Finite Group Databasebeta

← Group #10694749

Character table — Group #10694749

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order1222223444444446666666448888888812121212121212121212121224242424242424242424242424242424244466121212121212888888888888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9111111111-1-1-1-1-1-111111111-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−ii−ii−i
χ10111111111-1-1-1-1-1-111111111-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−ii−ii
χ11111111111-1-1-1-1-1-111111111-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−ii−ii
χ12111111111-1-1-1-1-1-111111111-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiii−ii−i
χ13111111111-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111ii−i−i−i−iiii−i−ii
χ14111111111-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111−i−iiiii−i−i−iii−i
χ15111111111-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1ii−i−i−i−iii−iii−i
χ16111111111-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1−i−iiiii−i−ii−i−ii
χ172222222-2-222-2-2222222222-2-200000000-2-22222-2-2-2-2-2-2000000000000000000000000000000002-22-20000
χ182222222-2-222-2-2222222222-2-200000000-2-22222-2-2-2-2-2-200000000000000000000000000000000-22-220000
χ192222222-2-2-2-222-2-22222222-2200000000-2-2-2-2-2-22222-2-2000000000000000000000000000000002i−2i−2i2i0000
χ202222222-2-2-2-222-2-22222222-2200000000-2-2-2-2-2-22222-2-200000000000000000000000000000000−2i2i2i−2i0000
χ21222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ23222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ24222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ25222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-111000000000000
χ26222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-1000000000000
χ27222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-12-2-22-1-11111-1-1000000000000
χ28222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1-222-211-1-1-1-111000000000000
χ292222-2-22222222-2-2-2-2-2-2222-2-222-2-222-2-2-2-222-2-222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ302222-2-22222222-2-2-2-2-2-2222-2-2-2-222-2-222-2-222-2-222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ312222-2-2222-2-2-2-222-2-2-2-2222-2222-2-2-2-222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ322222-2-2222-2-2-2-222-2-2-2-2222-22-2-22222-2-2-2-2-2-222-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ332222-2-22-2-222-2-2-2-2-2-2-2-222222000000002222-2-2-2-222-2-200000000000000000000000000002i−2i2i−2i00000000
χ342222-2-22-2-222-2-2-2-2-2-2-2-222222000000002222-2-2-2-222-2-20000000000000000000000000000−2i2i−2i2i00000000
χ352222-2-22-2-2-2-22222-2-2-2-22222-20000000022-2-22222-2-2-2-200000000000000000000000000002-2-2200000000
χ362222-2-22-2-2-2-22222-2-2-2-22222-20000000022-2-22222-2-2-2-20000000000000000000000000000-222-200000000
χ372222-2-2-1222222-2-21111-1-1-1-2-222-2-222-2-211-1-111-1-111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ382222-2-2-1222222-2-21111-1-1-1-2-222-2-222-2-211-1-111-1-111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ392222-2-2-1222222-2-21111-1-1-1-2-2-2-222-2-22211-1-111-1-111-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ402222-2-2-1222222-2-21111-1-1-1-2-2-2-222-2-22211-1-111-1-111-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ412222-2-2-122-2-2-2-2221111-1-1-1-2222-2-2-2-2221111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ422222-2-2-122-2-2-2-2221111-1-1-1-2222-2-2-2-2221111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ432222-2-2-122-2-2-2-2221111-1-1-1-22-2-22222-2-21111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i3000000000000
χ442222-2-2-122-2-2-2-2221111-1-1-1-22-2-22222-2-21111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i3000000000000
χ45444444-2-4-444-4-444-2-2-2-2-2-2-2-4-40000000022-2-2-2-22222220000000000000000000000000000000000000000
χ46444444-2-4-4-4-444-4-4-2-2-2-2-2-2-2-4400000000222222-2-2-2-2220000000000000000000000000000000000000000
χ474444-4-4-2-4-444-4-4-4-42222-2-2-24400000000-2-2-2-22222-2-2220000000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-444442222-2-2-24-400000000-2-222-2-2-2-222220000000000000000000000000000000000000000
χ4944-4-400400004i−4i0000004-4-4000022−2200−2i22i20000004i−4i000000002222−22−220000−2i2−2i22i22i2000000000000000000000000
χ5044-4-400400004i−4i0000004-4-40000−2222002i2−2i20000004i−4i00000000−22−22222200002i22i2−2i2−2i2000000000000000000000000
χ5144-4-40040000−4i4i0000004-4-4000022−22002i2−2i2000000−4i4i000000002222−22−2200002i22i2−2i2−2i2000000000000000000000000
χ5244-4-40040000−4i4i0000004-4-40000−222200−2i22i2000000−4i4i00000000−22−2222220000−2i2−2i22i22i2000000000000000000000000
χ5344-4-400-200004i−4i00−2i3−2i32i32i3-222000022−2200−2i22i2000000−2i2i23−2300i6i6−i6−i6−2−22266−6−6i2i2−i2−i2000000000000000000000000
χ5444-4-400-200004i−4i00−2i3−2i32i32i3-2220000−2222002i2−2i2000000−2i2i23−2300−i6−i6i6i622−2−2−6−666−i2−i2i2i2000000000000000000000000
χ5544-4-400-200004i−4i002i32i3−2i3−2i3-222000022−2200−2i22i2000000−2i2i−232300−i6−i6i6i6−2−222−6−666i2i2−i2−i2000000000000000000000000
χ5644-4-400-200004i−4i002i32i3−2i3−2i3-2220000−2222002i2−2i2000000−2i2i−232300i6i6−i6−i622−2−266−6−6−i2−i2i2i2000000000000000000000000
χ5744-4-400-20000−4i4i00−2i3−2i32i32i3-222000022−22002i2−2i20000002i−2i−232300i6i6−i6−i6−2−222−6−666−i2−i2i2i2000000000000000000000000
χ5844-4-400-20000−4i4i00−2i3−2i32i32i3-2220000−222200−2i22i20000002i−2i−232300−i6−i6i6i622−2−266−6−6i2i2−i2−i2000000000000000000000000
χ5944-4-400-20000−4i4i002i32i3−2i3−2i3-222000022−22002i2−2i20000002i−2i23−2300−i6−i6i6i6−2−22266−6−6−i2−i2i2i2000000000000000000000000
χ6044-4-400-20000−4i4i002i32i3−2i3−2i3-2220000−222200−2i22i20000002i−2i23−2300i6i6−i6−i622−2−2−6−666i2i2−i2−i2000000000000000000000000
χ614-44-40044-40000000000-44-40000004i−4i0000000000004-4000000004i−4i4i−4i0000000000000000000000000000
χ624-44-40044-40000000000-44-4000000−4i4i0000000000004-400000000−4i4i−4i4i0000000000000000000000000000
χ634-44-4004-440000000000-44-4004i−4i0000000000000000-444i−4i4i−4i000000000000000000000000000000000000
χ644-44-4004-440000000000-44-400−4i4i0000000000000000-44−4i4i−4i4i000000000000000000000000000000000000
χ654-44-400-24-4000000−2i32i3−2i32i32-220000004i−4i00−2i32i300000000-2200000000−2i2i−2i2i23−2323−23000000000000000000000000
χ664-44-400-24-4000000−2i32i3−2i32i32-22000000−4i4i00−2i32i300000000-22000000002i−2i2i−2i−2323−2323000000000000000000000000
χ674-44-400-24-40000002i3−2i32i3−2i32-220000004i−4i002i3−2i300000000-2200000000−2i2i−2i2i−2323−2323000000000000000000000000
χ684-44-400-24-40000002i3−2i32i3−2i32-22000000−4i4i002i3−2i300000000-22000000002i−2i2i−2i23−2323−23000000000000000000000000
χ694-44-400-2-44000000−2i32i3−2i32i32-22004i−4i0000002i3−2i3000000002-2−2i2i−2i2i23−2323−2300000000000000000000000000000000
χ704-44-400-2-44000000−2i32i3−2i32i32-2200−4i4i0000002i3−2i3000000002-22i−2i2i−2i−2323−232300000000000000000000000000000000
χ714-44-400-2-440000002i3−2i32i3−2i32-22004i−4i000000−2i32i3000000002-2−2i2i−2i2i−2323−232300000000000000000000000000000000
χ724-44-400-2-440000002i3−2i32i3−2i32-2200−4i4i000000−2i32i3000000002-22i−2i2i−2i23−2323−2300000000000000000000000000000000
χ734-4-444-44004i−4i004i−4i4-4-44-4-440000000000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ744-4-444-4400−4i4i00−4i4i4-4-44-4-44000000000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ754-4-444-4-2004i−4i004i−4i-222-222-2000000000000−2i2i−2i2i0000006−6−66−666−6i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ764-4-444-4-2004i−4i004i−4i-222-222-2000000000000−2i2i−2i2i000000−666−66−6−66−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ774-4-444-4-200−4i4i00−4i4i-222-222-20000000000002i−2i2i−2i0000006−6−66−666−6−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ784-4-444-4-200−4i4i00−4i4i-222-222-20000000000002i−2i2i−2i000000−666−66−6−66i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ794-4-44-444004i−4i00−4i4i-444-4-4-440000000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ804-4-44-44400−4i4i004i−4i-444-4-4-44000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ814-4-44-44-2004i−4i00−4i4i2-2-2222-2000000000000−2i2i2i−2i0000006−6−666−6−66i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ824-4-44-44-2004i−4i00−4i4i2-2-2222-2000000000000−2i2i2i−2i000000−666−6−666−6−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ834-4-44-44-200−4i4i004i−4i2-2-2222-20000000000002i−2i−2i2i0000006−6−666−6−66−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ844-4-44-44-200−4i4i004i−4i2-2-2222-20000000000002i−2i−2i2i000000−666−6−666−6i6−i6−i6i6i6−i6−i6i6000000000000000000000000

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