Finite Group Databasebeta

← Group #10694752

Character table — Group #10694752

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444444466612121212446688888888121212121212121212122424242424242424242424242424242488882424242424242424888888882244
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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-11
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-11-1
χ9111111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-1
χ10111111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111
χ11111111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111
χ12111111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-1
χ13111111111-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iiiii−i−i−i−iii1-1-11
χ14111111111-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iii−i−iiiii−i−i-111-1
χ15111111111-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−iii−i−i−i−iii-111-1
χ16111111111-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ172222222-2-22222-2-22222222-2-22200000000-2-222-2-2-2-2-2-2000000000000000000000000000000002-22-20000
χ182222222-2-22222-2-22222222-2-22200000000-2-222-2-2-2-2-2-200000000000000000000000000000000-22-220000
χ192222222-2-2-2-2-2-222222-2-2-2-22-22200000000-2-2-2-22222-2-2000000000000000000000000000000002i−2i−2i2i0000
χ202222222-2-2-2-2-2-222222-2-2-2-22-22200000000-2-2-2-22222-2-200000000000000000000000000000000−2i2i2i−2i0000
χ21222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ23222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ24222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ25222222-122-2-2-2-2-2-2-1-1-11111-22-1-12222-2-2-2-2-1-1111111-1-1-1-1-1-1-1-1-1-1111111112i−2i2i−2i−i−iii−i−iii000000000000
χ26222222-122-2-2-2-2-2-2-1-1-11111-22-1-12222-2-2-2-2-1-1111111-1-1-1-1-1-1-1-1-1-111111111−2i2i−2i2iii−i−iii−i−i000000000000
χ27222222-122-2-2-2-2-2-2-1-1-11111-22-1-1-2-2-2-22222-1-1111111-1-111111111-1-1-1-1-1-1-1-12i−2i−2i2i−i−iiiii−i−i000000000000
χ28222222-122-2-2-2-2-2-2-1-1-11111-22-1-1-2-2-2-22222-1-1111111-1-111111111-1-1-1-1-1-1-1-1−2i2i2i−2iii−i−i−i−iii000000000000
χ292222-2-222222-2-2-2-222222222-2-2-222-2-222-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ302222-2-222222-2-2-2-222222222-2-2-2-2-222-2-222-2-2-2-222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ312222-2-2222-2-22222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ322222-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ332222-2-22-2-222-2-2222222222-22-2-20000000022-2-2-2-222-2-200000000000000000000000000002-22-200000000
χ342222-2-22-2-222-2-2222222222-22-2-20000000022-2-2-2-222-2-20000000000000000000000000000-22-2200000000
χ352222-2-22-2-2-2-222-2-2222-2-2-2-222-2-200000000222222-2-2-2-200000000000000000000000000002i−2i−2i2i00000000
χ362222-2-22-2-2-2-222-2-2222-2-2-2-222-2-200000000222222-2-2-2-20000000000000000000000000000−2i2i2i−2i00000000
χ372222-2-2-12222-2-2-2-2-1-1-1-1-1-1-12-21122-2-222-2-21111-1-111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ382222-2-2-12222-2-2-2-2-1-1-1-1-1-1-12-21122-2-222-2-21111-1-111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ392222-2-2-12222-2-2-2-2-1-1-1-1-1-1-12-211-2-222-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ402222-2-2-12222-2-2-2-2-1-1-1-1-1-1-12-211-2-222-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ412222-2-2-122-2-22222-1-1-11111-2-21122-2-2-2-22211-1-111-1-1-1-1-1-1-1-111111111-1-1-1-100003−3−333−3−33000000000000
χ422222-2-2-122-2-22222-1-1-11111-2-21122-2-2-2-22211-1-111-1-1-1-1-1-1-1-111111111-1-1-1-10000−333−3−333−3000000000000
χ432222-2-2-122-2-22222-1-1-11111-2-211-2-22222-2-211-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111100003−3−33−333−3000000000000
χ442222-2-2-122-2-22222-1-1-11111-2-211-2-22222-2-211-1-111-1-1-1-11111-1-1-1-1-1-1-1-111110000−333−33−3−33000000000000
χ45444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-4-2-20000000022-2-22222220000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-4-444-2-2-222224-4-2-2000000002222-2-2-2-2220000000000000000000000000000000000000000
χ474444-4-4-2-4-444-4-444-2-2-2-2-2-2-2-442200000000-2-22222-2-2220000000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-444-4-4-2-2-22222442200000000-2-2-2-2-2-222220000000000000000000000000000000000000000
χ4944-4-40040000004i−4i4-4-4000000000022−22−2i22i2000000004i−4i0000002222−22−22−2i2−2i22i22i20000000000000000000000000000
χ5044-4-40040000004i−4i4-4-40000000000−22222i2−2i2000000004i−4i000000−22−2222222i22i2−2i2−2i20000000000000000000000000000
χ5144-4-4004000000−4i4i4-4-4000000000022−222i2−2i200000000−4i4i0000002222−22−222i22i2−2i2−2i20000000000000000000000000000
χ5244-4-4004000000−4i4i4-4-40000000000−2222−2i22i200000000−4i4i000000−22−222222−2i2−2i22i22i20000000000000000000000000000
χ5344-4-400-20000004i−4i-222−2i3−2i32i32i300000022−22−2i22i20023−230000−2i2i0066−6−6−2−222i2i2−i2−i2i6i6−i6−i6000000000000000000000000
χ5444-4-400-20000004i−4i-222−2i3−2i32i32i3000000−22222i2−2i20023−230000−2i2i00−6−66622−2−2−i2−i2i2i2−i6−i6i6i6000000000000000000000000
χ5544-4-400-20000004i−4i-2222i32i3−2i3−2i300000022−22−2i22i200−23230000−2i2i00−6−666−2−222i2i2−i2−i2−i6−i6i6i6000000000000000000000000
χ5644-4-400-20000004i−4i-2222i32i3−2i3−2i3000000−22222i2−2i200−23230000−2i2i0066−6−622−2−2−i2−i2i2i2i6i6−i6−i6000000000000000000000000
χ5744-4-400-2000000−4i4i-222−2i3−2i32i32i300000022−222i2−2i200−232300002i−2i00−6−666−2−222−i2−i2i2i2i6i6−i6−i6000000000000000000000000
χ5844-4-400-2000000−4i4i-222−2i3−2i32i32i3000000−2222−2i22i200−232300002i−2i0066−6−622−2−2i2i2−i2−i2−i6−i6i6i6000000000000000000000000
χ5944-4-400-2000000−4i4i-2222i32i3−2i3−2i300000022−222i2−2i20023−2300002i−2i0066−6−6−2−222−i2−i2i2i2−i6−i6i6i6000000000000000000000000
χ6044-4-400-2000000−4i4i-2222i32i3−2i3−2i3000000−2222−2i22i20023−2300002i−2i00−6−66622−2−2i2i2−i2−i2i6i6−i6−i6000000000000000000000000
χ614-44-44-44004i−4i4i−4i00-44-44i−4i4i−4i004-400000000004i−4i0000000000000000000000000000000000000000000000
χ624-44-44-4400−4i4i−4i4i00-44-4−4i4i−4i4i004-40000000000−4i4i0000000000000000000000000000000000000000000000
χ634-44-44-4-2004i−4i4i−4i002-22−2i2i−2i2i00-220000000000−2i2i0000006−66−66−66−6i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ644-44-44-4-2004i−4i4i−4i002-22−2i2i−2i2i00-220000000000−2i2i000000−66−66−66−66−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ654-44-44-4-200−4i4i−4i4i002-222i−2i2i−2i00-2200000000002i−2i0000006−66−66−66−6−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ664-44-44-4-200−4i4i−4i4i002-222i−2i2i−2i00-2200000000002i−2i000000−66−66−66−66i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ674-44-4-444004i−4i−4i4i00-44-44i−4i4i−4i00-440000000000−4i4i0000000000000000000000000000000000000000000000
χ684-44-4-44400−4i4i4i−4i00-44-4−4i4i−4i4i00-4400000000004i−4i0000000000000000000000000000000000000000000000
χ694-44-4-44-2004i−4i−4i4i002-22−2i2i−2i2i002-200000000002i−2i0000006−66−6−66−66i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ704-44-4-44-2004i−4i−4i4i002-22−2i2i−2i2i002-200000000002i−2i000000−66−666−66−6−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ714-44-4-44-200−4i4i4i−4i002-222i−2i2i−2i002-20000000000−2i2i0000006−66−6−66−66−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ724-44-4-44-200−4i4i4i−4i002-222i−2i2i−2i002-20000000000−2i2i000000−66−666−66−6i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ734-4-440044-4000000-4-44000000000000004-4000000004-40000000000004-4-44000000000000000000000000
χ744-4-440044-4000000-4-4400000000000000-44000000004-4000000000000-444-4000000000000000000000000
χ754-4-44004-44000000-4-44000000004-400000000000000-444-4-44000000000000000000000000000000000000
χ764-4-44004-44000000-4-4400000000-4400000000000000-44-444-4000000000000000000000000000000000000
χ774-4-4400-24-400000022-223−23−232300000000004-4000023−2300-22000023−23−23230000-222-2000000000000000000000000
χ784-4-4400-24-400000022-223−23−23230000000000-44000023−2300-220000−232323−2300002-2-22000000000000000000000000
χ794-4-4400-24-400000022-2−232323−2300000000004-40000−232300-220000−232323−230000-222-2000000000000000000000000
χ804-4-4400-24-400000022-2−232323−230000000000-440000−232300-22000023−23−232300002-2-22000000000000000000000000
χ814-4-4400-2-4400000022-223−23−232300004-40000000000−2323002-2-222-20000−232323−230000000000000000000000000000
χ824-4-4400-2-4400000022-223−23−23230000-440000000000−2323002-22-2-22000023−23−23230000000000000000000000000000
χ834-4-4400-2-4400000022-2−232323−2300004-4000000000023−23002-2-222-2000023−23−23230000000000000000000000000000
χ844-4-4400-2-4400000022-2−232323−230000-44000000000023−23002-22-2-220000−232323−230000000000000000000000000000

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