Finite Group Databasebeta

← Group #11778028

Character table — Group #11778028

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222244444444444444444444444488888888888888888888824242424242424242424242424242424242424242424242472727272
order1222223366666622344666666666666666121212124666666121212121212121212121212121244448888121212121212121224242424242424242244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ922222222222222222-2-2222222222222222-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ1022222222222222-2-22-2-22222-2-2-2-22222222-2-2-2-22-2-2-2-2-2-222-2-222-2-2-2-222220000000000000000000000000000
χ112222222-12-122-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ122222222-12-122-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ132222222-12-122-1-122-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-1-1-1-1-2-211111111111100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ142222222-12-122-1-122-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-1-1-1-1-2-211111111111100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ152222222-12-122-1-1-2-2-12222-1-11111-1-1-1-1-1-1-12222-2-2-21111-2-2-1-111-1-1-1-1111122-2-20000-1-1-1-11111000000000000
χ162222222-12-122-1-1-2-2-12222-1-11111-1-1-1-1-1-1-12222-2-2-21111-2-2-1-111-1-1-1-11111-2-22200001111-1-1-1-1000000000000
χ172222222-12-122-1-1-2-2-1-2-222-1-11111-1-1-1-1-1-1-1-2-2-2-22-2-211112211-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ182222222-12-122-1-1-2-2-1-2-222-1-11111-1-1-1-1-1-1-1-2-2-2-22-2-211112211-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ19222222-12-12-1-12222-122-1-1222222-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ20222222-12-12-1-12222-122-1-1222222-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ21222222-12-12-1-12222-1-2-2-1-1222222-1-1-1-1-1-1-11111-2-1-1-1-1-1-111-2-2-2-211111111000000000000000033−3−333−3−30000
χ22222222-12-12-1-12222-1-2-2-1-1222222-1-1-1-1-1-1-11111-2-1-1-1-1-1-111-2-2-2-2111111110000000000000000−3−333−3−3330000
χ23222222-12-12-1-122-2-2-122-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-21111111122-2-2-1-1-1-11111000022-2-200000000-1-1-1-111110000
χ24222222-12-12-1-122-2-2-122-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-21111111122-2-2-1-1-1-111110000-2-222000000001111-1-1-1-10000
χ25222222-12-12-1-122-2-2-1-2-2-1-122-2-2-2-2-1-1-1-1-1-1-111112111111-1-1-2-2221111-1-1-1-1000000000000000033−3−3−3−3330000
χ26222222-12-12-1-122-2-2-1-2-2-1-122-2-2-2-2-1-1-1-1-1-1-111112111111-1-1-2-2221111-1-1-1-10000000000000000−3−33333−3−30000
χ272222-2-2222222220022-2-2-2-2-200002-2-2-2-22222-2-20000000002-20022-2-20000002-2000000002-22-2000000000000
χ282222-2-2222222220022-2-2-2-2-200002-2-2-2-22222-2-20000000002-20022-2-2000000-2200000000-22-22000000000000
χ292222-2-222222222002-22-2-2-2-200002-2-2-2-222-2-222000000000-2200-2-22200002-20000002-22-20000000000000000
χ302222-2-222222222002-22-2-2-2-200002-2-2-2-222-2-222000000000-2200-2-2220000-22000000-22-220000000000000000
χ312222-2-22-12-122-1-100-12-2-2-211−i3−i3i3i3-11111-1-122-2-2000−i3−i3i3i300-11−i3i3-1-111−i3−i3i3i3002-20000−i3i3i3−i3-11-11000000000000
χ322222-2-22-12-122-1-100-12-2-2-211−i3−i3i3i3-11111-1-122-2-2000−i3−i3i3i300-11−i3i3-1-111−i3−i3i3i300-220000i3−i3−i3i31-11-1000000000000
χ332222-2-22-12-122-1-100-12-2-2-211i3i3−i3−i3-11111-1-122-2-2000i3i3−i3−i300-11i3−i3-1-111i3i3−i3−i3002-20000i3−i3−i3i3-11-11000000000000
χ342222-2-22-12-122-1-100-12-2-2-211i3i3−i3−i3-11111-1-122-2-2000i3i3−i3−i300-11i3−i3-1-111i3i3−i3−i300-220000−i3i3i3−i31-11-1000000000000
χ352222-2-22-12-122-1-100-1-22-2-211−i3−i3i3i3-11111-1-1-2-222000−i3−i3i3i3001-1i3−i311-1-1i3i3−i3−i32-2000000-11-11−i3i3i3−i3000000000000
χ362222-2-22-12-122-1-100-1-22-2-211−i3−i3i3i3-11111-1-1-2-222000−i3−i3i3i3001-1i3−i311-1-1i3i3−i3−i3-220000001-11-1i3−i3−i3i3000000000000
χ372222-2-22-12-122-1-100-1-22-2-211i3i3−i3−i3-11111-1-1-2-222000i3i3−i3−i3001-1−i3i311-1-1−i3−i3i3i32-2000000-11-11i3−i3−i3i3000000000000
χ382222-2-22-12-122-1-100-1-22-2-211i3i3−i3−i3-11111-1-1-2-222000i3i3−i3−i3001-1−i3i311-1-1−i3−i3i3i3-220000001-11-1−i3i3i3−i3000000000000
χ3922-2-2-222222-2-2-2-22-22002-22-22-22-2222-2-2-2-2000002-22-22-2000000000000000000−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i20000
χ4022-2-2-222222-2-2-2-22-22002-22-22-22-2222-2-2-2-2000002-22-22-2000000000000000000i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i20000
χ4122-2-2-222222-2-2-2-2-222002-22-2-22-22222-2-2-2-200000-22-22-22000000000000000000−i2i2i2−i200000000−i2i2−i2i2i2−i2i2−i20000
χ4222-2-2-222222-2-2-2-2-222002-22-2-22-22222-2-2-2-200000-22-22-22000000000000000000i2−i2−i2i200000000i2−i2i2−i2−i2i2−i2i20000
χ4322-2-2-22-12-1211-2-22-2-100-112-22-22-2-1-1-111113−33−30-11-11-113−300003−33−33−33−30000−i2i2−i2i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ4422-2-2-22-12-1211-2-22-2-100-112-22-22-2-1-1-111113−33−30-11-11-113−300003−33−33−33−30000i2−i2i2−i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ4522-2-2-22-12-1211-2-22-2-100-112-22-22-2-1-1-11111−33−330-11-11-11−330000−33−33−33−330000−i2i2−i2i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ4622-2-2-22-12-1211-2-22-2-100-112-22-22-2-1-1-11111−33−330-11-11-11−330000−33−33−33−330000i2−i2i2−i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ4722-2-2-22-12-1211-2-2-22-100-112-2-22-22-1-1-111113−33−301-11-11-1−3300003−33−3−33−330000−i2i2i2−i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ4822-2-2-22-12-1211-2-2-22-100-112-2-22-22-1-1-111113−33−301-11-11-1−3300003−33−3−33−330000i2−i2−i2i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ4922-2-2-22-12-1211-2-2-22-100-112-2-22-22-1-1-11111−33−3301-11-11-13−30000−33−333−33−30000−i2i2i2−i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ5022-2-2-22-12-1211-2-2-22-100-112-2-22-22-1-1-11111−33−3301-11-11-13−30000−33−333−33−30000i2−i2−i2i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ51444444-2-2-2-2-2-2-2-244144-2-2-2-2-2-2-2-21111111-2-2-2-24-2-21111-2-2-2-2-2-2111111110000000000000000000000000000
χ52444444-2-2-2-2-2-2-2-2441-4-4-2-2-2-2-2-2-2-211111112222-4-2-21111222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ53444444-2-2-2-2-2-2-2-2-4-4144-2-2-2-222221111111-2-2-2-2-422-1-1-1-122-2-2221111-1-1-1-10000000000000000000000000000
χ54444444-2-2-2-2-2-2-2-2-4-41-4-4-2-2-2-2222211111112222422-1-1-1-1-2-222-2-2-1-1-1-111110000000000000000000000000000
χ554444-4-4-24-24-2-24400-24-422-4-40000-22222-2-2-2-2220000000004-400-2-22200000000000000000000000000000000
χ564444-4-4-24-24-2-24400-2-4422-4-40000-22222-2-222-2-2000000000-440022-2-200000000000000000000000000000000
χ574444-4-4-2-2-2-2-2-2-2-20014-42222−2i3−2i32i32i31-1-1-1-111-2-222000i3i3−i3−i300-22−2i32i311-1-1i3i3−i3−i30000000000000000000000000000
χ584444-4-4-2-2-2-2-2-2-2-20014-422222i32i3−2i3−2i31-1-1-1-111-2-222000−i3−i3i3i300-222i3−2i311-1-1−i3−i3i3i30000000000000000000000000000
χ594444-4-4-2-2-2-2-2-2-2-2001-442222−2i3−2i32i32i31-1-1-1-11122-2-2000i3i3−i3−i3002-22i3−2i3-1-111−i3−i3i3i30000000000000000000000000000
χ604444-4-4-2-2-2-2-2-2-2-2001-4422222i32i3−2i3−2i31-1-1-1-11122-2-2000−i3−i3i3i3002-2−2i32i3-1-111i3i3−i3−i30000000000000000000000000000
χ6144-4-44-44444-4-4-4-400400-44-4400004-4-444-4-400000000000000000000000000000000000000000000000000000
χ6244-4-44-44-24-2-4-42200-200-442-2−2i32i32i3−2i3-222-2-2220000000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ6344-4-44-44-24-2-4-42200-200-442-22i3−2i3−2i32i3-222-2-22200000002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ6444-4-44-4-24-2422-4-400-2002-2-440000-222-2-22223−23−2323000000000000023−23−232300000000000000000000000000000000
χ6544-4-44-4-24-2422-4-400-2002-2-440000-222-2-222−232323−230000000000000−232323−2300000000000000000000000000000000
χ6644-4-44-4-2-2-2-22222001002-22-2−2i32i32i3−2i31-1-111-1-123−23−2323000i3−i3−i3i3000000−333−3−3i3i3i−3i0000000000000000000000000000
χ6744-4-44-4-2-2-2-22222001002-22-2−2i32i32i3−2i31-1-111-1-1−232323−23000i3−i3−i3i30000003−3−333i−3i−3i3i0000000000000000000000000000
χ6844-4-44-4-2-2-2-22222001002-22-22i3−2i3−2i32i31-1-111-1-123−23−2323000−i3i3i3−i3000000−333−33i−3i−3i3i0000000000000000000000000000
χ6944-4-44-4-2-2-2-22222001002-22-22i3−2i3−2i32i31-1-111-1-1−232323−23000−i3i3i3−i30000003−3−33−3i3i3i−3i0000000000000000000000000000
χ7044-4-4-444-24-2-4-4224-4-2004-4-22-22-22-2-2-22222000004-4-22-22000000000000000000000000000000000000000000
χ7144-4-4-444-24-2-4-422-44-2004-4-222-22-2-2-2-2222200000-442-22-2000000000000000000000000000000000000000000
χ7244-4-4-44-2-2-2-222224-4100-22-22-22-22111-1-1-1-123−2323−230-221-11-123−230000−33−33−33−330000000000000000000000000000
χ7344-4-4-44-2-2-2-222224-4100-22-22-22-22111-1-1-1-1−2323−23230-221-11-1−232300003−33−33−33−30000000000000000000000000000
χ7444-4-4-44-2-2-2-22222-44100-22-222-22-2111-1-1-1-123−2323−2302-2-11-11−23230000−33−333−33−30000000000000000000000000000
χ7544-4-4-44-2-2-2-22222-44100-22-222-22-2111-1-1-1-1−2323−232302-2-11-1123−2300003−33−3−33−330000000000000000000000000000
χ764-44-40044-4-44-44-40040000000000-400004-400000000000000000000000000000000000000000000000002-200
χ774-44-40044-4-44-44-40040000000000-400004-40000000000000000000000000000000000000000000000000-2200
χ784-4-440044-4-4-44-440040000000000-40000-440000000000000000000000000000000000000000000000000002-2
χ794-4-440044-4-4-44-440040000000000-40000-44000000000000000000000000000000000000000000000000000-22
χ808-88-8008-4-848-8-4400-4000000000040000-4400000000000000000000000000000000000000000000000000000
χ818-88-800-484-8-448-800-4000000000040000-4400000000000000000000000000000000000000000000000000000
χ828-88-800-4-444-44-440020000000000-26-66-62-200000000000000000000000000000000000000000000000000000
χ838-88-800-4-444-44-440020000000000-2-66-662-200000000000000000000000000000000000000000000000000000
χ848-8-88008-4-84-884-400-40000000000400004-400000000000000000000000000000000000000000000000000000
χ858-8-8800-484-84-4-8800-40000000000400004-400000000000000000000000000000000000000000000000000000
χ868-8-8800-4-4444-44-40020000000000-26-6-66-2200000000000000000000000000000000000000000000000000000
χ878-8-8800-4-4444-44-40020000000000-2-666-6-2200000000000000000000000000000000000000000000000000000

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