Finite Group Databasebeta

← Group #10706166

Character table — Group #10706166

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order1222344444466688881212121224446688888812121212121212121212242424242424242424242424242424248888242424242424242416161616161616164444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-1111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1
χ6111111111-1-1111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111
χ7111111111-1-1111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ8111111111-1-1111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ911111-1-11111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-111-1-11-11-1
χ1011111-1-11111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1-1-111-1-111-11-11
χ1111111-1-11111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-11111-1-111-1-1-11-11
χ1211111-1-11111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111-1-1111-11-1
χ1311111-1-111-1-1111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiiii−i−i−i−iii1-1-11
χ1411111-1-111-1-1111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iii−i−iiiii−i−i-111-1
χ1511111-1-111-1-1111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−iii−i−i−i−iii-111-1
χ1611111-1-111-1-1111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ1722222222222222-2-2-2-22222222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ18222222222-2-22222222-2-2-2-2-2-22-2-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ192222222-2-22222200002222-2-2-22-2-200000022-2-222-2-2-2-200000000000000000000000000002−22−22−22−20000
χ202222222-2-22222200002222-2-2-22-2-200000022-2-222-2-2-2-20000000000000000000000000000−22−22−22−220000
χ212222222-2-2-2-22220000-2-2-2-222-2-22200000022-2-2-2-222-2-20000000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ222222222-2-2-2-22220000-2-2-2-222-2-22200000022-2-2-2-222-2-20000000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ2322222-2-22222222-2-2-2-222222-2-2-222-2-22222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ2422222-2-222-2-22222222-2-2-2-2-22-22-2-2-2-222-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2522222-2-2-2-22222200002222-222-2-2-2000000-2-222-2-222-2-200000000000000000000000000002−2−222−2−220000
χ2622222-2-2-2-22222200002222-222-2-2-2000000-2-222-2-222-2-20000000000000000000000000000−222−2−222−20000
χ2722222-2-2-2-2-2-22220000-2-2-2-22-22222000000-2-22222-2-2-2-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ2822222-2-2-2-2-2-22220000-2-2-2-22-22222000000-2-22222-2-2-2-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ292222-1222222-1-1-12222-1-1-1-12222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ302222-1222222-1-1-12222-1-1-1-12222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ312222-1222222-1-1-1-2-2-2-2-1-1-1-12222-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ322222-1222222-1-1-1-2-2-2-2-1-1-1-12222-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ332222-12222-2-2-1-1-122221111-2-22-211-2-2-2-222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100003−33−3−33−33000000000000
χ342222-12222-2-2-1-1-122221111-2-22-211-2-2-2-222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-10000−33−333−33−3000000000000
χ352222-12222-2-2-1-1-1-2-2-2-21111-2-22-2112222-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111112i2i−2i−2i−i−i−i−iiiii000000000000
χ362222-12222-2-2-1-1-1-2-2-2-21111-2-22-2112222-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111−2i−2i2i2iiiii−i−i−i−i000000000000
χ372222-1-2-22222-1-1-12222-1-1-1-12-2-2-2-1-122-2-2-2-211111111-1-1-1-1-1-11111-1-1-1-111112-22-2-1-111-1-111000000000000
χ382222-1-2-22222-1-1-12222-1-1-1-12-2-2-2-1-122-2-2-2-211111111-1-1-1-1-1-11111-1-1-1-11111-22-2211-1-111-1-1000000000000
χ392222-1-2-22222-1-1-1-2-2-2-2-1-1-1-12-2-2-2-1-1-2-2222211111111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ402222-1-2-22222-1-1-1-2-2-2-2-1-1-1-12-2-2-2-1-1-2-2222211111111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ412222-1-2-222-2-2-1-1-122221111-22-2211-2-222-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100003−3−33−333−3000000000000
χ422222-1-2-222-2-2-1-1-122221111-22-2211-2-222-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000−333−33−3−33000000000000
χ432222-1-2-222-2-2-1-1-1-2-2-2-21111-22-221122-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-12i−2i−2i2i−i−iiiii−i−i000000000000
χ442222-1-2-222-2-2-1-1-1-2-2-2-21111-22-221122-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−2i2i2i−2iii−i−i−i−iii000000000000
χ454444-244-4-444-2-2-20000-2-2-2-2-4-4-4422000000-2-222-2-222220000000000000000000000000000000000000000
χ464444-244-4-4-4-4-2-2-20000222244-4-4-2-2000000-2-22222-2-2220000000000000000000000000000000000000000
χ474444-2-4-4-4-444-2-2-20000-2-2-2-2-444-42200000022-2-222-2-2220000000000000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-2000022224-444-2-200000022-2-2-2-222220000000000000000000000000000000000000000
χ4944-4-444-400004-4-42222−22−220000000000000022−224-400000000000000002222−22−222222−22−22000000000000000000000000
χ5044-4-444-400004-4-4−22−22222200000000000000−22224-40000000000000000−22−222222−22−222222000000000000000000000000
χ5144-4-44-4400004-4-42222−22−2200000000000000−2222-4400000000000000002222−22−22−22−222222000000000000000000000000
χ5244-4-44-4400004-4-4−22−2222220000000000000022−22-440000000000000000−22−2222222222−22−22000000000000000000000000
χ5344-4-4-24-40000-2222222−22−222323−23−23000000000022−22-220023−23000066−6−666−6−6−2−222−2−222000000000000000000000000
χ5444-4-4-24-40000-2222222−22−22−23−232323000000000022−22-2200−23230000−6−666−6−666−2−222−2−222000000000000000000000000
χ5544-4-4-24-40000-222−22−2222222323−23−230000000000−2222-220023−230000−6−666−6−66622−2−222−2−2000000000000000000000000
χ5644-4-4-24-40000-222−22−222222−23−2323230000000000−2222-2200−2323000066−6−666−6−622−2−222−2−2000000000000000000000000
χ5744-4-4-2-440000-2222222−22−222323−23−230000000000−22222-200−2323000066−6−6−6−666−2−22222−2−2000000000000000000000000
χ5844-4-4-2-440000-2222222−22−22−23−2323230000000000−22222-20023−230000−6−66666−6−6−2−22222−2−2000000000000000000000000
χ5944-4-4-2-440000-222−22−2222222323−23−23000000000022−222-200−23230000−6−66666−6−622−2−2−2−222000000000000000000000000
χ6044-4-4-2-440000-222−22−222222−23−232323000000000022−222-20023−23000066−6−6−6−66622−2−2−2−222000000000000000000000000
χ614-44-4400004i−4i-44-4−2i22i2−2i22i24i−4i4i−4i00000022−220000000000000022−2222−220000−2i22i2−2i22i20000000000000000000000000000
χ624-44-4400004i−4i-44-42i2−2i22i2−2i24i−4i4i−4i000000−222200000000000000−2222−222200002i2−2i22i2−2i20000000000000000000000000000
χ634-44-440000−4i4i-44-4−2i22i2−2i22i2−4i4i−4i4i000000−222200000000000000−2222−22220000−2i22i2−2i22i20000000000000000000000000000
χ644-44-440000−4i4i-44-42i2−2i22i2−2i2−4i4i−4i4i00000022−220000000000000022−2222−2200002i2−2i22i2−2i20000000000000000000000000000
χ654-44-4-200004i−4i2-22−2i22i2−2i22i2−2i2i−2i2i00000022−22000000−2i32i30023−2300−22−22i6−i6i6−i6i2−i2i2−i26−66−6000000000000000000000000
χ664-44-4-200004i−4i2-22−2i22i2−2i22i2−2i2i−2i2i00000022−220000002i3−2i300−232300−22−22−i6i6−i6i6i2−i2i2−i2−66−66000000000000000000000000
χ674-44-4-200004i−4i2-222i2−2i22i2−2i2−2i2i−2i2i000000−2222000000−2i32i30023−23002−22−2−i6i6−i6i6−i2i2−i2i2−66−66000000000000000000000000
χ684-44-4-200004i−4i2-222i2−2i22i2−2i2−2i2i−2i2i000000−22220000002i3−2i300−2323002−22−2i6−i6i6−i6−i2i2−i2i26−66−6000000000000000000000000
χ694-44-4-20000−4i4i2-22−2i22i2−2i22i22i−2i2i−2i000000−2222000000−2i32i300−2323002−22−2−i6i6−i6i6i2−i2i2−i26−66−6000000000000000000000000
χ704-44-4-20000−4i4i2-22−2i22i2−2i22i22i−2i2i−2i000000−22220000002i3−2i30023−23002−22−2i6−i6i6−i6i2−i2i2−i2−66−66000000000000000000000000
χ714-44-4-20000−4i4i2-222i2−2i22i2−2i22i−2i2i−2i00000022−22000000−2i32i300−232300−22−22i6−i6i6−i6−i2i2−i2i2−66−66000000000000000000000000
χ724-44-4-20000−4i4i2-222i2−2i22i2−2i22i−2i2i−2i00000022−220000002i3−2i30023−2300−22−22−i6i6−i6i6−i2i2−i2i26−66−6000000000000000000000000
χ734-4-444004-400-4-4400000000000000004i−4i00000000004-400004i−4i−4i4i00000000000000000000000000000000
χ744-4-444004-400-4-440000000000000000−4i4i00000000004-40000−4i4i4i−4i00000000000000000000000000000000
χ754-4-44400-4400-4-444i−4i−4i4i000000000000000000000000-44000000004i−4i−4i4i0000000000000000000000000000
χ764-4-44400-4400-4-44−4i4i4i−4i000000000000000000000000-4400000000−4i4i4i−4i0000000000000000000000000000
χ774-4-44-2004-40022-20000−2i32i32i3−2i30000−2i32i3004i−4i0000000000-220000−2i2i2i−2i000023−23−2323000000000000000000000000
χ784-4-44-2004-40022-20000−2i32i32i3−2i30000−2i32i300−4i4i0000000000-2200002i−2i−2i2i0000−232323−23000000000000000000000000
χ794-4-44-2004-40022-200002i3−2i3−2i32i300002i3−2i3004i−4i0000000000-220000−2i2i2i−2i0000−232323−23000000000000000000000000
χ804-4-44-2004-40022-200002i3−2i3−2i32i300002i3−2i300−4i4i0000000000-2200002i−2i−2i2i000023−23−2323000000000000000000000000
χ814-4-44-200-440022-24i−4i−4i4i−2i32i32i3−2i300002i3−2i3000000000000002-223−23−23230000−2i2i2i−2i0000000000000000000000000000
χ824-4-44-200-440022-24i−4i−4i4i2i3−2i3−2i32i30000−2i32i3000000000000002-2−232323−230000−2i2i2i−2i0000000000000000000000000000
χ834-4-44-200-440022-2−4i4i4i−4i−2i32i32i3−2i300002i3−2i3000000000000002-2−232323−2300002i−2i−2i2i0000000000000000000000000000
χ844-4-44-200-440022-2−4i4i4i−4i2i3−2i3−2i32i30000−2i32i3000000000000002-223−23−232300002i−2i−2i2i0000000000000000000000000000

Here i is the imaginary unit (i² = −1).