Finite Group Databasebeta

← Group #11772460

Character table — Group #11772460

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1122222444444444444488888888889912121212121212121818181818242424242424242424242424364848484872727272
order122448833668121212122424242466121224242424242444161616161616161622488888848484848484848488242424248888
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
χ511111-1-11111-11111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-11111-1-1iiii−i−i−i−i111-1-1ii−i−i
χ611111-1-11111-11111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-111-1-111iiii−i−i−i−i1-1-111−i−iii
χ711111-1-11111-11111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-11111-1-1−i−i−i−iiiii111-1-1−i−iii
χ811111-1-11111-11111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-111-1-111−i−i−i−iiiii1-1-111ii−i−i
χ911-11-1111111-111-1-11111-1-1-11-1-111-1-11111-1-111-1-11-1-111i−ii−i11-1-111-1-1-1i−ii−ii−ii−i
χ1011-11-1111111-111-1-11111-1-1-11-1-111-1-11111-1-111-1-11-1-111−ii−ii11-1-111-1-1-1−ii−ii−ii−ii
χ1111-11-1111111-111-1-11111-1-1-11-1-111-1-111-1-111-1-1111-1-111i−ii−i-1-111-1-111-1i−ii−i−ii−ii
χ1211-11-1111111-111-1-11111-1-1-11-1-111-1-111-1-111-1-1111-1-111−ii−ii-1-111-1-111-1−ii−iii−ii−i
χ1311-11-1-1-11111111-1-1-1-1-1-1-1-1-1111-1-111-1-1ii−i−i−i−iii-11111i−i−iiii−i−i−i−iii-1i−i−ii-111-1
χ1411-11-1-1-11111111-1-1-1-1-1-1-1-1-1111-1-111-1-1ii−i−i−i−iii-11111−iii−iii−i−i−i−iii-1−iii−i1-1-11
χ1511-11-1-1-11111111-1-1-1-1-1-1-1-1-1111-1-111-1-1−i−iiiii−i−i-11111i−i−ii−i−iiiii−i−i-1i−i−ii1-1-11
χ1611-11-1-1-11111111-1-1-1-1-1-1-1-1-1111-1-111-1-1−i−iiiii−i−i-11111−iii−i−i−iiiii−i−i-1−iii−i-111-1
χ17222222222222222222222222222222-2-200000000-2-2-2-2-2000000000000-200000000
χ1822222-2-22222-22222-2-2-2-22222-2-2-2-2-2-22200000000222-2-2000000000000-200000000
χ19222-2-20022220-2-2-2-2000022-2-200000022i2−i2i2−i2i2−i2i2−i2-2-22000000i2−i2i2−i2i2−i2i2−i2000000000
χ20222-2-20022220-2-2-2-2000022-2-200000022−i2i2−i2i2−i2i2−i2i2-2-22000000−i2i2−i2i2−i2i2−i2i2000000000
χ21222-2-20022220-2-2-2-2000022-2-2000000-2-22−22−2−22−2222-20000002−22−2−22−22000000000
χ22222-2-20022220-2-2-2-2000022-2-2000000-2-2−22−222−22−222-2000000−22−222−22−2000000000
χ2322-22-2222222-222-2-22222-2-2-22-2-222-2-2-2-200000000-222-2-2000000000000200000000
χ2422-22-2-2-22222222-2-2-2-2-2-2-2-2-2222-2-22222000000002-2-2-2-2000000000000200000000
χ2522-2-220022220-2-2220000-2-22-200000022i2−i2−i2i2i2−i2−i2i2-22-2000000i2−i2−i2i2i2−i2−i2i2000000000
χ2622-2-220022220-2-2220000-2-22-200000022−i2i2i2−i2−i2i2i2−i2-22-2000000−i2i2i2−i2−i2i2i2−i2000000000
χ2722-2-220022220-2-2220000-2-22-2000000-2-22−2−22−222−22-220000002−2−22−222−2000000000
χ2822-2-220022220-2-2220000-2-22-2000000-2-2−222−22−2−222-22000000−222−22−2−22000000000
χ2944444441-21-2411-2-211111-21-211-2-2-2-20022222222000000000-1-1-1-1-1-1-1-1000000000
χ3044444441-21-2411-2-211111-21-211-2-2-2-200-2-2-2-2-2-2-2-200000000011111111000000000
χ314444444-21-214-2-211-2-2-2-2-21-21-2-211110000000000000002222000000000-1-1-1-10000
χ324444444-21-214-2-211-2-2-2-2-21-21-2-21111000000000000000-2-2-2-200000000011110000
χ3344444-4-41-21-2-411-2-2-1-1-1-11-21-2-1-12222002i2i2i2i−2i−2i−2i−2i000000000−i−i−i−iiiii000000000
χ3444444-4-41-21-2-411-2-2-1-1-1-11-21-2-1-1222200−2i−2i−2i−2i2i2i2i2i000000000iiii−i−i−i−i000000000
χ3544444-4-4-21-21-4-2-2112222-21-2122-1-1-1-100000000000000022-2-2000000000-1-1110000
χ3644444-4-4-21-21-4-2-2112222-21-2122-1-1-1-1000000000000000-2-22200000000011-1-10000
χ37444-4-4001-21-20-1-1223i3i−3i−3i1-2-123i−3i0000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000−ζζ−ζζ−ζ3ζ3−ζ3ζ3000000000
χ38444-4-4001-21-20-1-1223i3i−3i−3i1-2-123i−3i000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000ζ−ζζ−ζζ3−ζ3ζ3−ζ3000000000
χ39444-4-4001-21-20-1-122−3i−3i3i3i1-2-12−3i3i0000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000−ζ3ζ3−ζ3ζ3−ζζ−ζζ000000000
χ40444-4-4001-21-20-1-122−3i−3i3i3i1-2-12−3i3i000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000ζ3−ζ3ζ3−ζ3ζ−ζζ−ζ000000000
χ4144-44-4441-21-2-411221111-12-1-2-1-1-2-2220022-2-222-2-2000000000-1-111-1-111000000000
χ4244-44-4441-21-2-411221111-12-1-2-1-1-2-22200-2-222-2-22200000000011-1-111-1-1000000000
χ4344-44-444-21-21-4-2-2-1-1-2-2-2-22-1212211-1-10000000000000002i−2i2i−2i000000000−ii−ii0000
χ4444-44-444-21-21-4-2-2-1-1-2-2-2-22-1212211-1-1000000000000000−2i2i−2i2i000000000i−ii−i0000
χ4544-44-4-4-41-21-241122-1-1-1-1-12-1-21122-2-2002i2i−2i−2i−2i−2i2i2i000000000−i−iiiii−i−i000000000
χ4644-44-4-4-41-21-241122-1-1-1-1-12-1-21122-2-200−2i−2i2i2i2i2i−2i−2i000000000ii−i−i−i−iii000000000
χ4744-44-4-4-4-21-214-2-2-1-122222-121-2-2-1-1110000000000000002i−2i−2i2i000000000−iii−i0000
χ4844-44-4-4-4-21-214-2-2-1-122222-121-2-2-1-111000000000000000−2i2i2i−2i000000000i−i−ii0000
χ4944-4-44001-21-20-1-1-2-23i3i−3i−3i-1212−3i3i0000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000−ζζζ−ζ−ζ3ζ3ζ3−ζ3000000000
χ5044-4-44001-21-20-1-1-2-23i3i−3i−3i-1212−3i3i000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000ζ−ζ−ζζζ3−ζ3−ζ3ζ3000000000
χ5144-4-44001-21-20-1-1-2-2−3i−3i3i3i-12123i−3i0000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000−ζ3ζ3ζ3−ζ3−ζζζ−ζ000000000
χ5244-4-44001-21-20-1-1-2-2−3i−3i3i3i-12123i−3i000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000ζ3−ζ3−ζ3ζ3ζ−ζ−ζζ000000000
χ534-400022−2244-4-40000022−2222−2200000022−22004i−4i000000000002i2−2i2000000000000000000000
χ544-400022−2244-4-40000022−2222−2200000022−2200−4i4i00000000000−2i22i2000000000000000000000
χ554-4000−222244-4-400000−2222−2222000000−2222004i−4i00000000000−2i22i2000000000000000000000
χ564-4000−222244-4-400000−2222−2222000000−222200−4i4i000000000002i2−2i2000000000000000000000
χ57888-8-800-42-42044-2-20000-424-2000000000000000000000000000000000000000000
χ5888-8-8800-42-420442200004-2-4-2000000000000000000000000000000000000000000
χ598-800042−422-4-2406i−6i004ζ+2ζ3−4ζ−2ζ3−2ζ−4ζ32ζ+4ζ3000000−222200000000000000000000000000000000000000
χ608-800042−422-4-240−6i6i00−2ζ−4ζ32ζ+4ζ34ζ+2ζ3−4ζ−2ζ3000000−222200000000000000000000000000000000000000
χ618-800042−42-424-20006i−6i−2222−22220000002−23i2−3i2000000000000000000000000000000000000
χ628-800042−42-424-2000−6i6i−2222−22220000002−2−3i23i2000000000000000000000000000000000000
χ638-8000−42422-4-2406i−6i00−4ζ−2ζ34ζ+2ζ32ζ+4ζ3−2ζ−4ζ300000022−2200000000000000000000000000000000000000
χ648-8000−42422-4-240−6i6i002ζ+4ζ3−2ζ−4ζ3−4ζ−2ζ34ζ+2ζ300000022−2200000000000000000000000000000000000000
χ658-8000−4242-424-20006i−6i22−2222−22000000−22−3i23i2000000000000000000000000000000000000
χ668-8000−4242-424-2000−6i6i22−2222−22000000−223i2−3i2000000000000000000000000000000000000

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