Finite Group Databasebeta

← Group #11776148

Character table — Group #11776148

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222244444444444448888888888999912121212121212121818181824242424242424242424242436363636363636363648484848
order12222244334666666121212126666121212121212444488888888444422442424242424242424488888888661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ5111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-11-11-1iiii−i−i−i−i1iiii−i−i−i−i1-11-1
χ6111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1-11-11iiii−i−i−i−i1−i−i−i−iiiii-11-11
χ7111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-11-11-1−i−i−i−iiiii1−i−i−i−iiiii1-11-1
χ8111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1-11-11−i−i−i−iiiii1iiii−i−i−i−i-11-11
χ91111-1-11111-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-111-1-1111-1-111-1-111-1-1
χ101111-1-11111-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-111-1-11-1-111-1-111-1-111
χ111111-1-11111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1111-1-111-1-11111-1-1
χ121111-1-11111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111111-1-111-1-1-1-111
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii-1-1-1-11-1-11ii−i−i−i−iii1ii−i−i−i−iii1-1-11
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii-1-1-1-1-111-1ii−i−i−i−iii1−i−iiiii−i−i-111-1
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i-1-1-1-11-1-11−i−iiiii−i−i1−i−iiiii−i−i1-1-11
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i-1-1-1-1-111-1−i−iiiii−i−i1ii−i−i−i−iii-111-1
χ172222222222222222222222222222222-2-2-2-200000000-2-2-2-2000000000000-2000000000000
χ18222222-2-222-2222222-2-2-2-22222-2-2-2-2-2-2222200000000-2-222000000000000-2000000000000
χ192222-2-22222-22222222222-2-2-2-222-2-2-2-222220000000022-2-2000000000000-2000000000000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2000000002222000000000000-2000000000000
χ2122-2-2002-2220-2-2-222-222-2-200002-200002i2i−2i−2i000000002i−2i0000000000000002−2i2−i22−2i2−i20000
χ2222-2-2002-2220-2-2-222-222-2-200002-200002i2i−2i−2i000000002i−2i000000000000000−22−i2i2−22−i2i20000
χ2322-2-2002-2220-2-2-222-222-2-200002-20000−2i−2i2i2i00000000−2i2i0000000000000002−2−i2i22−2−i2i20000
χ2422-2-2002-2220-2-2-222-222-2-200002-20000−2i−2i2i2i00000000−2i2i000000000000000−22i2−i2−22i2−i20000
χ2522-2-200-22220-2-2-222-2-2-2220000-2200002i2i−2i−2i00000000−2i2i000000000000000i2−i22−2−i2i2−220000
χ2622-2-200-22220-2-2-222-2-2-2220000-2200002i2i−2i−2i00000000−2i2i000000000000000−i2i2−22i2−i22−20000
χ2722-2-200-22220-2-2-222-2-2-2220000-220000−2i−2i2i2i000000002i−2i000000000000000i2−i2−22−i2i22−20000
χ2822-2-200-22220-2-2-222-2-2-2220000-220000−2i−2i2i2i000000002i−2i000000000000000−i2i22−2i2−i2−220000
χ292-2-222-2002202-2-2-2-2200002-22-20000002-22-2i2−i2i2−i2i2−i2i2−i2002-20000i2−i2i2−i2i2−i2i2−i20000000000000
χ302-2-222-2002202-2-2-2-2200002-22-20000002-22-2−i2i2−i2i2−i2i2−i2i2002-20000−i2i2−i2i2−i2i2−i2i20000000000000
χ312-2-222-2002202-2-2-2-2200002-22-2000000-22-222−22−2−22−2200-2200002−22−2−22−220000000000000
χ322-2-222-2002202-2-2-2-2200002-22-2000000-22-22−22−222−22−200-220000−22−222−22−20000000000000
χ332-2-22-22002202-2-2-2-220000-22-220000002-22-22−2−22−222−200-2200002−2−22−222−20000000000000
χ342-2-22-22002202-2-2-2-220000-22-220000002-22-2−222−22−2−2200-220000−222−22−2−220000000000000
χ352-2-22-22002202-2-2-2-220000-22-22000000-22-22i2−i2−i2i2i2−i2−i2i2002-20000i2−i2−i2i2i2−i2−i2i20000000000000
χ362-2-22-22002202-2-2-2-220000-22-22000000-22-22−i2i2i2−i2−i2i2i2−i2002-20000−i2i2i2−i2−i2i2i2−i20000000000000
χ37444444441-2411-21-2-2111111-2-2-2-211-2-200002222222200000000-1-1-1-1-1-1-1-10000000000000
χ38444444441-2411-21-2-2111111-2-2-2-211-2-20000-2-2-2-2-2-2-2-200000000111111110000000000000
χ3944444444-214-2-21-211-2-2-2-2-2-21111-2-2110000000000000000222200000000000000000-1-1-1-1
χ4044444444-214-2-21-211-2-2-2-2-2-21111-2-2110000000000000000-2-2-2-2000000000000000001111
χ41444444-4-41-2-411-21-2-2-1-1-1-111-2-222-1-12200002i2i2i2i−2i−2i−2i−2i00000000−i−i−i−iiiii0000000000000
χ42444444-4-41-2-411-21-2-2-1-1-1-111-2-222-1-1220000−2i−2i−2i−2i2i2i2i2i00000000iiii−i−i−i−i0000000000000
χ43444444-4-4-21-4-2-21-2112222-2-211-1-122-1-100000000000000002-22-200000000000000000-11-11
χ44444444-4-4-21-4-2-21-2112222-2-211-1-122-1-10000000000000000-22-22000000000000000001-11-1
χ454444-4-4441-2-411-21-2-21111-1-122-2-2-1-122000022-2-222-2-200000000-1-111-1-1110000000000000
χ464444-4-4441-2-411-21-2-21111-1-122-2-2-1-1220000-2-222-2-2220000000011-1-111-1-10000000000000
χ474444-4-444-21-4-2-21-211-2-2-2-222-1-11122-1-1000000000000000022-2-200000000000000000-1-111
χ484444-4-444-21-4-2-21-211-2-2-2-222-1-11122-1-10000000000000000-2-2220000000000000000011-1-1
χ494444-4-4-4-41-2411-21-2-2-1-1-1-1-1-1222211-2-200002i2i−2i−2i−2i−2i2i2i00000000−i−iiiii−i−i0000000000000
χ504444-4-4-4-41-2411-21-2-2-1-1-1-1-1-1222211-2-20000−2i−2i2i2i2i2i−2i−2i00000000ii−i−i−i−iii0000000000000
χ514444-4-4-4-4-214-2-21-211222222-1-1-1-1-2-21100000000000000002-2-2200000000000000000-111-1
χ524444-4-4-4-4-214-2-21-211222222-1-1-1-1-2-2110000000000000000-222-2000000000000000001-1-11
χ534-44-40000440-444-4-4-4000000000000004i−4i−4i4i0000000000000000000000000000000000000
χ544-44-40000440-444-4-4-400000000000000−4i4i4i−4i0000000000000000000000000000000000000
χ554-4-444-4001-201-12-12-23i−3i3i−3i1-1-22003i−3i0000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000−ζζ−ζζ−ζ3ζ3−ζ3ζ30000000000000
χ564-4-444-4001-201-12-12-23i−3i3i−3i1-1-22003i−3i000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000ζ−ζζ−ζζ3−ζ3ζ3−ζ30000000000000
χ574-4-444-4001-201-12-12-2−3i3i−3i3i1-1-2200−3i3i0000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000−ζ3ζ3−ζ3ζ3−ζζ−ζζ0000000000000
χ584-4-444-4001-201-12-12-2−3i3i−3i3i1-1-2200−3i3i000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000ζ3−ζ3ζ3−ζ3ζ−ζζ−ζ0000000000000
χ594-4-44-44001-201-12-12-23i−3i3i−3i-112-200−3i3i0000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000−ζζζ−ζ−ζ3ζ3ζ3−ζ30000000000000
χ604-4-44-44001-201-12-12-23i−3i3i−3i-112-200−3i3i000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000ζ−ζ−ζζζ3−ζ3−ζ3ζ30000000000000
χ614-4-44-44001-201-12-12-2−3i3i−3i3i-112-2003i−3i0000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000−ζ3ζ3ζ3−ζ3−ζζζ−ζ0000000000000
χ624-4-44-44001-201-12-12-2−3i3i−3i3i-112-2003i−3i000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000ζ3−ζ3−ζ3ζ3ζ−ζ−ζζ0000000000000
χ6388-8-8008-82-40-2-242-4422-2-20000-44000000000000000000000000000000000000000000000
χ6488-8-8008-8-42044-2-42-2-4-44400002-2000000000000000000000000000000000000000000000
χ6588-8-800-882-40-2-242-44-2-22200004-4000000000000000000000000000000000000000000000
χ6688-8-800-88-42044-2-42-244-4-40000-22000000000000000000000000000000000000000000000
χ678-88-800002-40-22-4-2446i−6i−6i6i000000000000000000000000000000000000000000000000000
χ688-88-800002-40-22-4-244−6i6i6i−6i000000000000000000000000000000000000000000000000000
χ698-88-80000-4204-424-2-20000000000006i−6i00000000000000000000000000000000000000000
χ708-88-80000-4204-424-2-2000000000000−6i6i00000000000000000000000000000000000000000
χ718-8-888-800-420-44-24-220000-442-200000000000000000000000000000000000000000000000
χ728-8-88-8800-420-44-24-2200004-4-2200000000000000000000000000000000000000000000000

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