Finite Group Databasebeta

← Group #11878511

Character table — Group #11878511

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222224444444444444444444488888888888888888888888242424242424242424242424242424243636363636364848484872
order12223344666666234666668812121212121212121212666812121224242424242424242424242424242424224444446612121212121222448861212128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-11-11111-1-1-1-1-1-1-1-1-1-111-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1111-11-1-1-1-11111-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ51111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1-11111-1-1-1-11111-1-11
χ61111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11-11-1-1-1-1-1-1-1-11111-1-11111-1
χ71111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-11-1111111111111-1-1-1-1-1-1-1
χ81111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-1-1-1-1-1-1-1-111-1-1111
χ911111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11-11-1-111-1-111-1-11-11-1111-1-11-1
χ1011111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-1-1111-1-1-1-111-11-11-1-11-11-11
χ1111111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-11111-1-1-11-11-1-1-11-111
χ1211111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1111-11-111-111-1-1
χ1311111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-11111-1-1-11-11111-11-1-1
χ1411111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111-1-1-111-1-1111-11-1-1-11-1-111
χ1511111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1111-1-111-1-11-11-1-1-1-111-11
χ1611111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-111-1-1-1-111-11-1111-11-11-1
χ17222222-2-222222222-22222200-2-2-2-2-2-2-2-2-2-22220-2-2-2000000000000000000000000000000002-2-220000000
χ18222222-2-222222222-22222200-2-2-2-2-2-2-2-2-2-22220-2-2-200000000000000000000000000000000-222-20000000
χ19222222-2-2222222-222-2-22220022-2-2-2-2-2-2-2-2-2-2-202220000000000000000000000000000000022-2-20000000
χ20222222-2-2222222-222-2-22220022-2-2-2-2-2-2-2-2-2-2-2022200000000000000000000000000000000-2-2220000000
χ2122222-1222-1-12-122-1222-1-1-122-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-122200020-1-1-1-10000000000-1-1000
χ2222222-1222-1-12-122-1222-1-1-122-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2000-201111000000000011000
χ2322222-1222-1-12-122-1222-1-1-1-2-2-1-122-1-1-1-1-1-1-1-1-1-22-1-1-2-2111111-2-21111112-22000-2011110000000000-1-1000
χ2422222-1222-1-12-122-1222-1-1-1-2-2-1-122-1-1-1-1-1-1-1-1-1-22-1-1-2-2111111-2-2111111-22-200020-1-1-1-1000000000011000
χ2522222-1222-1-12-12-2-1-2-2-2-1-1-1221122-1-1-1-1-1-1111-2-21122-1-1-1-1-1-1-2-211111122-2000-20-1-1110000000000-11000
χ2622222-1222-1-12-12-2-1-2-2-2-1-1-1221122-1-1-1-1-1-1111-2-21122-1-1-1-1-1-1-2-2111111-2-220002011-1-100000000001-1000
χ2722222-1222-1-12-12-2-1-2-2-2-1-1-1-2-21122-1-1-1-1-1-11112-211-2-211111122-1-1-1-1-1-12-2-20002011-1-10000000000-11000
χ2822222-1222-1-12-12-2-1-2-2-2-1-1-1-2-21122-1-1-1-1-1-11112-211-2-211111122-1-1-1-1-1-1-222000-20-1-11100000000001-1000
χ292222-1222-122-12-12-12-1-1-1-1-12222-1-122-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000222020000-1-1-1-100000000-1-10
χ302222-1222-122-12-12-12-1-1-1-1-12222-1-122-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000-2-2-20-20000111100000000110
χ312222-1222-122-12-12-12-1-1-1-1-1-2-222-1-122-1-1-1-12-1-1-2-1-1-111-2-2111111-2-2111100022-20-20000-1-1-1-100000000110
χ322222-1222-122-12-12-12-1-1-1-1-1-2-222-1-122-1-1-1-12-1-1-2-1-1-111-2-2111111-2-21111000-2-22020000111100000000-1-10
χ332222-1222-122-12-1-2-1-211-1-1-122-2-2-1-122-1-1-1-1-211-2111-1-122-1-1-1-111-2-211110002-220-20000-1-111000000001-10
χ342222-1222-122-12-1-2-1-211-1-1-122-2-2-1-122-1-1-1-1-211-2111-1-122-1-1-1-111-2-21111000-22-202000011-1-100000000-110
χ352222-1222-122-12-1-2-1-211-1-1-1-2-2-2-2-1-122-1-1-1-1-211211111-2-21111-1-122-1-1-1-10002-2-2020000-1-11100000000-110
χ362222-1222-122-12-1-2-1-211-1-1-1-2-2-2-2-1-122-1-1-1-1-211211111-2-21111-1-122-1-1-1-1000-2220-2000011-1-1000000001-10
χ3744444-2-4-44-2-24-244-2-444-2-2-20022-4-4222222-2-2-20-4220000000000000000000000000000000000000000000
χ3844444-2-4-44-2-24-24-4-24-4-4-2-2-200-2-2-4-422222222204-2-20000000000000000000000000000000000000000000
χ394444-24-4-4-244-24-24-2-4-2-2-2-2-200-4-422-4-422224-2-202220000000000000000000000000000000000000000000
χ404444-24-4-4-244-24-2-4-2422-2-2-2004422-4-42222-4220-2-2-20000000000000000000000000000000000000000000
χ414444-2-244-2-2-2-2-2-2414-2-211144-2-2-2-2-2-21111-2114-211-2-2-2-21111-2-2-2-21111000000000000000000000000000
χ424444-2-244-2-2-2-2-2-2414-2-2111-4-4-2-2-2-2-2-21111-211-4-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000
χ434444-2-244-2-2-2-2-2-2-41-4221114422-2-2-2-211112-1-1-42-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000
χ444444-2-244-2-2-2-2-2-2-41-422111-4-422-2-2-2-211112-1-142-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000
χ454444-2-2-4-4-2-2-2-2-2-241-4-2-211100222222-1-1-1-1-21102-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000
χ464444-2-2-4-4-2-2-2-2-2-241-4-2-211100222222-1-1-1-1-21102-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000
χ474444-2-2-4-4-2-2-2-2-2-2-4142211100-2-22222-1-1-1-12-1-10-21100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000
χ484444-2-2-4-4-2-2-2-2-2-2-4142211100-2-22222-1-1-1-12-1-10-2110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000
χ4944-4-4440044-4-4-4-4040004-4-422−220000000000000000022−2222−2222−2222−2200000000000000000000000000000000000
χ5044-4-4440044-4-4-4-4040004-4-4−222200000000000000000−2222−2222−2222−222200000000000000000000000000000000000
χ5144-4-44-2004-22-42-40-2000-22222−2223−23000000000000023−2322−22−22−22−22006−66−66−6000000000000000000000000000
χ5244-4-44-2004-22-42-40-2000-22222−22−23230000000000000−232322−22−22−22−2200−66−66−66000000000000000000000000000
χ5344-4-44-2004-22-42-40-2000-222−222223−23000000000000023−23−22222−22−22−200−66−66−66000000000000000000000000000
χ5444-4-44-2004-22-42-40-2000-222−2222−23230000000000000−2323−22222−22−22−2006−66−66−6000000000000000000000000000
χ5544-4-4-2400-24-42-420-20−2i32i3-22222−2200000000000−2i32i30000−2222−22−22−22i6−i600i6−i6−i6i6000000000000000000000000000
χ5644-4-4-2400-24-42-420-20−2i32i3-222−222200000000000−2i32i300002−2−22222−22−2−i6i600−i6i6i6−i6000000000000000000000000000
χ5744-4-4-2400-24-42-420-202i3−2i3-22222−22000000000002i3−2i30000−2222−22−22−22−i6i600−i6i6i6−i6000000000000000000000000000
χ5844-4-4-2400-24-42-420-202i3−2i3-222−2222000000000002i3−2i300002−2−22222−22−2i6−i600i6−i6−i6i6000000000000000000000000000
χ5944-4-4-2-200-2-22222010−2i32i31-1-122−2223−2300003i3i−3i−3i0i3−i300−33−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ6044-4-4-2-200-2-22222010−2i32i31-1-122−22−23230000−3i−3i3i3i0i3−i3003−3−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ6144-4-4-2-200-2-22222010−2i32i31-1-1−222223−2300003i3i−3i−3i0i3−i300−332−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ6244-4-4-2-200-2-22222010−2i32i31-1-1−2222−23230000−3i−3i3i3i0i3−i3003−32−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ6344-4-4-2-200-2-222220102i3−2i31-1-122−2223−230000−3i−3i3i3i0−i3i300−33−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ6444-4-4-2-200-2-222220102i3−2i31-1-122−22−232300003i3i−3i−3i0−i3i3003−3−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ6544-4-4-2-200-2-222220102i3−2i31-1-1−222223−230000−3i−3i3i3i0−i3i300−332−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ6644-4-4-2-200-2-222220102i3−2i31-1-1−2222−232300003i3i−3i−3i0−i3i3003−32−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ674-44-44400-4-44-4-4404000-44-4000000000000000000000000000000000000000000000000000000022−2200000
χ684-44-44400-4-44-4-4404000-44-40000000000000000000000000000000000000000000000000000000−222200000
χ694-4-44444-4-4-4-444-404000-4-4400004-44-44-44-400000000000000000000000000000000000000000000000000
χ704-4-4444-44-4-4-444-404000-4-440000-44-44-44-4400000000000000000000000000000000000000000000000000
χ714-4-444-24-4-4224-2-40-200022-200004-4-22-22-220000000000000000000000000000000−2i32i300000000000000000
χ724-4-444-24-4-4224-2-40-200022-200004-4-22-22-2200000000000000000000000000000002i3−2i300000000000000000
χ734-4-444-2-44-4224-2-40-200022-20000-442-22-22-2000000000000000000000000000000000−2i32i3000000000000000
χ744-4-444-2-44-4224-2-40-200022-20000-442-22-22-20000000000000000000000000000000002i3−2i3000000000000000
χ754-4-44-244-42-4-4-2420-200022-20000-224-4-22-220000000000000000000000000000000000023−230000000000000
χ764-4-44-244-42-4-4-2420-200022-20000-224-4-22-2200000000000000000000000000000000000−23230000000000000
χ774-4-44-24-442-4-4-2420-200022-200002-2-442-22-2000000000000000000000000000000000000023−2300000000000
χ784-4-44-24-442-4-4-2420-200022-200002-2-442-22-20000000000000000000000000000000000000−232300000000000
χ798-88-88-400-84-4-8480-40004-4400000000000000000000000000000000000000000000000000000000000000
χ808-88-8-48004-884-8-40-40004-4400000000000000000000000000000000000000000000000000000000000000
χ818-88-8-4-40044-444-402000-22-2000000006i−6i−6i6i00000000000000000000000000000000000000000000000000
χ828-88-8-4-40044-444-402000-22-200000000−6i6i6i−6i00000000000000000000000000000000000000000000000000
χ838-8-88-4-48-8444-4-4402000-2-220000-44-442-22-200000000000000000000000000000000000000000000000000
χ848-8-88-4-4-88444-4-4402000-2-2200004-44-4-22-2200000000000000000000000000000000000000000000000000

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