Finite Group Databasebeta

← Group #11771248

Character table — Group #11771248

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111224444444444444444448888888888888888888888888818181818363672727272727272727272
order1222442334666666121212121212121266668812121212242424242424242424242424242424242244244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1ii−i−i-1-1ii−i−i
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1−i−iii-1-1−i−iii
χ51111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ71111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i11−i−iii
χ81111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii11ii−i−i
χ91111-1-1111-1111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11-11-11-1i−ii−ii−i
χ101111-1-1111-1111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11-1-11-11i−i−ii−ii
χ111111-1-1111-1111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-11i−i−ii−ii-111-1
χ121111-1-1111-1111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-11−iii−i−ii1-1-11
χ131111-1-1111-1111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11-11-11-1−ii−ii−ii
χ141111-1-1111-1111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11-1-11-11−iii−ii−i
χ151111-1-1111-1111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-11i−i−iii−i1-1-11
χ161111-1-1111-1111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-11−iii−ii−i-111-1
χ17222222-222-222222222222222-2-2-2-200-2-2-2-2000000000000000022-2-2-220000000000
χ18222222-222-222222222222222-2-2-2-200-2-2-2-20000000000000000-2-2222-20000000000
χ192222-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-200222200000000000000002222-2-20000000000
χ202222-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-20022220000000000000000-2-2-2-2220000000000
χ2144444441-2411-2-21-21111-2-2-2-211-2-24411-2-21111-2-2-2-21111-2-2-2-20000000000000000
χ2244444441-2411-2-21-21111-2-2-2-211-2-2-4-411-2-2-1-1-1-12222-1-1-1-122220000000000000000
χ234444444-214-2-211-21-2-2-2-21111-2-21144-2-211-2-2-2-21111-2-2-2-211110000000000000000
χ244444444-214-2-211-21-2-2-2-21111-2-211-4-4-2-2112222-1-1-1-12222-1-1-1-10000000000000000
χ25444444-41-2-411-2-21-21111-2-2-2-2-1-12200-1-12233-3-3000033-3-300000000000000000000
χ26444444-41-2-411-2-21-21111-2-2-2-2-1-12200-1-122-3-3330000-3-33300000000000000000000
χ27444444-4-21-4-2-211-21-2-2-2-2111122-1-10022-1-1000033-3-3000033-3-30000000000000000
χ28444444-4-21-4-2-211-21-2-2-2-2111122-1-10022-1-10000-3-3330000-3-3330000000000000000
χ294444-4-441-2-411-2-21-2-1-1-1-1222211-2-24i−4i-1-122iiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i0000000000000000
χ304444-4-441-2-411-2-21-2-1-1-1-1222211-2-2−4i4i-1-122−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i0000000000000000
χ314444-4-44-21-4-2-211-212222-1-1-1-1-2-2114i−4i22-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000
χ324444-4-44-21-4-2-211-212222-1-1-1-1-2-211−4i4i22-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000
χ334444-4-4-41-2411-2-21-2-1-1-1-12222-1-1220011-2-23i3i−3i−3i0000−3i−3i3i3i00000000000000000000
χ344444-4-4-41-2411-2-21-2-1-1-1-12222-1-1220011-2-2−3i−3i3i3i00003i3i−3i−3i00000000000000000000
χ354444-4-4-4-214-2-211-212222-1-1-1-122-1-100-2-21100003i3i−3i−3i0000−3i−3i3i3i0000000000000000
χ364444-4-4-4-214-2-211-212222-1-1-1-122-1-100-2-2110000−3i−3i3i3i00003i3i−3i−3i0000000000000000
χ3744-4-40004404-44-4-4-40000000000000000000000000000000000004i−4i000000000000
χ3844-4-40004404-44-4-4-4000000000000000000000000000000000000−4i4i000000000000
χ394-44-44i−4i01-20-112-2-12ii−i−i2i2i−2i−2i3-300003i−3i00−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300−2ζ7+2ζ232ζ7−2ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13002ζ5−2ζ13−2ζ5+2ζ130000000000000000
χ404-44-44i−4i01-20-112-2-12ii−i−i2i2i−2i−2i3-300003i−3i00ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23002ζ7−2ζ23−2ζ7+2ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300−2ζ5+2ζ132ζ5−2ζ130000000000000000
χ414-44-44i−4i01-20-112-2-12ii−i−i2i2i−2i−2i-330000−3i3i00−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−2ζ7+2ζ232ζ7−2ζ2300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ132ζ5−2ζ13−2ζ5+2ζ13000000000000000000
χ424-44-44i−4i01-20-112-2-12ii−i−i2i2i−2i−2i-330000−3i3i00ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ232ζ7−2ζ23−2ζ7+2ζ2300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−2ζ5+2ζ132ζ5−2ζ13000000000000000000
χ434-44-44i−4i0440-44-44-4-44i4i−4i−4i−4i−4i4i4i000000000000000000000000000000000000000000
χ444-44-44i−4i0-2102-2-112-1−2i−2i2i2i−i−iii003-300003i−3i00−2ζ7+2ζ232ζ7−2ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23002ζ5−2ζ13−2ζ5+2ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ454-44-44i−4i0-2102-2-112-1−2i−2i2i2i−i−iii003-300003i−3i002ζ7−2ζ23−2ζ7+2ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300−2ζ5+2ζ132ζ5−2ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ464-44-44i−4i0-2102-2-112-1−2i−2i2i2i−i−iii00-330000−3i3i−2ζ7+2ζ232ζ7−2ζ2300ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ232ζ5−2ζ13−2ζ5+2ζ1300−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ474-44-44i−4i0-2102-2-112-1−2i−2i2i2i−i−iii00-330000−3i3i2ζ7−2ζ23−2ζ7+2ζ2300−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−2ζ5+2ζ132ζ5−2ζ1300ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ484-44-4−4i4i01-20-112-2-12−i−iii−2i−2i2i2i3-30000−3i3i00ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13002ζ5−2ζ13−2ζ5+2ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300−2ζ7+2ζ232ζ7−2ζ230000000000000000
χ494-44-4−4i4i01-20-112-2-12−i−iii−2i−2i2i2i3-30000−3i3i00−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300−2ζ5+2ζ132ζ5−2ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23002ζ7−2ζ23−2ζ7+2ζ230000000000000000
χ504-44-4−4i4i01-20-112-2-12−i−iii−2i−2i2i2i-3300003i−3i00ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ132ζ5−2ζ13−2ζ5+2ζ1300−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−2ζ7+2ζ232ζ7−2ζ23000000000000000000
χ514-44-4−4i4i01-20-112-2-12−i−iii−2i−2i2i2i-3300003i−3i00−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−2ζ5+2ζ132ζ5−2ζ1300ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ232ζ7−2ζ23−2ζ7+2ζ23000000000000000000
χ524-44-4−4i4i0440-44-44-4-4−4i−4i4i4i4i4i−4i−4i000000000000000000000000000000000000000000
χ534-44-4−4i4i0-2102-2-112-12i2i−2i−2iii−i−i003-30000−3i3i002ζ5−2ζ13−2ζ5+2ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300−2ζ7+2ζ232ζ7−2ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ544-44-4−4i4i0-2102-2-112-12i2i−2i−2iii−i−i003-30000−3i3i00−2ζ5+2ζ132ζ5−2ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13002ζ7−2ζ23−2ζ7+2ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000000000
χ554-44-4−4i4i0-2102-2-112-12i2i−2i−2iii−i−i00-3300003i−3i2ζ5−2ζ13−2ζ5+2ζ1300−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−2ζ7+2ζ232ζ7−2ζ2300ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ564-44-4−4i4i0-2102-2-112-12i2i−2i−2iii−i−i00-3300003i−3i−2ζ5+2ζ132ζ5−2ζ1300ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ132ζ7−2ζ23−2ζ7+2ζ2300−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000000
χ574-4-44000440-4-4-4-44400000000000000000000000000000000004-400000000000000
χ584-4-44000440-4-4-4-4440000000000000000000000000000000000-4400000000000000
χ5988-8-80002-402-2-44-246i−6i6i−6i0000000000000000000000000000000000000000000000
χ6088-8-80002-402-2-44-24−6i6i−6i6i0000000000000000000000000000000000000000000000
χ6188-8-8000-420-442-24-200006i−6i6i−6i000000000000000000000000000000000000000000
χ6288-8-8000-420-442-24-20000−6i6i−6i6i000000000000000000000000000000000000000000
χ638-8-880002-40-2-2442-46-6-660000000000000000000000000000000000000000000000
χ648-8-880002-40-2-2442-4-666-60000000000000000000000000000000000000000000000
χ658-8-88000-42044-2-2-4200006-6-66000000000000000000000000000000000000000000
χ668-8-88000-42044-2-2-420000-666-6000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.