Finite Group Databasebeta

← Group #11790152

Character table — Group #11790152

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222288888888888888889999181818181818181818181818181818181818181818187272727272727272
order122244888836661212121224242424242424242222444444444488888888888844444444
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-111
χ8111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-11111-1-1
χ91-1-11-1111-1-11-1-11-1-1111111-1-1-1-11-11-11ii−i−iii−i−i-111-1-1iiii−i−i−i−i1-11-1i−ii−i
χ101-1-11-1111-1-11-1-11-1-1111111-1-1-1-11-11-11ii−i−iii−i−i-111-1-1iiii−i−i−i−i-11-11−ii−ii
χ111-1-11-1111-1-11-1-11-1-1111111-1-1-1-11-11-11−i−iii−i−iii-111-1-1−i−i−i−iiiii1-11-1−ii−ii
χ121-1-11-1111-1-11-1-11-1-1111111-1-1-1-11-11-11−i−iii−i−iii-111-1-1−i−i−i−iiiii-11-11i−ii−i
χ131-1-11-11-1-1111-1-11-1-111-1-1-1-111111-11-11ii−i−iii−i−i-1-1-111−i−i−i−iiiii1-1-11i−i−ii
χ141-1-11-11-1-1111-1-11-1-111-1-1-1-111111-11-11ii−i−iii−i−i-1-1-111−i−i−i−iiiii-111-1−iii−i
χ151-1-11-11-1-1111-1-11-1-111-1-1-1-111111-11-11−i−iii−i−iii-1-1-111iiii−i−i−i−i1-1-11−iii−i
χ161-1-11-11-1-1111-1-11-1-111-1-1-1-111111-11-11−i−iii−i−iii-1-1-111iiii−i−i−i−i-111-1i−i−ii
χ1722222222222222222222222222-2-2-2-2-200000000-2-2-2-2-20000000000000000
χ18222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-200000000-222220000000000000000
χ192222-2-200002222-2-2-2-2000000002222-22222-2-2-2-2-200000000000000000000
χ202222-2-200002222-2-2-2-2000000002222-2-2-2-2-22222-200000000000000000000
χ212222-2-200002222-2-2-2-200000000-2-2-2-22000000002000022-2-222-2-200000000
χ222222-2-200002222-2-2-2-200000000-2-2-2-220000000020000-2-222-2-22200000000
χ2322-2-2002−22−222-2-2000022−2−222−2−222-2-202-22-2000002−22−22−22−22−22−200000000
χ2422-2-2002−22−222-2-2000022−2−222−2−222-2-20-22-22000002−22−2−22−22−22−2200000000
χ2522-2-2002−22−222-2-2000022−2−222−2−2-2-222000002-22-20−22−222−2−222−2−2200000000
χ2622-2-2002−22−222-2-2000022−2−222−2−2-2-22200000-22-220−22−22−222−2−222−200000000
χ2722-2-200−22−2222-2-20000−2−222−2−22222-2-202-22-200000−22−22−22−22−22−2200000000
χ2822-2-200−22−2222-2-20000−2−222−2−22222-2-20-22-2200000−22−222−22−22−22−200000000
χ2922-2-200−22−2222-2-20000−2−222−2−222-2-222000002-22-202−22−2−222−2−222−200000000
χ3022-2-200−22−2222-2-20000−2−222−2−222-2-22200000-22-2202−22−22−2−222−2−2200000000
χ312-22-2002−2−222-22-2000022−2−2−2−2222-2-2202i−2i−2i2i000002−2−22i2−i2i2−i2−i2i2−i2i200000000
χ322-22-2002−2−222-22-2000022−2−2−2−2222-2-220−2i2i2i−2i000002−2−22−i2i2−i2i2i2−i2i2−i200000000
χ332-22-2002−2−222-22-2000022−2−2−2−222-222-2000002i−2i−2i2i0−222−2i2−i2−i2i2−i2i2i2−i200000000
χ342-22-2002−2−222-22-2000022−2−2−2−222-222-200000−2i2i2i−2i0−222−2−i2i2i2−i2i2−i2−i2i200000000
χ352-22-200−222−22-22-20000−2−22222−2−22-2-2202i−2i−2i2i00000−222−2−i2i2−i2i2i2−i2i2−i200000000
χ362-22-200−222−22-22-20000−2−22222−2−22-2-220−2i2i2i−2i00000−222−2i2−i2i2−i2−i2i2−i2i200000000
χ372-22-200−222−22-22-20000−2−22222−2−2-222-2000002i−2i−2i2i02−2−22−i2i2i2−i2i2−i2−i2i200000000
χ382-22-200−222−22-22-20000−2−22222−2−2-222-200000−2i2i2i−2i02−2−22i2−i2−i2i2−i2i2i2−i200000000
χ392-2-222-200002-2-2222-2-2000000002-22-2-22i2i−2i−2i−2i−2i2i2i200000000000000000000
χ402-2-222-200002-2-2222-2-2000000002-22-2-2−2i−2i2i2i2i2i−2i−2i200000000000000000000
χ412-2-222-200002-2-2222-2-200000000-22-22200000000-200002i2i−2i−2i−2i−2i2i2i00000000
χ422-2-222-200002-2-2222-2-200000000-22-22200000000-20000−2i−2i2i2i2i2i−2i−2i00000000
χ432-2-22-2222-2-22-2-22-2-2222222-2-2-2-2-22-22-2000000002-2-2220000000000000000
χ442-2-22-22-2-2222-2-22-2-222-2-2-2-22222-22-22-200000000222-2-20000000000000000
χ458888888888-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ46888888-8-8-8-8-1-1-1-1-1-1-1-1111111110000000000000000000000000000000000
χ478888-8-80000-1-1-1-111113i−3i3i−3i3i−3i3i−3i0000000000000000000000000000000000
χ488888-8-80000-1-1-1-11111−3i3i−3i3i−3i3i−3i3i0000000000000000000000000000000000
χ4988-8-80042−4242−42-1-1113i−3i3i−3iζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000000000000000000000000
χ5088-8-80042−4242−42-1-111−3i3i−3i3i−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000000000000000000000000
χ5188-8-800−4242−4242-1-1113i−3i3i−3i−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000000000000000000000000
χ5288-8-800−4242−4242-1-111−3i3i−3i3i2ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000000000000000000000000
χ538-88-80042−42−4242-11-113i−3i−3i3i−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000000000000000000000000
χ548-88-80042−42−4242-11-11−3i3i3i−3iζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000000000000000000000000
χ558-88-800−424242−42-11-113i−3i−3i3i2ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000000000000000000000000
χ568-88-800−424242−42-11-11−3i3i3i−3i−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000000000000000000000000
χ578-8-888-80000-111-1-1-1113i−3i3i−3i−3i3i−3i3i0000000000000000000000000000000000
χ588-8-888-80000-111-1-1-111−3i3i−3i3i3i−3i3i−3i0000000000000000000000000000000000
χ598-8-88-8888-8-8-111-111-1-1-1-1-1-111110000000000000000000000000000000000
χ608-8-88-88-8-888-111-111-1-11111-1-1-1-10000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.