Finite Group Databasebeta

← Group #13088745

Character table — Group #13088745

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122222224444444558888888888888888810101010101010151515151818202020202030303030303030303030303030306060606072729090
order12233666635666610221015151515303030303030303030303030266666644442466666444444121212121212121212121212102024
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-111111-1-111-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ51111111111111111-1-111111111111111111-1-1-1-1-1-1-1ii−i−i11-1-1-1-1-1i−ii−ii−iiiii−i−i−i−iii−i−i11-1-1
χ61111111111111111-1-111111111111111111-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1−iii−i−iiiiii−i−i−i−i−i−iii-1-111
χ71111111111111111-1-111111111111111111-1-1-1-1-1-1-1−i−iii11-1-1-1-1-1−ii−ii−ii−i−i−i−iiiii−i−iii11-1-1
χ81111111111111111-1-111111111111111111-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1i−i−iii−i−i−i−i−iiiiiii−i−i-1-111
χ911-11111-1-111-11-1-1111-111111111-1-1-1-1-1-1-1-1-11-1-111111111-1-111-1-1-1-1-1-11111-1-111-1-11-11-11-11-1
χ1011-11111-1-111-11-1-1111-111111111-1-1-1-1-1-1-1-1-11-1-11111111-11-111-1-111-1-1-1-111-1-111-1-1-11-11-11-11
χ1111-11111-1-111-11-1-1111-111111111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11-1-111-1-11111-1-1-1-111-1-111-11-111-11-1
χ1211-11111-1-111-11-1-1111-111111111-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-11-111-1-1-1-11111-1-111-1-1111-11-1-11-11
χ1311-11111-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1-1ii−i−i1-11-1-111−ii−iii−iii−i−i−i−iiii−i−ii1-1-11
χ1411-11111-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1-1ii−i−i-111-1-111i−i−ii−iiii−i−i−i−iii−iii−i-111-1
χ1511-11111-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1-1−i−iii1-11-1-111i−ii−i−ii−i−iiiii−i−i−iii−i1-1-11
χ1611-11111-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1-1−i−iii-111-1-111−iii−ii−i−i−iiiii−i−ii−i−ii-111-1
χ172222-12-122-12-1-1-1-122222-1-1-12-1-1-122-1-1-1-1-1-12222-1-12000000-1-1-1-1-122002200000000-1-1-1-10000
χ182222-12-122-12-1-1-1-122222-1-1-12-1-1-122-1-1-1-1-1-12222-1-12000000-1-1-1-1-1-2-200-2-20000000011110000
χ192222-12-122-12-1-1-1-12-2-222-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-211-2000000111112i−2i002i−2i00000000−i−iii0000
χ202222-12-122-12-1-1-1-12-2-222-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-211-200000011111−2i2i00−2i2i00000000ii−i−i0000
χ21222-12-12-1-1-122-1-1-12222-12-1-1-12-1-1-1-122-1-1-1-12-1-1-122-12222002-1-1-1-1002200-1-1-1-1-1-1-1-100000000
χ22222-12-12-1-1-122-1-1-12222-12-1-1-12-1-1-1-122-1-1-1-12-1-1-122-1-2-2-2-2002-1-1-1-100-2-2001111111100000000
χ23222-12-12-1-1-122-1-1-12-2-22-12-1-1-12-1-1-1-122-1-1-1-1-2111-2-212i2i−2i−2i00-21111002i−2i00−i−i−i−iiiii00000000
χ24222-12-12-1-1-122-1-1-12-2-22-12-1-1-12-1-1-1-122-1-1-1-1-2111-2-21−2i−2i2i2i00-2111100−2i2i00iiii−i−i−i−i00000000
χ2522-22-12-1-2-2-121-111222-22-1-1-12-1-1-1-2-2111111-22-2-2-1-120000001-1-1112200-2-2000000001-11-10000
χ2622-22-12-1-2-2-121-111222-22-1-1-12-1-1-1-2-2111111-22-2-2-1-120000001-1-111-2-2002200000000-11-110000
χ2722-22-12-1-2-2-121-1112-2-2-22-1-1-12-1-1-1-2-21111112-22211-2000000-111-1-12i−2i00−2i2i00000000i−i−ii0000
χ2822-22-12-1-2-2-121-1112-2-2-22-1-1-12-1-1-1-2-21111112-22211-2000000-111-1-1−2i2i002i−2i00000000−iii−i0000
χ2922-2-12-1211-12-2-111222-2-12-1-1-12-1-111-2-21111-2-11122-1222200-2-1-11100-2-200-1-111-1-11100000000
χ3022-2-12-1211-12-2-111222-2-12-1-1-12-1-111-2-21111-2-11122-1-2-2-2-200-2-1-11100220011-1-111-1-100000000
χ3122-2-12-1211-12-2-1112-2-2-2-12-1-1-12-1-111-2-2111121-1-1-2-212i2i−2i−2i00211-1-100−2i2i00−i−iiiii−i−i00000000
χ3222-2-12-1211-12-2-1112-2-2-2-12-1-1-12-1-111-2-2111121-1-1-2-21−2i−2i2i2i00211-1-1002i−2i00ii−i−i−i−iii00000000
χ332-2022-2-200220-200-22-202222-2-2-2-20000000002002-2-22i−2i2i−2i0002-2000000002i−2i002i−2i0000000000
χ342-2022-2-200220-200-22-202222-2-2-2-20000000002002-2-2−2i2i−2i2i0002-200000000−2i2i00−2i2i0000000000
χ352-2022-2-200220-200-2-2202222-2-2-2-2000000000-200-2222-2-22000-22000000002-200-220000000000
χ362-2022-2-200220-200-2-2202222-2-2-2-2000000000-200-222-222-2000-2200000000-22002-20000000000
χ372-20-121-2−i3i3-1201−i3i3-22-20-12-1-11-211−i3i300−i3−i3i3i30-1−i3i32-212i−2i2i−2i000-11−i3i3000000−ii3−3−ii3−300000000
χ382-20-121-2−i3i3-1201−i3i3-22-20-12-1-11-211−i3i300−i3−i3i3i30-1−i3i32-21−2i2i−2i2i000-11−i3i3000000i−i−33i−i−3300000000
χ392-20-121-2−i3i3-1201−i3i3-2-220-12-1-11-211−i3i300−i3−i3i3i301i3−i3-22-12-2-220001-1i3−i3000000-11−i3i31-1i3−i300000000
χ402-20-121-2−i3i3-1201−i3i3-2-220-12-1-11-211−i3i300−i3−i3i3i301i3−i3-22-1-222-20001-1i3−i30000001-1i3−i3-11−i3i300000000
χ412-20-121-2i3−i3-1201i3−i3-22-20-12-1-11-211i3−i300i3i3−i3−i30-1i3−i32-212i−2i2i−2i000-11i3−i3000000−ii−33−ii−3300000000
χ422-20-121-2i3−i3-1201i3−i3-22-20-12-1-11-211i3−i300i3i3−i3−i30-1i3−i32-21−2i2i−2i2i000-11i3−i3000000i−i3−3i−i3−300000000
χ432-20-121-2i3−i3-1201i3−i3-2-220-12-1-11-211i3−i300i3i3−i3−i301−i3i3-22-12-2-220001-1−i3i3000000-11i3−i31-1−i3i300000000
χ442-20-121-2i3−i3-1201i3−i3-2-220-12-1-11-211i3−i300i3i3−i3−i301−i3i3-22-1-222-20001-1−i3i30000001-1−i3i3-11i3−i300000000
χ454444444444-14444-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000004400000000000000000000000-1-100
χ464444444444-14444-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000-4-4000000000000000000000001100
χ47444-2-2-2-2-2-214-21114444-2-211-2-211-2-2-2-211114-2-2-2-2-2-2000000-211110000000000000000000000
χ48444-2-2-2-2-2-214-21114-4-44-2-211-2-211-2-2-2-21111-42222220000002-1-1-1-10000000000000000000000
χ4944-44444-4-44-1-44-4-4-1001-1-1-1-1-1-1-1-111111111000000000004-400000000000000000000000-1100
χ5044-44444-4-44-1-44-4-4-1001-1-1-1-1-1-1-1-11111111100000000000-44000000000000000000000001-100
χ5144-4-2-2-2-2221421-1-1444-4-2-211-2-2112222-1-1-1-1-4-222-2-2-2000000211-1-10000000000000000000000
χ5244-4-2-2-2-2221421-1-14-4-4-4-2-211-2-2112222-1-1-1-142-2-2222000000-2-1-1110000000000000000000000
χ534-404-2-4200-240200-44-404-2-2-2-4222000000000400-22-40000000-22000000000000000000000000
χ544-404-2-4200-240200-4-4404-2-2-2-4222000000000-4002-2400000002-2000000000000000000000000
χ554-40-2-222−2i32i3140-1i3−i3-44-40-2-21122-1-1−2i32i300i3i3−i3−i30-2−2i32i3-22200000001-1i3−i30000000000000000000000
χ564-40-2-222−2i32i3140-1i3−i3-4-440-2-21122-1-1−2i32i300i3i3−i3−i3022i3−2i32-2-20000000-11−i3i30000000000000000000000
χ574-40-2-2222i3−2i3140-1−i3i3-44-40-2-21122-1-12i3−2i300−i3−i3i3i30-22i3−2i3-22200000001-1−i3i30000000000000000000000
χ584-40-2-2222i3−2i3140-1−i3i3-4-440-2-21122-1-12i3−2i300−i3−i3i3i302−2i32i32-2-20000000-11i3−i30000000000000000000000
χ598888-48-488-4-2-4-4-4-4-200-2-2111-2111-2-21111110000000000000000000000000000000000000000
χ60888-48-48-4-4-4-28-4-4-4-200-21-2111-21111-2-211110000000000000000000000000000000000000000
χ61888-4-4-4-4-4-42-2-4222-200-211−1−352−1+35211−1−352−1+3521111−1−352−1+352−1−352−1+3520000000000000000000000000000000000000000
χ62888-4-4-4-4-4-42-2-4222-200-211−1+352−1−35211−1+352−1−3521111−1+352−1−352−1+352−1−3520000000000000000000000000000000000000000
χ6388-88-48-4-8-8-4-24-444-2002-2111-211122-1-1-1-1-1-10000000000000000000000000000000000000000
χ6488-8-48-4844-4-2-8-444-20021-2111-211-1-122-1-1-1-10000000000000000000000000000000000000000
χ6588-8-4-4-4-4442-242-2-2-200211−1−352−1+35211−1−352−1+352-1-1-1-11+3521−3521+3521−3520000000000000000000000000000000000000000
χ6688-8-4-4-4-4442-242-2-2-200211−1+352−1−35211−1+352−1−352-1-1-1-11−3521+3521−3521+3520000000000000000000000000000000000000000
χ678-8088-8-8008-20-8002000-2-2-2-22222000000000000000000000000000000000000000000000000
χ688-808-4-8400-4-204002000-21112-1-1-100−i15i15−i15i15i15−i150000000000000000000000000000000000000000
χ698-808-4-8400-4-204002000-21112-1-1-100i15−i15i15−i15−i15i150000000000000000000000000000000000000000
χ708-80-484-8−4i34i3-4-204−4i34i320001-211-12-1-1i3−i300i3i3−i3−i30000000000000000000000000000000000000000
χ718-80-484-84i3−4i3-4-2044i3−4i320001-211-12-1-1−i3i300−i3−i3i3i30000000000000000000000000000000000000000
χ728-80-4-444−4i34i32-20-22i3−2i3200011−1−352−1+352-1-11+3521−352i3−i3−i15i15−ζ2+ζ22−ζ38+ζ58−ζ14−ζ26+ζ34+ζ46ζ2−ζ22+ζ38−ζ58ζ14+ζ26−ζ34−ζ460000000000000000000000000000000000000000
χ738-80-4-444−4i34i32-20-22i3−2i3200011−1+352−1−352-1-11−3521+352i3−i3i15−i15−ζ14−ζ26+ζ34+ζ46−ζ2+ζ22−ζ38+ζ58ζ14+ζ26−ζ34−ζ46ζ2−ζ22+ζ38−ζ580000000000000000000000000000000000000000
χ748-80-4-4444i3−4i32-20-2−2i32i3200011−1−352−1+352-1-11+3521−352−i3i3i15−i15ζ2−ζ22+ζ38−ζ58ζ14+ζ26−ζ34−ζ46−ζ2+ζ22−ζ38+ζ58−ζ14−ζ26+ζ34+ζ460000000000000000000000000000000000000000
χ758-80-4-4444i3−4i32-20-2−2i32i3200011−1+352−1−352-1-11−3521+352−i3i3−i15i15ζ14+ζ26−ζ34−ζ46ζ2−ζ22+ζ38−ζ58−ζ14−ζ26+ζ34+ζ46−ζ2+ζ22−ζ38+ζ580000000000000000000000000000000000000000

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