Finite Group Databasebeta

← Group #11872812

Character table — Group #11872812

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222224444444444444444444488888888888888888888888121212121212121218181818242424242424242424242424363636364848484872
order1222334466666623466666881212121212121212121266681212122424242424242424242424242424242422224444444444446666121212124488121212128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-1-1-111-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-111-1
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
χ51111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1
χ61111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1-111-1-1111
χ71111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-1-1-1-11111-1-11111-1-11
χ81111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1
χ911111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111111-1-1111-1-111-1-1-1-111-11-11-1
χ1011111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-111-11
χ1111111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-11-1-111
χ1211111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-111-1-1-111-1-111-1-1111-11-1-1
χ1311111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-111-111-1-111-1-1-1-1-1-11-11-11
χ1411111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-11-1
χ1511111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11111-111-1-1
χ1611111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111111-1-11-1-111-1-111-1-1-1-1-11-111
χ17222222-2-222222222-22222200-2-2-2-2-2-2-2-2-2-22220-2-2-200000000000000000000000022-2-20000000000002-20000000
χ18222222-2-222222222-22222200-2-2-2-2-2-2-2-2-2-22220-2-2-2000000000000000000000000-2-222000000000000-220000000
χ19222222-2-2222222-222-2-22220022-2-2-2-2-2-2-2-2-2-2-2022200000000000000000000000022-2-2000000000000-220000000
χ20222222-2-2222222-222-2-22220022-2-2-2-2-2-2-2-2-2-2-20222000000000000000000000000-2-2220000000000002-20000000
χ2122222-122-12-12-122-12-1-1-1-1-1222222-1-1-1-1-1-12-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222000000002020-1-1-1-100000000-1-1000
χ2222222-122-12-12-122-12-1-1-1-1-1222222-1-1-1-1-1-12-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-200000000-20-2011110000000011000
χ2322222-122-12-12-122-12-1-1-1-1-1-2-22222-1-1-1-1-1-12-1-1-2-1-1-1-2-2111111-2-2111111222200000000-20-20-1-1-1-10000000011000
χ2422222-122-12-12-122-12-1-1-1-1-1-2-22222-1-1-1-1-1-12-1-1-2-1-1-1-2-2111111-2-2111111-2-2-2-2000000002020111100000000-1-1000
χ2522222-122-12-12-12-2-1-211-1-1-122-2-222-1-1-1-1-1-1-211-211122-1-1-1-1-1-1-2-211111122-2-20000000020-20-1-111000000001-1000
χ2622222-122-12-12-12-2-1-211-1-1-122-2-222-1-1-1-1-1-1-211-211122-1-1-1-1-1-1-2-2111111-2-22200000000-202011-1-100000000-11000
χ2722222-122-12-12-12-2-1-211-1-1-1-2-2-2-222-1-1-1-1-1-1-2112111-2-211111122-1-1-1-1-1-122-2-200000000-2020-1-11100000000-11000
χ2822222-122-12-12-12-2-1-211-1-1-1-2-2-2-222-1-1-1-1-1-1-2112111-2-211111122-1-1-1-1-1-1-2-2220000000020-2011-1-1000000001-1000
χ292222-12222-12-12-12-1222-1-1-122-1-1-1-122-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-100002222000002020000-1-1-1-1000000-1-10
χ302222-12222-12-12-12-1222-1-1-122-1-1-1-122-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-2-2-200000-20-200001111000000110
χ312222-12222-12-12-12-1222-1-1-1-2-2-1-1-1-122-1-1-1-1-1-1-1-22-1-111-2-2111111-2-211110000222200000-20-20000-1-1-1-1000000110
χ322222-12222-12-12-12-1222-1-1-1-2-2-1-1-1-122-1-1-1-1-1-1-1-22-1-111-2-2111111-2-211110000-2-2-2-20000020200001111000000-1-10
χ332222-12222-12-12-1-2-1-2-2-2-1-1-12211-1-122-1-1-1-1111-2-211-1-122-1-1-1-111-2-21111000022-2-200000-2020000-1-1110000001-10
χ342222-12222-12-12-1-2-1-2-2-2-1-1-12211-1-122-1-1-1-1111-2-211-1-122-1-1-1-111-2-211110000-2-2220000020-2000011-1-1000000-110
χ352222-12222-12-12-1-2-1-2-2-2-1-1-1-2-211-1-122-1-1-1-11112-21111-2-21111-1-122-1-1-1-1000022-2-20000020-20000-1-111000000-110
χ362222-12222-12-12-1-2-1-2-2-2-1-1-1-2-211-1-122-1-1-1-11112-21111-2-21111-1-122-1-1-1-10000-2-22200000-202000011-1-10000001-10
χ3722-2-2222-2-2-2-222-202000-2-2200002-22-222-2-2000000000000000000000002-2002i−2i002i−2i2i−2i00002-2002i−2i00000000000
χ3822-2-2222-2-2-2-222-202000-2-2200002-22-222-2-2000000000000000000000002-200−2i2i00−2i2i−2i2i00002-200−2i2i00000000000
χ3922-2-2222-2-2-2-222-202000-2-2200002-22-222-2-200000000000000000000000-22002i−2i00−2i2i−2i2i0000-22002i−2i00000000000
χ4022-2-2222-2-2-2-222-202000-2-2200002-22-222-2-200000000000000000000000-2200−2i2i002i−2i2i−2i0000-2200−2i2i00000000000
χ4122-2-222-22-2-2-222-202000-2-220000-22-22-2-22200000000000000000000000002-2002i−2i2i−2i−2i2i0000002-2002i−2i000000000
χ4222-2-222-22-2-2-222-202000-2-220000-22-22-2-22200000000000000000000000002-200−2i2i−2i2i2i−2i0000002-200−2i2i000000000
χ4322-2-222-22-2-2-222-202000-2-220000-22-22-2-2220000000000000000000000000-22002i−2i−2i2i2i−2i000000-22002i−2i000000000
χ4422-2-222-22-2-2-222-202000-2-220000-22-22-2-2220000000000000000000000000-2200−2i2i2i−2i−2i2i000000-2200−2i2i000000000
χ4544444-2-4-4-24-24-244-2-4-2-2-2-2-200-4-4-4-42222224-2-202220000000000000000000000000000000000000000000000000
χ4644444-2-4-4-24-24-24-4-2422-2-2-20044-4-4222222-4220-2-2-20000000000000000000000000000000000000000000000000
χ474444-24-4-44-24-24-24-2-444-2-2-2002222-4-42222-2-2-20-4220000000000000000000000000000000000000000000000000
χ484444-24-4-44-24-24-2-4-24-4-4-2-2-200-2-222-4-4222222204-2-20000000000000000000000000000000000000000000000000
χ494444-2-244-2-2-2-2-2-2414-2-211144-2-2-2-2-2-21111-2114-211-2-2-2-21111-2-2-2-21111000000000000000000000000000000000
χ504444-2-244-2-2-2-2-2-2414-2-2111-4-4-2-2-2-2-2-21111-211-4-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000
χ514444-2-244-2-2-2-2-2-2-41-4221114422-2-2-2-211112-1-1-42-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000000
χ524444-2-244-2-2-2-2-2-2-41-422111-4-422-2-2-2-211112-1-142-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000000
χ534444-2-2-4-4-2-2-2-2-2-241-4-2-211100222222-1-1-1-1-21102-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000000
χ544444-2-2-4-4-2-2-2-2-2-241-4-2-211100222222-1-1-1-1-21102-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000000
χ554444-2-2-4-4-2-2-2-2-2-2-4142211100-2-22222-1-1-1-12-1-10-21100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000000
χ564444-2-2-4-4-2-2-2-2-2-2-4142211100-2-22222-1-1-1-12-1-10-2110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000000
χ5744-4-44-24-42-424-2-40-200022-200004-4-22-2-222000000000000000000000004-400000000000000-22000000000000000
χ5844-4-44-24-42-424-2-40-200022-200004-4-22-2-22200000000000000000000000-44000000000000002-2000000000000000
χ5944-4-44-2-442-424-2-40-200022-20000-442-222-2-200000000000000000000000004-400000000000000-220000000000000
χ6044-4-44-2-442-424-2-40-200022-20000-442-222-2-20000000000000000000000000-44000000000000002-20000000000000
χ6144-4-4-244-4-42-4-2420-200022-20000-224-4-2-2220000000000000000000000000004i−4i00000000000000−2i2i00000000000
χ6244-4-4-244-4-42-4-2420-200022-20000-224-4-2-222000000000000000000000000000−4i4i000000000000002i−2i00000000000
χ6344-4-4-24-44-42-4-2420-200022-200002-2-4422-2-2000000000000000000000000000004i−4i00000000000000−2i2i000000000
χ6444-4-4-24-44-42-4-2420-200022-200002-2-4422-2-200000000000000000000000000000−4i4i000000000000002i−2i000000000
χ654-44-444004-4-4-4-44040004-4-4−2i22i200000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000
χ664-44-444004-4-4-4-44040004-4-42i2−2i2000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000
χ674-44-44-200-2-42-4240-20−2i32i3-222−2i22i200000000000−2i32i30000−2i22i2i2−i2i2−i2i2−i2006−66−66−6000000000000000000000000000000000
χ684-44-44-200-2-42-4240-20−2i32i3-2222i2−2i200000000000−2i32i300002i2−2i2−i2i2−i2i2−i2i200−66−66−66000000000000000000000000000000000
χ694-44-44-200-2-42-4240-202i3−2i3-222−2i22i2000000000002i3−2i30000−2i22i2i2−i2i2−i2i2−i200−66−66−66000000000000000000000000000000000
χ704-44-44-200-2-42-4240-202i3−2i3-2222i2−2i2000000000002i3−2i300002i2−2i2−i2i2−i2i2−i2i2006−66−66−6000000000000000000000000000000000
χ714-44-4-240042-42-4-20-2000-222−2i22i223−23000000000000023−23i2−i2−2i22i2i2−i2i2−i2i6−i600i6−i6−i6i6000000000000000000000000000000000
χ724-44-4-240042-42-4-20-2000-222−2i22i2−23230000000000000−2323i2−i2−2i22i2i2−i2i2−i2−i6i600−i6i6i6−i6000000000000000000000000000000000
χ734-44-4-240042-42-4-20-2000-2222i2−2i223−23000000000000023−23−i2i22i2−2i2−i2i2−i2i2−i6i600−i6i6i6−i6000000000000000000000000000000000
χ744-44-4-240042-42-4-20-2000-2222i2−2i2−23230000000000000−2323−i2i22i2−2i2−i2i2−i2i2i6−i600i6−i6−i6i6000000000000000000000000000000000
χ754-44-4-2-200-22222-2010−2i32i31-1-1−2i22i223−2300003i−3i3i−3i0i3−i300−33i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ764-44-4-2-200-22222-2010−2i32i31-1-1−2i22i2−23230000−3i3i−3i3i0i3−i3003−3i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ774-44-4-2-200-22222-2010−2i32i31-1-12i2−2i223−2300003i−3i3i−3i0i3−i300−33−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ784-44-4-2-200-22222-2010−2i32i31-1-12i2−2i2−23230000−3i3i−3i3i0i3−i3003−3−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ794-44-4-2-200-22222-20102i3−2i31-1-1−2i22i223−230000−3i3i−3i3i0−i3i300−33i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ804-44-4-2-200-22222-20102i3−2i31-1-1−2i22i2−232300003i−3i3i−3i0−i3i3003−3i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ814-44-4-2-200-22222-20102i3−2i31-1-12i2−2i223−230000−3i3i−3i3i0−i3i300−33−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ824-44-4-2-200-22222-20102i3−2i31-1-12i2−2i2−232300003i−3i3i−3i0−i3i3003−3−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ834-4-444400-444-4-4-404000-44-40000000000000000000000000000000000000000000000000000000000000−2i22i200000
χ844-4-444400-444-4-4-404000-44-400000000000000000000000000000000000000000000000000000000000002i2−2i200000
χ8588-8-8-4-48-8444-4-4402000-2-220000-44-4422-2-200000000000000000000000000000000000000000000000000000000
χ8688-8-8-4-4-88444-4-4402000-2-2200004-44-4-2-22200000000000000000000000000000000000000000000000000000000
χ878-8-888-40048-4-84-80-40004-4400000000000000000000000000000000000000000000000000000000000000000000
χ888-8-88-4800-8-484-840-40004-4400000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88-4-4004-4-444402000-22-2000000006i−6i−6i6i00000000000000000000000000000000000000000000000000000000
χ908-8-88-4-4004-4-444402000-22-200000000−6i6i6i−6i00000000000000000000000000000000000000000000000000000000

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