Finite Group Databasebeta

← Group #11772125

Character table — Group #11772125

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45
size11222888888889912121212121212121818181818242424242424242436363672727272144144
order1248836121224242424221616161616161616444884848484848484848488888844
χ1111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1
χ3111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1
χ4111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-111
χ5111-1-11111-1-1-1-111iiii−i−i−i−i-11-1-1-1iiii−i−i−i−i-111ii−i−i1-1
χ6111-1-11111-1-1-1-111iiii−i−i−i−i-11-1-1-1iiii−i−i−i−i-111−i−iii-11
χ7111-1-11111-1-1-1-111−i−i−i−iiiii-11-1-1-1−i−i−i−iiiii-111ii−i−i-11
χ8111-1-11111-1-1-1-111−i−i−i−iiiii-11-1-1-1−i−i−i−iiiii-111−i−iii1-1
χ922222222222222200000000-22-22200000000-2-2-2000000
χ102222222222222-2-2000000000-20-2-200000000000i2−i2i2−i200
χ112222222222222-2-2000000000-20-2-200000000000−i2i2−i2i200
χ12222-2-22222-2-2-2-22200000000222-2-2000000002-2-2000000
χ13222-2-22222-2-2-2-2-2-2000000000-2022000000000002−2−2200
χ14222-2-22222-2-2-2-2-2-2000000000-202200000000000−222−200
χ1522-20022-2-2000022i2i2−i2−i2i2i2−i2−i2-2-2-200i2i2−i2−i2i2i2−i2−i2200000000
χ1622-20022-2-200002222−2−2−2−2222-220022−2−2−2−222-200000000
χ1722-20022-2-2000022−2−22222−2−22-2200−2−22222−2−2-200000000
χ1822-20022-2-2000022−i2−i2i2i2−i2−i2i2i2-2-2-200−i2−i2i2i2−i2−i2i2i2200000000
χ192-202−22-20022−2−2-22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ720-22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ702−2000000
χ202-202−22-20022−2−2-22ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7-2022−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70−22000000
χ212-202−22-20022−2−2-22−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7-2022−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70−22000000
χ222-202−22-20022−2−2-22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ720-22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ702−2000000
χ232-20−222-200−2−222-22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ520-2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50−22000000
χ242-20−222-200−2−222-22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5-202−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ502−2000000
χ252-20−222-200−2−222-22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5-202−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ502−2000000
χ262-20−222-200−2−222-22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ520-2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50−22000000
χ2744-40044-4-40000-4-4000000000400000000000000000000
χ284-4022−224-4002222−22−224-400000000000−222200000000000000000
χ294-40−22224-400−22−2222224-40000000000022−2200000000000000000
χ3088888-1-1-1-1-1-1-1-1002222222200000-1-1-1-1-1-1-1-1000000000
χ3188888-1-1-1-1-1-1-1-100-2-2-2-2-2-2-2-20000011111111000000000
χ32888-8-8-1-1-1-11111002i2i2i2i−2i−2i−2i−2i00000−i−i−i−iiiii000000000
χ33888-8-8-1-1-1-1111100−2i−2i−2i−2i2i2i2i2i00000iiii−i−i−i−i000000000
χ3488-800-1-1113i−3i3i−3i002ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ600000−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6000000000
χ3588-800-1-1113i−3i3i−3i00−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ600000ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6000000000
χ3688-800-1-111−3i3i−3i3i002ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ200000−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2000000000
χ3788-800-1-111−3i3i−3i3i00−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ200000ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2000000000
χ388-8042−42-113i−3iζ2+2ζ6−2ζ2−ζ6−ζ2−2ζ62ζ2+ζ6002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ700000−ζζ−ζ5ζ5−ζ3ζ3−ζ7ζ7000000000
χ398-8042−42-113i−3iζ2+2ζ6−2ζ2−ζ6−ζ2−2ζ62ζ2+ζ600−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ700000ζ−ζζ5−ζ5ζ3−ζ3ζ7−ζ7000000000
χ408-8042−42-11−3i3i−2ζ2−ζ6ζ2+2ζ62ζ2+ζ6−ζ2−2ζ6002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ00000−ζ7ζ7−ζ3ζ3−ζ5ζ5−ζζ000000000
χ418-8042−42-11−3i3i−2ζ2−ζ6ζ2+2ζ62ζ2+ζ6−ζ2−2ζ600−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ00000ζ7−ζ7ζ3−ζ3ζ5−ζ5ζ−ζ000000000
χ428-80−4242-113i−3i−ζ2−2ζ62ζ2+ζ6ζ2+2ζ6−2ζ2−ζ6002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ300000−ζ5ζ5ζ−ζζ7−ζ7−ζ3ζ3000000000
χ438-80−4242-113i−3i−ζ2−2ζ62ζ2+ζ6ζ2+2ζ6−2ζ2−ζ600−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ300000ζ5−ζ5−ζζ−ζ7ζ7ζ3−ζ3000000000
χ448-80−4242-11−3i3i2ζ2+ζ6−ζ2−2ζ6−2ζ2−ζ6ζ2+2ζ6002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ500000−ζ3ζ3ζ7−ζ7ζ−ζ−ζ5ζ5000000000
χ458-80−4242-11−3i3i2ζ2+ζ6−ζ2−2ζ6−2ζ2−ζ6ζ2+2ζ600−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ500000ζ3−ζ3−ζ7ζ7−ζζζ5−ζ5000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.