Finite Group Databasebeta

← Group #11772543

Character table — Group #11772543

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1122222444444444444488888888889912121212121212121818181818242424242424242424242424364848484872727272
order12244883366668121224242424612121224242424242444161616161616161622488444448484848484848488121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ511111-1-1111111-111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-11111-1-1iiii−i−i−i−i111-1-1ii−i−i
χ611111-1-1111111-111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-111-1-111iiii−i−i−i−i1-1-111−i−iii
χ711111-1-1111111-111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-11111-1-1−i−i−i−iiiii111-1-1−i−iii
χ811111-1-1111111-111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-111-1-111−i−i−i−iiiii1-1-111ii−i−i
χ911-1-111111-111-1-1111111-1-1-11-1-111-1-1-1-111-1-111-1-11-11-1-1i−ii−i11-1-111-1-11i−ii−ii−ii−i
χ1011-1-111111-111-1-1111111-1-1-11-1-111-1-1-1-111-1-111-1-11-11-1-1−ii−ii11-1-111-1-11−ii−ii−ii−ii
χ1111-1-111111-111-1-1111111-1-1-11-1-111-1-1-1-1-1-111-1-1111-11-1-1i−ii−i-1-111-1-1111i−ii−i−ii−ii
χ1211-1-111111-111-1-1111111-1-1-11-1-111-1-1-1-1-1-111-1-1111-11-1-1−ii−ii-1-111-1-1111−ii−iii−ii−i
χ1311-1-11-1-111-111-1111-1-1-1-1-1-1-1111-1-11111ii−i−i−i−iii-11-1-1-1i−i−iiii−i−i−i−iii1i−i−ii-111-1
χ1411-1-11-1-111-111-1111-1-1-1-1-1-1-1111-1-11111ii−i−i−i−iii-11-1-1-1−iii−iii−i−i−i−iii1−iii−i1-1-11
χ1511-1-11-1-111-111-1111-1-1-1-1-1-1-1111-1-11111−i−iiiii−i−i-11-1-1-1i−i−ii−i−iiiii−i−i1i−i−ii1-1-11
χ1611-1-11-1-111-111-1111-1-1-1-1-1-1-1111-1-11111−i−iiiii−i−i-11-1-1-1−iii−i−i−iiiii−i−i1−iii−i-111-1
χ17222222222222222222222222222222-2-200000000-2-2-2-2-2000000000000-200000000
χ1822222-2-2222222-222-2-2-2-22222-2-2-2-2-2-22200000000222-2-2000000000000-200000000
χ19222-2-2002222220-2-200002-2-2-2000000222−22−22−22−2-2-220000002−22−22−22−2000000000
χ20222-2-2002222220-2-200002-2-2-200000022−22−22−22−22-2-22000000−22−22−22−22000000000
χ21222-2-2002222220-2-200002-2-2-2000000-2-2i2−i2i2−i2−i2i2−i2i222-2000000i2−i2i2−i2−i2i2−i2i2000000000
χ22222-2-2002222220-2-200002-2-2-2000000-2-2−i2i2−i2i2i2−i2i2−i222-2000000−i2i2−i2i2i2−i2i2−i2000000000
χ2322-22-20022-222-20-2-20000-222-200000022i2−i2−i2i2−i2i2i2−i22-2-2000000i2−i2−i2i2−i2i2i2−i2000000000
χ2422-22-20022-222-20-2-20000-222-200000022−i2i2i2−i2i2−i2−i2i22-2-2000000−i2i2i2−i2i2−i2−i2i2000000000
χ2522-22-20022-222-20-2-20000-222-2000000-2-22−2−222−2−22-2220000002−2−222−2−22000000000
χ2622-22-20022-222-20-2-20000-222-2000000-2-2−222−2−222−2-222000000−222−2−222−2000000000
χ2722-2-222222-222-2-2222222-2-2-22-2-222-2-22200000000-22-222000000000000-200000000
χ2822-2-22-2-222-222-2222-2-2-2-2-2-2-2222-2-222-2-2000000002-2222000000000000-200000000
χ2944444441-211-214-2-2-2-2-2-2-21-21-2-211110000000000000002222000000000-1-1-1-10000
χ3044444441-211-214-2-2-2-2-2-2-21-21-2-21111000000000000000-2-2-2-200000000011110000
χ314444444-21-2-21-241111111-21-211-2-2-2-20022222222000000000-1-1-1-1-1-1-1-1000000000
χ324444444-21-2-21-241111111-21-211-2-2-2-200-2-2-2-2-2-2-2-200000000011111111000000000
χ3344444-4-41-211-21-4-2-22222-21-2122-1-1-1-100000000000000022-2-2000000000-1-1110000
χ3444444-4-41-211-21-4-2-22222-21-2122-1-1-1-1000000000000000-2-22200000000011-1-10000
χ3544444-4-4-21-2-21-2-411-1-1-1-11-21-2-1-12222002i2i2i2i−2i−2i−2i−2i000000000−i−i−i−iiiii000000000
χ3644444-4-4-21-2-21-2-411-1-1-1-11-21-2-1-1222200−2i−2i−2i−2i2i2i2i2i000000000iiii−i−i−i−i000000000
χ37444-4-400-21-2-21-20-1-13i3i−3i−3i12-123i−3i0000002ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3000000000−ζζ−ζζζ3−ζ3ζ3−ζ3000000000
χ38444-4-400-21-2-21-20-1-13i3i−3i−3i12-123i−3i000000−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ3000000000ζ−ζζ−ζ−ζ3ζ3−ζ3ζ3000000000
χ39444-4-400-21-2-21-20-1-1−3i−3i3i3i12-12−3i3i0000002ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ000000000−ζ3ζ3−ζ3ζ3ζ−ζζ−ζ000000000
χ40444-4-400-21-2-21-20-1-1−3i−3i3i3i12-12−3i3i000000−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ000000000ζ3−ζ3ζ3−ζ3−ζζ−ζζ000000000
χ4144-44-400-212-2120-1-13i3i−3i−3i-1-212−3i3i0000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000−ζζζ−ζζ3−ζ3−ζ3ζ3000000000
χ4244-44-400-212-2120-1-13i3i−3i−3i-1-212−3i3i000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000ζ−ζ−ζζ−ζ3ζ3ζ3−ζ3000000000
χ4344-44-400-212-2120-1-1−3i−3i3i3i-1-2123i−3i0000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000−ζ3ζ3ζ3−ζ3ζ−ζ−ζζ000000000
χ4444-44-400-212-2120-1-1−3i−3i3i3i-1-2123i−3i000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000ζ3−ζ3−ζ3ζ3−ζζζ−ζ000000000
χ4544-4-44441-2-11-2-1-4-2-2-2-2-2-22-1212211-1-10000000000000002i−2i2i−2i000000000−ii−ii0000
χ4644-4-44441-2-11-2-1-4-2-2-2-2-2-22-1212211-1-1000000000000000−2i2i−2i2i000000000i−ii−i0000
χ4744-4-4444-212-212-4111111-12-1-2-1-1-2-2220022-2-222-2-2000000000-1-111-1-111000000000
χ4844-4-4444-212-212-4111111-12-1-2-1-1-2-22200-2-222-2-22200000000011-1-111-1-1000000000
χ4944-4-44-4-41-2-11-2-14-2-222222-121-2-2-1-1110000000000000002i−2i−2i2i000000000−iii−i0000
χ5044-4-44-4-41-2-11-2-14-2-222222-121-2-2-1-111000000000000000−2i2i2i−2i000000000i−i−ii0000
χ5144-4-44-4-4-212-212411-1-1-1-1-12-1-21122-2-2002i2i−2i−2i−2i−2i2i2i000000000−i−iiiii−i−i000000000
χ5244-4-44-4-4-212-212411-1-1-1-1-12-1-21122-2-200−2i−2i2i2i2i2i−2i−2i000000000ii−i−i−i−iii000000000
χ534-400022−22440-4-4000022−2222−2200000022−22004i−4i000000000002i2−2i2000000000000000000000
χ544-400022−22440-4-4000022−2222−2200000022−2200−4i4i00000000000−2i22i2000000000000000000000
χ554-4000−2222440-4-40000−2222−2222000000−2222004i−4i00000000000−2i22i2000000000000000000000
χ564-4000−2222440-4-40000−2222−2222000000−222200−4i4i000000000002i2−2i2000000000000000000000
χ57888-8-8002-422-420440000-4-24-2000000000000000000000000000000000000000000
χ5888-88-8002-4-22-4-2044000042-4-2000000000000000000000000000000000000000000
χ598-800042−422-46-24-6000−2222−22220000002−232−32000000000000000000000000000000000000
χ608-800042−422-4-6-246000−2222−22220000002−2−3232000000000000000000000000000000000000
χ618-800042−42-4204-2006i−6i4ζ+2ζ3−4ζ−2ζ3−2ζ−4ζ32ζ+4ζ3000000−222200000000000000000000000000000000000000
χ628-800042−42-4204-200−6i6i−2ζ−4ζ32ζ+4ζ34ζ+2ζ3−4ζ−2ζ3000000−222200000000000000000000000000000000000000
χ638-8000−42422-46-24-600022−2222−22000000−22−3232000000000000000000000000000000000000
χ648-8000−42422-4-6-24600022−2222−22000000−2232−32000000000000000000000000000000000000
χ658-8000−4242-4204-2006i−6i−4ζ−2ζ34ζ+2ζ32ζ+4ζ3−2ζ−4ζ300000022−2200000000000000000000000000000000000000
χ668-8000−4242-4204-200−6i6i2ζ+4ζ3−2ζ−4ζ3−4ζ−2ζ34ζ+2ζ300000022−2200000000000000000000000000000000000000

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