Finite Group Databasebeta

← Group #11872761

Character table — Group #11872761

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222224444444444444444444488888888888888888888888121212121212121218181818242424242424242424242424363636364848484872
order1222334466666634466688121212121212121212121212812121212121224242424242424242424242424242424222244444444224466661212121224886612128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ511111111111111111111-1-1111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1
χ611111111111111111111-1-1111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1111
χ711111111111111111111-1-1111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-11
χ811111111111111111111-1-1111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1
χ9111111111111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-11111-1-1-1-111-1-11-11-11
χ10111111111111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-11-1-111-1-111-1-1111-1-11-1
χ11111111111111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-111-111-1-111-1-1-1-111-111-1-1
χ12111111111111111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-1-1-1111111-1-1-11-111
χ13111111111111111-1-1111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-111111-1-1-1-11111-11-11-1
χ14111111111111111-1-1111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-111-1-1-111-1-111-1-1-1-1-111-11
χ15111111111111111-1-1111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111111-1-1111-1-111-1-1-1-1-1-11-1-111
χ16111111111111111-1-1111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-11-1-1-1-1-1111111111-11-1-1
χ17222222-2-222222222-222200-2-222-2-2-2-2-2-2-2-20-2222-2-200000000000000000000000022-2-20000000000002-20000000
χ18222222-2-222222222-222200-2-222-2-2-2-2-2-2-2-20-2222-2-2000000000000000000000000-2-222000000000000-220000000
χ19222222-2-22222222-2222200-2-2-2-222-2-2-2-2-2-202-2-2-22200000000000000000000000022-2-2000000000000-220000000
χ20222222-2-22222222-2222200-2-2-2-222-2-2-2-2-2-202-2-2-222000000000000000000000000-2-2220000000000002-20000000
χ2122222-1222-1-12-12-122-1-1-1222-1-1-122-1-12-1-1-12-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1220022000000220000-1-1-1-1000000-1-1000
χ2222222-1222-1-12-12-122-1-1-1222-1-1-122-1-12-1-1-12-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-2000000-2-20000111100000011000
χ2322222-1222-1-12-12-122-1-1-1-2-22-1-1-122-1-12-1-1-1-2-12-1-1-1-1-2-2111111-2-2111111220022000000-2-20000-1-1-1-100000011000
χ2422222-1222-1-12-12-122-1-1-1-2-22-1-1-122-1-12-1-1-1-2-12-1-1-1-1-2-2111111-2-2111111-2-200-2-20000002200001111000000-1-1000
χ2522222-1222-1-12-12-1-2-2-1-1-1222-111-2-2-1-12-1-1-1-21-2111122-1-1-1-1-1-1-2-21111112200-2-20000002-20000-1-111000000-11000
χ2622222-1222-1-12-12-1-2-2-1-1-1222-111-2-2-1-12-1-1-1-21-2111122-1-1-1-1-1-1-2-2111111-2-20022000000-22000011-1-10000001-1000
χ2722222-1222-1-12-12-1-2-2-1-1-1-2-22-111-2-2-1-12-1-1-121-21111-2-211111122-1-1-1-1-1-12200-2-2000000-220000-1-1110000001-1000
χ2822222-1222-1-12-12-1-2-2-1-1-1-2-22-111-2-2-1-12-1-1-121-21111-2-211111122-1-1-1-1-1-1-2-200220000002-2000011-1-1000000-11000
χ292222-1222-122-12-1-122-1-1-122-1222-1-1-1-1-12-1-122-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10022002200000022-1-10000-1-1000000-1-10
χ302222-1222-122-12-1-122-1-1-122-1222-1-1-1-1-12-1-122-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100-2-200-2-2000000-2-211000011000000110
χ312222-1222-122-12-1-122-1-1-1-2-2-1222-1-1-1-1-12-1-1-22-1-1-1-1-111-2-2111111-2-2111100220022000000-2-2-1-10000-1-1000000110
χ322222-1222-122-12-1-122-1-1-1-2-2-1222-1-1-1-1-12-1-1-22-1-1-1-1-111-2-2111111-2-2111100-2-200-2-20000002211000011000000-1-10
χ332222-1222-122-12-1-1-2-2-1-1-122-12-2-211-1-1-12-1-1-2-211111-1-122-1-1-1-111-2-21111002200-2-20000002-2-1-1000011000000-110
χ342222-1222-122-12-1-1-2-2-1-1-122-12-2-211-1-1-12-1-1-2-211111-1-122-1-1-1-111-2-2111100-2-20022000000-22110000-1-10000001-10
χ352222-1222-122-12-1-1-2-2-1-1-1-2-2-12-2-211-1-1-12-1-12-21111111-2-21111-1-122-1-1-1-1002200-2-2000000-22-1-10000110000001-10
χ362222-1222-122-12-1-1-2-2-1-1-1-2-2-12-2-211-1-1-12-1-12-21111111-2-21111-1-122-1-1-1-100-2-200220000002-2110000-1-1000000-110
χ3722-2-2222-222-2-2-2-22002-2-200-2-20000-2-22222000000000000000000000002-200002i−2i2i−2i2i−2i0000002-2002i−2i000000000
χ3822-2-2222-222-2-2-2-22002-2-200-2-20000-2-22222000000000000000000000002-20000−2i2i−2i2i−2i2i0000002-200−2i2i000000000
χ3922-2-2222-222-2-2-2-22002-2-200-2-20000-2-2222200000000000000000000000-2200002i−2i−2i2i−2i2i000000-22002i−2i000000000
χ4022-2-2222-222-2-2-2-22002-2-200-2-20000-2-2222200000000000000000000000-220000−2i2i2i−2i2i−2i000000-2200−2i2i000000000
χ4122-2-222-2222-2-2-2-22002-2-20022000022-2-2-2-200000000000000000000000002-22i−2i002i−2i−2i2i00002-2002i−2i00000000000
χ4222-2-222-2222-2-2-2-22002-2-20022000022-2-2-2-200000000000000000000000002-2−2i2i00−2i2i2i−2i00002-200−2i2i00000000000
χ4322-2-222-2222-2-2-2-22002-2-20022000022-2-2-2-20000000000000000000000000-222i−2i00−2i2i2i−2i0000-22002i−2i00000000000
χ4422-2-222-2222-2-2-2-22002-2-20022000022-2-2-2-20000000000000000000000000-22−2i2i002i−2i−2i2i0000-2200−2i2i00000000000
χ4544444-2-4-44-2-24-24-24-4-2-2-200-42-2-2-4-422-4222024-2-2220000000000000000000000000000000000000000000000000
χ4644444-2-4-44-2-24-24-2-44-2-2-200-42224422-42220-2-422-2-20000000000000000000000000000000000000000000000000
χ474444-24-4-4-244-24-2-24-4-2-2-2002-44422222-4220-4-2-2-2220000000000000000000000000000000000000000000000000
χ484444-24-4-4-244-24-2-2-44-2-2-2002-4-4-4-2-2222-42204222-2-20000000000000000000000000000000000000000000000000
χ494444-2-244-2-2-2-2-2-214411144-2-2-2-2-2-211-2-2114-2-21111-2-2-2-21111-2-2-2-21111000000000000000000000000000000000
χ504444-2-244-2-2-2-2-2-2144111-4-4-2-2-2-2-2-211-2-211-4-2-211112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000
χ514444-2-244-2-2-2-2-2-21-4-411144-2-2222211-2-211-422-1-1-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000000
χ524444-2-244-2-2-2-2-2-21-4-4111-4-4-2-2222211-2-211422-1-1-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000000
χ534444-2-2-4-4-2-2-2-2-2-214-41110022-2-222-1-122-1-102-211-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000000
χ544444-2-2-4-4-2-2-2-2-2-214-41110022-2-222-1-122-1-102-211-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000000
χ554444-2-2-4-4-2-2-2-2-2-21-44111002222-2-2-1-122-1-10-22-1-11100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000000
χ564444-2-2-4-4-2-2-2-2-2-21-44111002222-2-2-1-122-1-10-22-1-1110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000000
χ5744-4-44-24-44-22-42-4-200-22200-420000224-2-2-2000000000000000000000004-40000000000000000-220000000000000
χ5844-4-44-24-44-22-42-4-200-22200-420000224-2-2-200000000000000000000000-4400000000000000002-20000000000000
χ5944-4-44-2-444-22-42-4-200-222004-20000-2-2-42220000000000000000000000000004i−4i00000000000000−2i2i00000000000
χ6044-4-44-2-444-22-42-4-200-222004-20000-2-2-4222000000000000000000000000000−4i4i000000000000002i−2i00000000000
χ6144-4-4-244-4-24-42-42-200-222002-4000022-24-2-2000000000000000000000000000004i−4i00000000000000−2i2i000000000
χ6244-4-4-244-4-24-42-42-200-222002-4000022-24-2-200000000000000000000000000000−4i4i000000000000002i−2i000000000
χ6344-4-4-24-44-24-42-42-200-22200-240000-2-22-42200000000000000000000000004-4000000000000-22000000000000000
χ6444-4-4-24-44-24-42-42-200-22200-240000-2-22-4220000000000000000000000000-440000000000002-2000000000000000
χ654-44-44400-4-44-4-44400-44-400000000000000000000000000000000000000000000000000000000000000022−2200000
χ664-44-44400-4-44-4-44400-44-4000000000000000000000000000000000000000000000000000000000000000−222200000
χ674-4-444400-4-4-444-4400-4-4422−22000000000000000000022−2222−2222−2222−2200000000000000000000000000000000000000000
χ684-4-444400-4-4-444-4400-4-44−22220000000000000000000−2222−2222−2222−222200000000000000000000000000000000000000000
χ694-4-444-200-4224-2-4-20022-222−2200−2i32i300000000000−2i32i30022−22−22−22−2200i6−i6i6−i6i6−i6000000000000000000000000000000000
χ704-4-444-200-4224-2-4-20022-222−22002i3−2i3000000000002i3−2i30022−22−22−22−2200−i6i6−i6i6−i6i6000000000000000000000000000000000
χ714-4-444-200-4224-2-4-20022-2−222200−2i32i300000000000−2i32i300−22222−22−22−200−i6i6−i6i6−i6i6000000000000000000000000000000000
χ724-4-444-200-4224-2-4-20022-2−2222002i3−2i3000000000002i3−2i300−22222−22−22−200i6−i6i6−i6i6−i6000000000000000000000000000000000
χ734-4-44-24002-4-4-242-20022-222−22000023−230000000000023−23−2222−22−22−226−6006−6−66000000000000000000000000000000000
χ744-4-44-24002-4-4-242-20022-222−220000−232300000000000−2323−2222−22−22−22−6600−666−6000000000000000000000000000000000
χ754-4-44-24002-4-4-242-20022-2−2222000023−230000000000023−232−2−22222−22−2−6600−666−6000000000000000000000000000000000
χ764-4-44-24002-4-4-242-20022-2−22220000−232300000000000−23232−2−22222−22−26−6006−6−66000000000000000000000000000000000
χ774-4-44-2-200222-2-22100-1-1122−2200−2i32i323−233i−3i003i−3i000i3−i3−33−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ784-4-44-2-200222-2-22100-1-1122−2200−2i32i3−2323−3i3i00−3i3i000i3−i33−3−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ794-4-44-2-200222-2-22100-1-1122−22002i3−2i323−23−3i3i00−3i3i000−i3i3−33−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ236−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ804-4-44-2-200222-2-22100-1-1122−22002i3−2i3−23233i−3i003i−3i000−i3i33−3−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ814-4-44-2-200222-2-22100-1-11−222200−2i32i323−233i−3i003i−3i000i3−i3−332−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ824-4-44-2-200222-2-22100-1-11−222200−2i32i3−2323−3i3i00−3i3i000i3−i33−32−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ236−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ834-4-44-2-200222-2-22100-1-11−2222002i3−2i323−23−3i3i00−3i3i000−i3i3−332−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ844-4-44-2-200222-2-22100-1-11−2222002i3−2i3−23233i−3i003i−3i000−i3i33−32−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ8588-8-8-4-48-8-4-444442002-2-200440000-2-2-4-42200000000000000000000000000000000000000000000000000000000
χ8688-8-8-4-4-88-4-444442002-2-200-4-400002244-2-200000000000000000000000000000000000000000000000000000000
χ878-88-88-400-84-4-848-4004-440000000000000000000000000000000000000000000000000000000000000000000000
χ888-88-8-48004-884-8-4-4004-440000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8-4-40044-444-4200-22-2000000006i−6i00−6i6i00000000000000000000000000000000000000000000000000000000
χ908-88-8-4-40044-444-4200-22-200000000−6i6i006i−6i00000000000000000000000000000000000000000000000000000000

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