62+2ζ86−2ζ94−2ζ118−2ζ14−2ζ22+2ζ38+2ζ46−2ζ62+2ζ86−2ζ94+2ζ1182ζ14+2ζ22−2ζ38−2ζ46+2ζ62−2ζ86+2ζ94−2ζ118-11-10000000000−55−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ11800000000000000000000000000000000
χ718-88-8-4-4440-2-2220000125−25−2ζ14+2ζ22−2ζ38+2ζ46+2ζ62+2ζ86−2ζ94−2ζ1182ζ14−2ζ22+2ζ38−2ζ46−2ζ62−2ζ86+2ζ94+2ζ1182ζ14+2ζ22−2ζ38−2ζ46+2ζ62−2ζ86+2ζ94−2ζ118−2ζ14−2ζ22+2ζ38+2ζ46−2ζ62+2ζ86−2ζ94+2ζ118-11-10000000000−55ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ11800000000000000000000000000000000
χ728-8-888-8-880-222-20000-200000022-200000−252525−25000000000000000000000000000000000000000
χ738-8-888-8-880-222-20000-200000022-20000025−25−2525000000000000000000000000000000000000000
χ741616-16-16-88-880-44-44000020000002-2-2000000000000000000000000000000000000000000000000
χ7516-16-1616-888-80-444-400002000000-2-22000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.