Finite Group Databasebeta

← Group #11777059

Character table — Group #11777059

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1111222248888888888888888999918181818363636363636363636363636363636363672727272
order12224444236666666121212121212121244444444488888888888888888888
χ1111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-1-1111-1-1-1-111111-1-1-1-11111-1-111-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111-1-1-1111-1-1-1-111111-1-1-1-11111-1-111-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111-1-1-1111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111-1-1-1111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-111-1111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1111ii−i−iii−i−i11-1-111-1-1i−ii−i
χ101111-1-111-1111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1111ii−i−iii−i−i-1-111-1-111−ii−ii
χ111111-1-111-1111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1111−i−iii−i−iii11-1-111-1-1−ii−ii
χ121111-1-111-1111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1111−i−iii−i−iii-1-111-1-111i−ii−i
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1ii−i−i−i−iii11-1-1-1-111i−i−ii
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1ii−i−i−i−iii-1-11111-1-1−iii−i
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1−i−iiiii−i−i11-1-1-1-111−iii−i
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1−i−iiiii−i−i-1-11111-1-1i−i−ii
χ172222222222222222222222222-2-2-2-2-2-2-2-2-200000000000000000000
χ18222222-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-222-2-2200000000000000000000
χ192222-2-222-2222-2-2-2-22-2-2-2-22222222222-2-2-200000000000000000000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-2200000000000000000000
χ212-22-2002i−2i022-20000-200002i2i−2i−2i22-2-22i−2i00000000000i2−i2i2−i22−22−20000
χ222-22-2002i−2i022-20000-200002i2i−2i−2i22-2-22i−2i00000000000−i2i2−i2i2−22−220000
χ232-22-2002i−2i022-20000-200002i2i−2i−2i-2-222−2i2i00000000000i2−i2−i2i22−2−220000
χ242-22-2002i−2i022-20000-200002i2i−2i−2i-2-222−2i2i00000000000−i2i2i2−i2−222−20000
χ252-22-200−2i2i022-20000-20000−2i−2i2i2i22-2-2−2i2i00000000000i2−i2i2−i2−22−220000
χ262-22-200−2i2i022-20000-20000−2i−2i2i2i22-2-2−2i2i00000000000−i2i2−i2i22−22−20000
χ272-22-200−2i2i022-20000-20000−2i−2i2i2i-2-2222i−2i00000000000i2−i2−i2i2−222−20000
χ282-22-200−2i2i022-20000-20000−2i−2i2i2i-2-2222i−2i00000000000−i2i2i2−i22−2−220000
χ292-2-222i−2i0002-220000-22i2i−2i−2i00002i−2i2i−2i002-2000002ζ3−2ζ32ζ−2ζ000000000000
χ302-2-222i−2i0002-220000-22i2i−2i−2i00002i−2i2i−2i002-200000−2ζ32ζ3−2ζ2ζ000000000000
χ312-2-222i−2i0002-220000-22i2i−2i−2i0000−2i2i−2i2i00-2202ζ3−2ζ32ζ−2ζ0000000000000000
χ322-2-222i−2i0002-220000-22i2i−2i−2i0000−2i2i−2i2i00-220−2ζ32ζ3−2ζ2ζ0000000000000000
χ332-2-22−2i2i0002-220000-2−2i−2i2i2i00002i−2i2i−2i00-2202ζ−2ζ2ζ3−2ζ30000000000000000
χ342-2-22−2i2i0002-220000-2−2i−2i2i2i00002i−2i2i−2i00-220−2ζ2ζ−2ζ32ζ30000000000000000
χ352-2-22−2i2i0002-220000-2−2i−2i2i2i0000−2i2i−2i2i002-2000002ζ−2ζ2ζ3−2ζ3000000000000
χ362-2-22−2i2i0002-220000-2−2i−2i2i2i0000−2i2i−2i2i002-200000−2ζ2ζ−2ζ32ζ3000000000000
χ3744-4-4000004-4-400004000000004i−4i−4i4i0000000000000000000000000
χ3844-4-4000004-4-40000400000000−4i4i4i−4i0000000000000000000000000
χ39888888888-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000
χ40888888-8-8-8-1-1-11111-1-1-1-1-1111100000000000000000000000000000
χ418888-8-888-8-1-1-11111-11111-1-1-1-100000000000000000000000000000
χ428888-8-8-8-88-1-1-1-1-1-1-1-11111111100000000000000000000000000000
χ4388-8-800000-11133-3-3-13-33-33-33-300000000000000000000000000000
χ4488-8-800000-11133-3-3-1-33-33-33-3300000000000000000000000000000
χ4588-8-800000-111-3-333-13-33-3-33-3300000000000000000000000000000
χ4688-8-800000-111-3-333-1-33-333-33-300000000000000000000000000000
χ478-88-8008i−8i0-1-113-33-313i−3i−3i3i−i−iii00000000000000000000000000000
χ488-88-8008i−8i0-1-11-33-331−3i3i3i−3i−i−iii00000000000000000000000000000
χ498-88-800−8i8i0-1-113-33-31−3i3i3i−3iii−i−i00000000000000000000000000000
χ508-88-800−8i8i0-1-11-33-3313i−3i−3i3iii−i−i00000000000000000000000000000
χ518-8-888i−8i000-11-13-3-331−i−iii3i−3i−3i3i00000000000000000000000000000
χ528-8-888i−8i000-11-1-333-31−i−iii−3i3i3i−3i00000000000000000000000000000
χ538-8-88−8i8i000-11-13-3-331ii−i−i−3i3i3i−3i00000000000000000000000000000
χ548-8-88−8i8i000-11-1-333-31ii−i−i3i−3i−3i3i00000000000000000000000000000

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