Finite Group Databasebeta

← Group #11788358

Character table — Group #11788358

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222444444444444488888888881818181818182424242424242424242424242424242436363636363636363648484848
order1222224433466666612121212666612121212121222444444448888242424242424242428888888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ5111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-11-1ii−i−iiiii−i−i−i−i1iiii−i−i−i−i1-11-1
χ6111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-11-1−i−iii−i−i−i−iiiii1−i−i−i−iiiii1-11-1
χ7111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-11-11ii−i−iiiii−i−i−i−i1−i−i−i−iiiii-11-11
χ8111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-11-11−i−iii−i−i−i−iiiii1iiii−i−i−i−i-11-11
χ91111-1-11111-11111111111-1-1-1-1-1-111-1-1111-1-1111-1-11-11-111-1-111-1-1-111-1-111-1-111-1-1
χ101111-1-11111-11111111111-1-1-1-1-1-111-1-1111-1-1111-1-1-11-11-1-111-1-111-1-1-111-1-11111-1-1
χ111111-1-11111-11111111111-1-1-1-1-1-111-1-1111-1-11-1-1111-11-111-1-111-1-1-1-1-111-1-111-1-111
χ121111-1-11111-11111111111-1-1-1-1-1-111-1-1111-1-11-1-111-11-11-1-111-1-111-111-1-111-1-1-1-111
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-11111-111-11-1-11i−i−iiii−i−i−i−iii-1ii−i−i−i−iii1-1-11
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-11111-111-11-1-11−iii−i−i−iiiii−i−i-1−i−iiiii−i−i1-1-11
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-11111-111-1-111-1i−i−iiii−i−i−i−iii-1−i−iiiii−i−i-111-1
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-11111-111-1-111-1−iii−i−i−iiiii−i−i-1ii−i−i−i−iii-111-1
χ172222222222222222222222222222222-2-2-2-2-2-20000000000000000-2000000000000
χ18222222-2-222-2222222-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000-2000000000000
χ192222-2-22222-22222222222-2-2-2-2-2-222-2-2-2-2-222-200000000000000002000000000000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-222-2-222-2-22-2-2200000000000000002000000000000
χ212-2-22002-2220-2-2-22-2222-2-20000002-2002-2200-2000000000000000002i−2i002i−2i000000
χ222-2-22002-2220-2-2-22-2222-2-20000002-2002-2200-200000000000000000−2i2i00−2i2i000000
χ232-2-22002-2220-2-2-22-2222-2-20000002-200-22-200200000000000000000002-2002-20000
χ242-2-22002-2220-2-2-22-2222-2-20000002-200-22-20020000000000000000000-2200-220000
χ252-2-2200-22220-2-2-22-22-2-222000000-22002-2-2002000000000000000002-200-22000000
χ262-2-2200-22220-2-2-22-22-2-222000000-22002-2-200200000000000000000-22002-2000000
χ272-2-2200-22220-2-2-22-22-2-222000000-2200-22200-200000000000000000002i−2i00−2i2i0000
χ282-2-2200-22220-2-2-22-22-2-222000000-2200-22200-20000000000000000000−2i2i002i−2i0000
χ29444444441-2411-21-2-2111111-2-211-2-2-2-200000000002222-1-1-1-1-1-1-1-10000000000000
χ30444444441-2411-21-2-2111111-2-211-2-2-2-20000000000-2-2-2-2111111110000000000000
χ3144444444-214-2-21-211-2-2-2-2-2-211-2-211110000002222000000000000000000000-1-1-1-1
χ3244444444-214-2-21-211-2-2-2-2-2-211-2-21111000000-2-2-2-20000000000000000000001111
χ33444444-4-41-2-411-21-2-2-1-1-1-111-2-2-1-1222200000000002i2i−2i−2i−i−i−i−iiiii0000000000000
χ34444444-4-41-2-411-21-2-2-1-1-1-111-2-2-1-122220000000000−2i−2i2i2iiiii−i−i−i−i0000000000000
χ35444444-4-4-21-4-2-21-2112222-2-21122-1-1-1-10000002-22-2000000000000000000000-11-11
χ36444444-4-4-21-4-2-21-2112222-2-21122-1-1-1-1000000-22-220000000000000000000001-11-1
χ374444-4-4441-2-411-21-2-21111-1-122-1-1-2-22200000000002-22-2-1-111-1-1110000000000000
χ384444-4-4441-2-411-21-2-21111-1-122-1-1-2-2220000000000-22-2211-1-111-1-10000000000000
χ394444-4-444-21-4-2-21-211-2-2-2-222-1-12211-1-100000022-2-2000000000000000000000-1-111
χ404444-4-444-21-4-2-21-211-2-2-2-222-1-12211-1-1000000-2-22200000000000000000000011-1-1
χ414444-4-4-4-41-2411-21-2-2-1-1-1-1-1-1221122-2-200000000002i−2i−2i2i−i−iiiii−i−i0000000000000
χ424444-4-4-4-41-2411-21-2-2-1-1-1-1-1-1221122-2-20000000000−2i2i2i−2iii−i−i−i−iii0000000000000
χ434444-4-4-4-4-214-2-21-211222222-1-1-2-2-1-1110000002-2-22000000000000000000000-111-1
χ444444-4-4-4-4-214-2-21-211222222-1-1-2-2-1-111000000-222-20000000000000000000001-1-11
χ4544-4-44-4001-201-1-2-1223i−3i3i−3i1-12-23i−3i000000000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000
χ4644-4-44-4001-201-1-2-1223i−3i3i−3i1-12-23i−3i000000000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000
χ4744-4-44-4001-201-1-2-122−3i3i−3i3i1-12-2−3i3i000000000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000
χ4844-4-44-4001-201-1-2-122−3i3i−3i3i1-12-2−3i3i000000000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000
χ4944-4-44-4004404-44-4-4-400004-4-4400000000000000000000000000000000000000000
χ5044-4-4-44001-201-1-2-1223i−3i3i−3i-11-22−3i3i000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000000
χ5144-4-4-44001-201-1-2-1223i−3i3i−3i-11-22−3i3i000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000000
χ5244-4-4-44001-201-1-2-122−3i3i−3i3i-11-223i−3i000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000
χ5344-4-4-44001-201-1-2-122−3i3i−3i3i-11-223i−3i000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000
χ5444-4-4-44004404-44-4-4-40000-444-400000000000000000000000000000000000000000
χ554-44-40000440-44-4-44-4000000000000000004i−4i000000000000000000000000000000
χ564-44-40000440-44-4-44-400000000000000000−4i4i000000000000000000000000000000
χ5788-8-88-800-420-4424-2-20000-44-2200000000000000000000000000000000000000000
χ5888-8-8-8800-420-4424-2-200004-42-200000000000000000000000000000000000000000
χ598-88-800002-40-224-2-446i−6i−6i6i000000000000000000000000000000000000000000000
χ608-88-800002-40-224-2-44−6i6i6i−6i000000000000000000000000000000000000000000000
χ618-88-80000-4204-4-242-20000000000006i−6i00000000000000000000000000000000000
χ628-88-80000-4204-4-242-2000000000000−6i6i00000000000000000000000000000000000
χ638-8-88008-82-40-2-2424-422-2-2000000-440000000000000000000000000000000000000
χ648-8-88008-8-42044-2-4-22-4-4440000002-20000000000000000000000000000000000000
χ658-8-8800-882-40-2-2424-4-2-2220000004-40000000000000000000000000000000000000
χ668-8-8800-88-42044-2-4-2244-4-4000000-220000000000000000000000000000000000000

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