Finite Group Databasebeta

← Group #14512421

Character table — Group #14512421

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size11233444468810101212121216202024242424242424242424303032323232404060608080808080120120120120120120
order122225101010236221010101064424101010102020202022153030306644612121212444444
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1
χ31111111111111111111-1-1111111111111111111-1-11-1-1-1-111-1-1-1-1
χ41111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-11111
χ5111111111111-1-111111i−i1111111111-1-11111-1-1i−i-1ii−i−i-1-1i−ii−i
χ6111111111111-1-111111i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1i−i-1ii−i−i11−ii−ii
χ7111111111111-1-111111−ii1111111111-1-11111-1-1−ii-1−i−iii-1-1−ii−ii
χ8111111111111-1-111111−ii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−ii-1−i−iii11i−ii−i
χ92222222222-1-1222222-122000000000022-1-1-1-1-1-122-1-1-1-1-1000000
χ102222222222-1-1222222-1-2-2000000000022-1-1-1-1-1-1-2-2-11111000000
χ112222222222-1-1-2-22222-12i−2i0000000000-2-2-1-1-1-1112i−2i1−i−iii000000
χ122222222222-1-1-2-22222-1−2i2i0000000000-2-2-1-1-1-111−2i2i1ii−i−i000000
χ1322-22222-2-2-2222-22-2-22-20000000000002-222-2-22200-20000000000
χ1422-22222-2-2-222-222-2-22-2000000000000-2222-2-2-2-20020000000000
χ1522-22222-2-2-2-1-12-22-2-2210000000000002-2-1-111-1-1001−i3i3−i3i3000000
χ1622-22222-2-2-2-1-12-22-2-2210000000000002-2-1-111-1-1001i3−i3i3−i3000000
χ1722-22222-2-2-2-1-1-222-2-221000000000000-22-1-1111100-13−3−33000000
χ1822-22222-2-2-2-1-1-222-2-221000000000000-22-1-1111100-1−333−3000000
χ19333-1-13333-10033-1-1-1-10331-11111-1-1-1-1-1-1000000-1-1000001-111-1-1
χ20333-1-13333-10033-1-1-1-1033-11-1-1-1-11111-1-1000000-1-100000-11-1-111
χ21333-1-13333-10033-1-1-1-10-3-31-11111-1-1-1-1-1-100000011000001-1-1-111
χ22333-1-13333-10033-1-1-1-10-3-3-11-1-1-1-11111-1-10000001100000-1111-1-1
χ23333-1-13333-100-3-3-1-1-1-103i−3i1-11111-1-1-1-111000000−ii00000-11i−i−ii
χ24333-1-13333-100-3-3-1-1-1-103i−3i-11-1-1-1-1111111000000−ii000001-1−iii−i
χ25333-1-13333-100-3-3-1-1-1-10−3i3i1-11111-1-1-1-111000000i−i00000-11−iii−i
χ26333-1-13333-100-3-3-1-1-1-10−3i3i-11-1-1-1-1111111000000i−i000001-1i−i−ii
χ2744444-1-1-1-144400-1-1-1-140044-1-1-1-1-1-1-1-100-1-1-1-1000000000000000
χ2844444-1-1-1-144400-1-1-1-1400-4-41111111100-1-1-1-1000000000000000
χ2944-444-1-111-44400-111-1-40000−5−555−5−55500-1-111000000000000000
χ3044-444-1-111-44400-111-1-4000055−5−555−5−500-1-111000000000000000
χ314-404-44-40004-400-40040000000000000004-400000000000000000
χ324-404-44-4000-2200-4004000000000000000-2200−2i32i30000000000000
χ334-404-44-4000-2200-4004000000000000000-22002i3−2i30000000000000
χ344-404-4-11−5504-4001−55-100000ζ2−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+ζ58ζ2−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+ζ5800-11−55000000000000000
χ354-404-4-11−5504-4001−55-100000−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−ζ58−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−ζ5800-11−55000000000000000
χ364-404-4-115−504-40015−5-100000ζ2+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−ζ58ζ2+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−ζ5800-115−5000000000000000
χ374-404-4-115−504-40015−5-100000−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+ζ58−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+ζ5800-115−5000000000000000
χ3866-6-2-266-6-62006-6-222-20000000000000-220000000000000000000
χ3966-6-2-266-6-6200-66-222-200000000000002-20000000000000000000
χ4088888-2-2-2-28-4-400-2-2-2-2-4000000000000001111000000000000000
χ4188-888-2-222-8-4-400-222-240000000000000011-1-1000000000000000
χ428-808-8-22−25250-44002−2525-20000000000000001-15−5000000000000000
χ438-808-8-2225−250-4400225−25-20000000000000001-1−55000000000000000
χ44121212-4-4-3-3-3-3-4000011110004-4-1-1-1-11111000000000000000000000
χ45121212-4-4-3-3-3-3-400001111000-441111-1-1-1-1000000000000000000000
χ461212-12-4-4-3-333400001-1-1100000−5−55555−5−5000000000000000000000
χ471212-12-4-4-3-333400001-1-110000055−5−5−5−555000000000000000000000
χ4812-120-4412-120000000400-40000000000000000000000000000000000
χ4912-120-44-33−353500000-15−5100000ζ2−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+ζ58−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−ζ58000000000000000000000
χ5012-120-44-33−353500000-15−5100000−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−ζ58ζ2−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+ζ58000000000000000000000
χ5112-120-44-3335−3500000-1−55100000ζ2+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−ζ58−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+ζ58000000000000000000000
χ5212-120-44-3335−3500000-1−55100000−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+ζ58ζ2+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−ζ58000000000000000000000

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