Finite Group Databasebeta

← Group #11778407

Character table — Group #11778407

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222244444444444444444444444488888888888888888888824242424242424242424242424242424242424242424242472727272
order1222223366666634444666666666661212121212121212266666666121212121212121212121212244466888812121212121224242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
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
χ5111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ922222222222222222-2-2222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-222220000000000000000000000000000
χ10222222222222222-2-2-2-222222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ112222222-1222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-10000-1-1-1-1-1-1000000000000
χ122222222-1222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2110000111111000000000000
χ132222222-1222-1-1-1-122-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-211111122111111-1-1-1-10000−i3i30000−i3i3−i3−i3i3i3000000000000
χ142222222-1222-1-1-1-122-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-211111122111111-1-1-1-10000i3−i30000i3−i3i3i3−i3−i3000000000000
χ152222222-1222-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-111112222-2-2-2111111-2-2-1-1-1-1-1-1111122-2-2-1-10000-1-11111000000000000
χ162222222-1222-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-111112222-2-2-2111111-2-2-1-1-1-1-1-11111-2-22211000011-1-1-1-1000000000000
χ172222222-1222-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-11111-2-2-2-2222-1-1-1-1-1-1-2-211111111110000−i3i30000−i3i3i3i3−i3−i3000000000000
χ182222222-1222-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-11111-2-2-2-2222-1-1-1-1-1-1-2-211111111110000i3−i30000i3−i3−i3−i3i3i3000000000000
χ19222222-12-1-1-1222-12222-1-122-1-1-1-1-1-1-12222-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-10000002222000000-1-1-1-1-1-1-1-10000
χ20222222-12-1-1-1222-12222-1-122-1-1-1-1-1-1-12222-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000-2-2-2-2000000111111110000
χ21222222-12-1-1-1222-122-2-2-1-122-1-1-1-1-1-1-122221111-211-2-21111-1-1-2-21111-1-1-1-1000000000000000033−3−333−3−30000
χ22222222-12-1-1-1222-122-2-2-1-122-1-1-1-1-1-1-122221111-211-2-21111-1-1-2-21111-1-1-1-10000000000000000−3−333−3−3330000
χ23222222-12-1-1-1222-1-2-222-1-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-211-2-211111122-1-1-1-1111100000022-2-2000000-1-1-1-111110000
χ24222222-12-1-1-1222-1-2-222-1-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-211-2-211111122-1-1-1-11111000000-2-2220000001111-1-1-1-10000
χ25222222-12-1-1-1222-1-2-2-2-2-1-122-1-1-1-1-1-1-1-2-2-2-211112-1-122-1-1-1-111-2-211111111000000000000000033−3−3−3−3330000
χ26222222-12-1-1-1222-1-2-2-2-2-1-122-1-1-1-1-1-1-1-2-2-2-211112-1-122-1-1-1-111-2-2111111110000000000000000−3−33333−3−30000
χ272222-2-2222222222002-2-2-2-2-22-2-2-2-222000022-2-2000000000002-222-2-20000002-2000000002-22-2000000000000
χ282222-2-2222222222002-2-2-2-2-22-2-2-2-222000022-2-2000000000002-222-2-2000000-2200000000-22-22000000000000
χ292222-2-222222222200-22-2-2-2-22-2-2-2-2220000-2-22200000000000-22-2-22200002-200220000-2-20000000000000000
χ302222-2-222222222200-22-2-2-2-22-2-2-2-2220000-2-22200000000000-22-2-2220000-2200-2-20000220000000000000000
χ312222-2-22-1222-1-1-1-1002-2-2-211-11111-1-1−i3−i3i3i322-2-2000−i3i3−i3−i3i3i300-11-1-111−i3−i3i3i3002-2−i3i30000i3−i3-11-11000000000000
χ322222-2-22-1222-1-1-1-1002-2-2-211-11111-1-1−i3−i3i3i322-2-2000−i3i3−i3−i3i3i300-11-1-111−i3−i3i3i300-22i3−i30000−i3i31-11-1000000000000
χ332222-2-22-1222-1-1-1-1002-2-2-211-11111-1-1i3i3−i3−i322-2-2000i3−i3i3i3−i3−i300-11-1-111i3i3−i3−i3002-2i3−i30000−i3i3-11-11000000000000
χ342222-2-22-1222-1-1-1-1002-2-2-211-11111-1-1i3i3−i3−i322-2-2000i3−i3i3i3−i3−i300-11-1-111i3i3−i3−i300-22−i3i30000i3−i31-11-1000000000000
χ352222-2-22-1222-1-1-1-100-22-2-211-11111-1-1−i3−i3i3i3-2-222000i3−i3i3i3−i3−i3001-111-1-1−i3−i3i3i32-200-1-1000011−i3i3i3−i3000000000000
χ362222-2-22-1222-1-1-1-100-22-2-211-11111-1-1−i3−i3i3i3-2-222000i3−i3i3i3−i3−i3001-111-1-1−i3−i3i3i3-2200110000-1-1i3−i3−i3i3000000000000
χ372222-2-22-1222-1-1-1-100-22-2-211-11111-1-1i3i3−i3−i3-2-222000−i3i3−i3−i3i3i3001-111-1-1i3i3−i3−i32-200-1-1000011i3−i3−i3i3000000000000
χ382222-2-22-1222-1-1-1-100-22-2-211-11111-1-1i3i3−i3−i3-2-222000−i3i3−i3−i3i3i3001-111-1-1i3i3−i3−i3-2200110000-1-1−i3i3i3−i3000000000000
χ3922-2-2-22222-2-22-2-222i−2i002-22-2222-2-2-2-22i−2i2i−2i00000000000002i−2i0000002i−2i2i−2i000000−i2i22−2000000−i2i2−i2i22−22−20000
χ4022-2-2-22222-2-22-2-222i−2i002-22-2222-2-2-2-22i−2i2i−2i00000000000002i−2i0000002i−2i2i−2i000000i2−i2−22000000i2−i2i2−i2−22−220000
χ4122-2-2-22222-2-22-2-22−2i2i002-22-2222-2-2-2-2−2i2i−2i2i0000000000000−2i2i000000−2i2i−2i2i000000−i2i2−22000000−i2i2−i2i2−22−220000
χ4222-2-2-22222-2-22-2-22−2i2i002-22-2222-2-2-2-2−2i2i−2i2i0000000000000−2i2i000000−2i2i−2i2i000000i2−i22−2000000i2−i2i2−i22−22−20000
χ4322-2-2-22-12-1112-2-2-12i−2i00-112-2-1-1-111112i−2i2i−2i3−33−30−i3i300−i3i3−i3i3−ii003−33−3−ii−ii000000−i2i22−2000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ4422-2-2-22-12-1112-2-2-12i−2i00-112-2-1-1-111112i−2i2i−2i3−33−30−i3i300−i3i3−i3i3−ii003−33−3−ii−ii000000i2−i2−22000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ4522-2-2-22-12-1112-2-2-12i−2i00-112-2-1-1-111112i−2i2i−2i−33−330i3−i300i3−i3i3−i3−ii00−33−33−ii−ii000000−i2i22−2000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ4622-2-2-22-12-1112-2-2-12i−2i00-112-2-1-1-111112i−2i2i−2i−33−330i3−i300i3−i3i3−i3−ii00−33−33−ii−ii000000i2−i2−22000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ4722-2-2-22-12-1112-2-2-1−2i2i00-112-2-1-1-11111−2i2i−2i2i3−33−30i3−i300i3−i3i3−i3i−i003−33−3i−ii−i000000−i2i2−22000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ4822-2-2-22-12-1112-2-2-1−2i2i00-112-2-1-1-11111−2i2i−2i2i3−33−30i3−i300i3−i3i3−i3i−i003−33−3i−ii−i000000i2−i22−2000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ4922-2-2-22-12-1112-2-2-1−2i2i00-112-2-1-1-11111−2i2i−2i2i−33−330−i3i300−i3i3−i3i3i−i00−33−33i−ii−i000000−i2i2−22000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ5022-2-2-22-12-1112-2-2-1−2i2i00-112-2-1-1-11111−2i2i−2i2i−33−330−i3i300−i3i3−i3i3i−i00−33−33i−ii−i000000i2−i22−2000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ51444444-2-2-2-2-2-2-2-214444-2-2-2-21111111-2-2-2-2-2-2-2-24-2-2-2-21111-2-2-2-2111111110000000000000000000000000000
χ52444444-2-2-2-2-2-2-2-2144-4-4-2-2-2-21111111-2-2-2-22222-42222-1-1-1-1-2-222-1-1-1-111110000000000000000000000000000
χ53444444-2-2-2-2-2-2-2-21-4-444-2-2-2-211111112222-2-2-2-2-42222-1-1-1-122-2-21111-1-1-1-10000000000000000000000000000
χ54444444-2-2-2-2-2-2-2-21-4-4-4-4-2-2-2-21111111222222224-2-2-2-211112222-1-1-1-1-1-1-1-10000000000000000000000000000
χ554444-4-4-24-2-2-2444-2004-422-4-4-22222-2-20000-2-222000000000004-4-2-22200000000000000000000000000000000
χ564444-4-4-24-2-2-2444-200-4422-4-4-22222-2-2000022-2-200000000000-4422-2-200000000000000000000000000000000
χ574444-4-4-2-2-2-2-2-2-2-21004-422221-1-1-1-111−2i3−2i32i32i3-2-222000−2i32i3i3i3−i3−i300-2211-1-1i3i3−i3−i30000000000000000000000000000
χ584444-4-4-2-2-2-2-2-2-2-21004-422221-1-1-1-1112i32i3−2i3−2i3-2-2220002i3−2i3−i3−i3i3i300-2211-1-1−i3−i3i3i30000000000000000000000000000
χ594444-4-4-2-2-2-2-2-2-2-2100-4422221-1-1-1-111−2i3−2i32i32i322-2-20002i3−2i3−i3−i3i3i3002-2-1-111i3i3−i3−i30000000000000000000000000000
χ604444-4-4-2-2-2-2-2-2-2-2100-4422221-1-1-1-1112i32i3−2i3−2i322-2-2000−2i32i3i3i3−i3−i3002-2-1-111−i3−i3i3i30000000000000000000000000000
χ6144-4-44-4444-4-44-4-440000-44-444-4-444-4-4000000000000000000000000000000000000000000000000000000000
χ6244-4-44-44-24-4-4-222-20000-442-2-222-2-22223−23−232300000000000000000000023−23−23230000000000000000000000000000
χ6344-4-44-44-24-4-4-222-20000-442-2-222-2-222−232323−23000000000000000000000−232323−230000000000000000000000000000
χ6444-4-44-4-24-2224-4-4-200002-2-44-222-2-222000023−23−2323000000000000023−23−232300000000000000000000000000000000
χ6544-4-44-4-24-2224-4-4-200002-2-44-222-2-2220000−232323−230000000000000−232323−2300000000000000000000000000000000
χ6644-4-44-4-2-2-222-222100002-22-21-1-111-1-123−23−232323−23−232300000-333-30000−333−3−333−30000000000000000000000000000
χ6744-4-44-4-2-2-222-222100002-22-21-1-111-1-123−23−2323−232323−23000003-3-3300003−3−33−333−30000000000000000000000000000
χ6844-4-44-4-2-2-222-222100002-22-21-1-111-1-1−232323−2323−23−2323000003-3-330000−333−33−3−330000000000000000000000000000
χ6944-4-44-4-2-2-222-222100002-22-21-1-111-1-1−232323−23−232323−2300000-333-300003−3−333−3−330000000000000000000000000000
χ7044-4-4-444-24-4-4-222-24i−4i004-4-22-2-2-22222−2i2i−2i2i00000000000004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ7144-4-4-444-24-4-4-222-2−4i4i004-4-22-2-2-222222i−2i2i−2i0000000000000−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ7244-4-4-44-2-2-222-22214i−4i00-22-22111-1-1-1-1−2i2i−2i2i23−2323−230−2i32i300i3−i3i3−i3−2i2i00−33−33i−ii−i0000000000000000000000000000
χ7344-4-4-44-2-2-222-22214i−4i00-22-22111-1-1-1-1−2i2i−2i2i−2323−232302i3−2i300−i3i3−i3i3−2i2i003−33−3i−ii−i0000000000000000000000000000
χ7444-4-4-44-2-2-222-2221−4i4i00-22-22111-1-1-1-12i−2i2i−2i23−2323−2302i3−2i300−i3i3−i3i32i−2i00−33−33−ii−ii0000000000000000000000000000
χ7544-4-4-44-2-2-222-2221−4i4i00-22-22111-1-1-1-12i−2i2i−2i−2323−23230−2i32i300i3−i3i3−i32i−2i003−33−3−ii−ii0000000000000000000000000000
χ764-44-40044-44-4-44-4400000000-400004-400000000000000000000000000000000000000000000000000000002i−2i
χ774-44-40044-44-4-44-4400000000-400004-40000000000000000000000000000000000000000000000000000000−2i2i
χ784-4-440044-4-44-4-44400000000-40000-44000000000000000000000000000000000000000000000000000002-200
χ794-4-440044-4-44-4-44400000000-40000-4400000000000000000000000000000000000000000000000000000-2200
χ808-88-8008-4-88-84-44-40000000040000-44000000000000000000000000000000000000000000000000000000000
χ818-88-800-484-44-88-8-40000000040000-44000000000000000000000000000000000000000000000000000000000
χ828-88-800-4-44-444-44200000000-26-66-62-2000000000000000000000000000000000000000000000000000000000
χ838-88-800-4-44-444-44200000000-2-66-662-2000000000000000000000000000000000000000000000000000000000
χ848-8-88008-4-8-8844-4-400000000400004-4000000000000000000000000000000000000000000000000000000000
χ858-8-8800-4844-4-8-88-400000000400004-4000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4-444-444-4200000000-26-6-66-22000000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-444-444-4200000000-2-666-6-22000000000000000000000000000000000000000000000000000000000

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