Finite Group Databasebeta

← Group #11774409

Character table — Group #11774409

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222244444444444448888888888999912121212121212121818181824242424242424242424242436363636363636363648484848
order1222224433466666612121212666612121212121244448888888844444444242424242424242448888888812121212
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−i-1-1111-11-1iiii−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−i-1-111-11-11iiii−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−iiiii-1-1111-11-1−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−iiiii-1-111-11-11−i−i−i−iiiii1iiii−i−i−i−i-11-11
χ91111-1-11111-11111111111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1111-1-1111-1-111-1-1-111-1-111-1-1-111-1
χ101111-1-11111-11111111111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-111-111-111-1-111-1-1-1-1-111-1-1111-1-11
χ111111-1-11111-11111111111-1-1-1-1-1-111-1-11111-1-111-1-111-1-1111-1-11-1-111-1-111-1-1-111-1-111-111-1
χ121111-1-11111-11111111111-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-111-1-1-111-1-111-111-1-111-1-11-1-11
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1ii−i−i−i−iii111111-1-1ii−i−i−i−iii-1ii−i−i−i−iii-1-111
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1ii−i−i−i−iii1111-1-111ii−i−i−i−iii-1−i−iiiii−i−i11-1-1
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1−i−iiiii−i−i111111-1-1−i−iiiii−i−i-1−i−iiiii−i−i-1-111
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1−i−iiiii−i−i1111-1-111−i−iiiii−i−i-1ii−i−i−i−iii11-1-1
χ172222222222222222222222222222222-2-2-2-200000000-2-2-2-2000000000000-2000000000000
χ18222222-2-222-2222222-2-2-2-22222-2-2-2-2-2-222220000000022-2-2000000000000-2000000000000
χ192222-2-22222-22222222222-2-2-2-2-2-222-2-2-2-2-2-20000000022-2-20000000000002000000000000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-222-2-222222200000000-2-2-2-20000000000002000000000000
χ212-22-22-20022022-2-2-2-2000022-2-200000022-2-22−22−22−22−22-20000002−22−22−22−20000000000000
χ222-22-22-20022022-2-2-2-2000022-2-200000022-2-2−22−22−22−222-2000000−22−22−22−220000000000000
χ232-22-22-20022022-2-2-2-2000022-2-2000000-2-222i2−i2i2−i2−i2i2−i2i2-22000000i2−i2i2−i2−i2i2−i2i20000000000000
χ242-22-22-20022022-2-2-2-2000022-2-2000000-2-222−i2i2−i2i2i2−i2i2−i2-22000000−i2i2−i2i2i2−i2i2−i20000000000000
χ252-22-2-220022022-2-2-2-20000-2-22200000022-2-22−2−222−2−22-220000002−2−222−2−220000000000000
χ262-22-2-220022022-2-2-2-20000-2-22200000022-2-2−222−2−222−2-22000000−222−2−222−20000000000000
χ272-22-2-220022022-2-2-2-20000-2-222000000-2-222i2−i2−i2i2−i2i2i2−i22-2000000i2−i2−i2i2−i2i2i2−i20000000000000
χ282-22-2-220022022-2-2-2-20000-2-222000000-2-222−i2i2i2−i2i2−i2−i2i22-2000000−i2i2i2−i2i2−i2−i2i20000000000000
χ292-2-22002i−2i220-2-22-22-22i2i−2i−2i0000002i−2i002i−2i2i−2i00000000002-20000000000000002ζ−2ζ002ζ3−2ζ30000
χ302-2-22002i−2i220-2-22-22-22i2i−2i−2i0000002i−2i002i−2i2i−2i00000000002-2000000000000000−2ζ2ζ00−2ζ32ζ30000
χ312-2-22002i−2i220-2-22-22-22i2i−2i−2i0000002i−2i00−2i2i−2i2i0000000000-2200000000000002ζ3−2ζ3002ζ−2ζ000000
χ322-2-22002i−2i220-2-22-22-22i2i−2i−2i0000002i−2i00−2i2i−2i2i0000000000-220000000000000−2ζ32ζ300−2ζ2ζ000000
χ332-2-2200−2i2i220-2-22-22-2−2i−2i2i2i000000−2i2i002i−2i2i−2i0000000000-2200000000000002ζ−2ζ002ζ3−2ζ3000000
χ342-2-2200−2i2i220-2-22-22-2−2i−2i2i2i000000−2i2i002i−2i2i−2i0000000000-220000000000000−2ζ2ζ00−2ζ32ζ3000000
χ352-2-2200−2i2i220-2-22-22-2−2i−2i2i2i000000−2i2i00−2i2i−2i2i00000000002-20000000000000002ζ3−2ζ3002ζ−2ζ0000
χ362-2-2200−2i2i220-2-22-22-2−2i−2i2i2i000000−2i2i00−2i2i−2i2i00000000002-2000000000000000−2ζ32ζ300−2ζ2ζ0000
χ37444444441-241-211-2-211111-21-211-2-2-2-200002222222200000000-1-1-1-1-1-1-1-10000000000000
χ38444444441-241-211-2-211111-21-211-2-2-2-20000-2-2-2-2-2-2-2-200000000111111110000000000000
χ3944444444-214-21-2-211-2-2-2-2-21-21-2-211110000000000000000222200000000000000000-1-1-1-1
χ4044444444-214-21-2-211-2-2-2-2-21-21-2-211110000000000000000-2-2-2-2000000000000000001111
χ41444444-4-41-2-41-211-2-2-1-1-1-11-21-2-1-1222200002i2i2i2i−2i−2i−2i−2i00000000−i−i−i−iiiii0000000000000
χ42444444-4-41-2-41-211-2-2-1-1-1-11-21-2-1-122220000−2i−2i−2i−2i2i2i2i2i00000000iiii−i−i−i−i0000000000000
χ43444444-4-4-21-4-21-2-2112222-21-2122-1-1-1-100000000000000002-22-200000000000000000-11-11
χ44444444-4-4-21-4-21-2-2112222-21-2122-1-1-1-10000000000000000-22-22000000000000000001-11-1
χ454444-4-4441-2-41-211-2-21111-12-12-1-1-2-222000022-2-222-2-200000000-1-111-1-1110000000000000
χ464444-4-4441-2-41-211-2-21111-12-12-1-1-2-2220000-2-222-2-2220000000011-1-111-1-10000000000000
χ474444-4-444-21-4-21-2-211-2-2-2-22-12-12211-1-100000000000000002-2-22000000000000000001-1-11
χ484444-4-444-21-4-21-2-211-2-2-2-22-12-12211-1-10000000000000000-222-200000000000000000-111-1
χ494444-4-4-4-41-241-211-2-2-1-1-1-1-12-121122-2-200002i2i−2i−2i−2i−2i2i2i00000000−i−iiiii−i−i0000000000000
χ504444-4-4-4-41-241-211-2-2-1-1-1-1-12-121122-2-20000−2i−2i2i2i2i2i−2i−2i00000000ii−i−i−i−iii0000000000000
χ514444-4-4-4-4-214-21-2-21122222-12-1-2-2-1-111000000000000000022-2-20000000000000000011-1-1
χ524444-4-4-4-4-214-21-2-21122222-12-1-2-2-1-1110000000000000000-2-22200000000000000000-1-111
χ5344-4-40000440-4-4-44-44000000000000004i−4i−4i4i0000000000000000000000000000000000000
χ5444-4-40000440-4-4-44-4400000000000000−4i4i4i−4i0000000000000000000000000000000000000
χ554-44-44-4001-201-2-1-1223i−3i3i−3i1-2-123i−3i000000002ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ300000000−ζζ−ζζζ3−ζ3ζ3−ζ30000000000000
χ564-44-44-4001-201-2-1-1223i−3i3i−3i1-2-123i−3i00000000−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ300000000ζ−ζζ−ζ−ζ3ζ3−ζ3ζ30000000000000
χ574-44-44-4001-201-2-1-122−3i3i−3i3i1-2-12−3i3i000000002ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ00000000−ζ3ζ3−ζ3ζ3ζ−ζζ−ζ0000000000000
χ584-44-44-4001-201-2-1-122−3i3i−3i3i1-2-12−3i3i00000000−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ00000000ζ3−ζ3ζ3−ζ3−ζζ−ζζ0000000000000
χ594-44-4-44001-201-2-1-1223i−3i3i−3i-121-2−3i3i000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000−ζζζ−ζζ3−ζ3−ζ3ζ30000000000000
χ604-44-4-44001-201-2-1-1223i−3i3i−3i-121-2−3i3i00000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000ζ−ζ−ζζ−ζ3ζ3ζ3−ζ30000000000000
χ614-44-4-44001-201-2-1-122−3i3i−3i3i-121-23i−3i000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000−ζ3ζ3ζ3−ζ3ζ−ζ−ζζ0000000000000
χ624-44-4-44001-201-2-1-122−3i3i−3i3i-121-23i−3i00000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000ζ3−ζ3−ζ3ζ3−ζζζ−ζ0000000000000
χ6388-8-800002-40-24-224-46-6-66000000000000000000000000000000000000000000000000000
χ6488-8-800002-40-24-224-4-666-6000000000000000000000000000000000000000000000000000
χ6588-8-80000-4204-24-4-220000000000006-600000000000000000000000000000000000000000
χ6688-8-80000-4204-24-4-22000000000000-6600000000000000000000000000000000000000000
χ678-88-88-800-420-4244-2-20000-424-200000000000000000000000000000000000000000000000
χ688-88-8-8800-420-4244-2-200004-2-4200000000000000000000000000000000000000000000000
χ698-8-88008i−8i2-40-242-2-442i2i−2i−2i000000−4i4i0000000000000000000000000000000000000000000
χ708-8-88008i−8i-4204-2-442-2−4i−4i4i4i0000002i−2i0000000000000000000000000000000000000000000
χ718-8-8800−8i8i2-40-242-2-44−2i−2i2i2i0000004i−4i0000000000000000000000000000000000000000000
χ728-8-8800−8i8i-4204-2-442-24i4i−4i−4i000000−2i2i0000000000000000000000000000000000000000000

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