Finite Group Databasebeta

← Group #10694606

Character table — Group #10694606

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order1222223444444446661212121244668888888812121212121212121212242424242424242424242424242424242244666612121212444488888888
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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-1111111-1-1
χ91111-1-11-1-111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−ii−ii−i
χ101111-1-11-1-111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−ii−ii
χ111111-1-11-1-111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−iii−i−i−ii−ii
χ121111-1-11-1-111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iii−i−iiii−ii−i
χ131111-1-11-1-111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111ii−i−i−i−iiii−i−ii
χ141111-1-11-1-111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111−i−iiiii−i−i−iii−i
χ151111-1-11-1-111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1ii−i−i−i−iii−iii−i
χ161111-1-11-1-111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1−i−iiiii−i−ii−i−ii
χ17222222222-2-2-2-2-2-22222222-222200000000-2-2-2-2-2-222-2-2000000000000000000000000000000002i−2i2i−2i0000
χ18222222222-2-2-2-2-2-22222222-222200000000-2-2-2-2-2-222-2-200000000000000000000000000000000−2i2i−2i2i0000
χ192222222-2-22222-2-2222-2-2-2-2-2-22222-2-222-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ202222222-2-22222-2-2222-2-2-2-2-2-222-2-222-2-222-2-222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ212222222-2-2-2-2-2-222222-2-2-2-22-2220000000022-2-222-2-2-2-200000000000000000000000000002-22-200000000
χ222222222-2-2-2-2-2-222222-2-2-2-22-2220000000022-2-222-2-2-2-20000000000000000000000000000-22-2200000000
χ23222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ24222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ25222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111112-22-2-1-111-1-111000000000000
χ26222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-22-2211-1-111-1-1000000000000
χ27222222-1-2-22222-2-2-1-1-11111-2-2-1-122-2-222-2-211-1-11111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-1-2-22222-2-2-1-1-11111-2-2-1-122-2-222-2-211-1-11111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-1-2-22222-2-2-1-1-11111-2-2-1-1-2-222-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ30222222-1-2-22222-2-2-1-1-11111-2-2-1-1-2-222-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ312222-2-222222-2-2222222222-2-2-2-222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ322222-2-222222-2-2222222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ332222-2-2222-2-222-2-222222222-2-2-2000000002222-2-2-2-2-2-200000000000000000000000000002i−2i−2i2i00000000
χ342222-2-2222-2-222-2-222222222-2-2-2000000002222-2-2-2-2-2-20000000000000000000000000000−2i2i2i−2i00000000
χ352222-2-22-2-2-2-22222222-2-2-2-2-22-2-200000000-2-2222222-2-2000000000000000000000000000000002-2-220000
χ362222-2-22-2-2-2-22222222-2-2-2-2-22-2-200000000-2-2222222-2-200000000000000000000000000000000-222-20000
χ372222-2-2-12222-2-222-1-1-1-1-1-1-1-2-21122-2-2-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ382222-2-2-12222-2-222-1-1-1-1-1-1-1-2-21122-2-2-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ392222-2-2-12222-2-222-1-1-1-1-1-1-1-2-211-2-22222-2-21111-1-111-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i3000000000000
χ402222-2-2-12222-2-222-1-1-1-1-1-1-1-2-211-2-22222-2-21111-1-111-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i3000000000000
χ412222-2-2-1-2-222-2-2-2-2-1-1-1111122112222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ422222-2-2-1-2-222-2-2-2-2-1-1-1111122112222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ432222-2-2-1-2-222-2-2-2-2-1-1-111112211-2-2-2-22222-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-12-2-22-1-11111-1-1000000000000
χ442222-2-2-1-2-222-2-2-2-2-1-1-111112211-2-2-2-22222-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-222-211-1-1-1-111000000000000
χ45444444-244-4-4-4-4-4-4-2-2-2-2-2-2-2-44-2-200000000222222-2-2220000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-4-444-2-2-222224-4-2-200000000-2-222-2-222220000000000000000000000000000000000000000
χ474444-4-4-244-4-444-4-4-2-2-2-2-2-2-24-42200000000-2-2-2-22222220000000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-44444-2-2-22222-44220000000022-2-2-2-2-2-2220000000000000000000000000000000000000000
χ4944-4-400400004i−4i004-4-4000000000022−2200−2i22i2004i−4i00000000002222−22−220000−2i2−2i22i22i2000000000000000000000000
χ5044-4-400400004i−4i004-4-40000000000−2222002i2−2i2004i−4i0000000000−22−22222200002i22i2−2i2−2i2000000000000000000000000
χ5144-4-40040000−4i4i004-4-4000000000022−22002i2−2i200−4i4i00000000002222−22−2200002i22i2−2i2−2i2000000000000000000000000
χ5244-4-40040000−4i4i004-4-40000000000−222200−2i22i200−4i4i0000000000−22−2222220000−2i2−2i22i22i2000000000000000000000000
χ5344-4-400-200004i−4i00-2222323−23−2300000022−2200−2i22i2−2i32i3−2i2i000000i6i6−i6−i6−2−22266−6−6i2i2−i2−i2000000000000000000000000
χ5444-4-400-200004i−4i00-2222323−23−23000000−2222002i2−2i2−2i32i3−2i2i000000−i6−i6i6i622−2−2−6−666−i2−i2i2i2000000000000000000000000
χ5544-4-400-200004i−4i00-222−23−23232300000022−2200−2i22i22i3−2i3−2i2i000000−i6−i6i6i6−2−222−6−666i2i2−i2−i2000000000000000000000000
χ5644-4-400-200004i−4i00-222−23−232323000000−2222002i2−2i22i3−2i3−2i2i000000i6i6−i6−i622−2−266−6−6−i2−i2i2i2000000000000000000000000
χ5744-4-400-20000−4i4i00-2222323−23−2300000022−22002i2−2i22i3−2i32i−2i000000−i6−i6i6i6−2−22266−6−6−i2−i2i2i2000000000000000000000000
χ5844-4-400-20000−4i4i00-2222323−23−23000000−222200−2i22i22i3−2i32i−2i000000i6i6−i6−i622−2−2−6−666i2i2−i2−i2000000000000000000000000
χ5944-4-400-20000−4i4i00-222−23−23232300000022−22002i2−2i2−2i32i32i−2i000000i6i6−i6−i6−2−222−6−666−i2−i2i2i2000000000000000000000000
χ6044-4-400-20000−4i4i00-222−23−232323000000−222200−2i22i2−2i32i32i−2i000000−i6−i6i6i622−2−266−6−6i2i2−i2−i2000000000000000000000000
χ614-44-40044i−4i4-4004i−4i-44-44i−4i4i−4i00000000000000004i−4i004-40000000000000000000000000000000000000000
χ624-44-40044i−4i-4400−4i4i-44-44i−4i4i−4i0000000000000000−4i4i00-440000000000000000000000000000000000000000
χ634-44-4004−4i4i4-400−4i4i-44-4−4i4i−4i4i0000000000000000−4i4i004-40000000000000000000000000000000000000000
χ644-44-4004−4i4i-44004i−4i-44-4−4i4i−4i4i00000000000000004i−4i00-440000000000000000000000000000000000000000
χ654-44-400-24i−4i4-4004i−4i2-22−2i2i−2i2i0000000000000000−2i2i00-22−2i32i3−2i32i30000000023−2323−23000000000000000000000000
χ664-44-400-24i−4i4-4004i−4i2-22−2i2i−2i2i0000000000000000−2i2i00-222i3−2i32i3−2i300000000−2323−2323000000000000000000000000
χ674-44-400-24i−4i-4400−4i4i2-22−2i2i−2i2i00000000000000002i−2i002-20000−2i32i3−2i32i323−2323−230000000000000000000000000000
χ684-44-400-24i−4i-4400−4i4i2-22−2i2i−2i2i00000000000000002i−2i002-200002i3−2i32i3−2i3−2323−23230000000000000000000000000000
χ694-44-400-2−4i4i4-400−4i4i2-222i−2i2i−2i00000000000000002i−2i00-22−2i32i3−2i32i300000000−2323−2323000000000000000000000000
χ704-44-400-2−4i4i4-400−4i4i2-222i−2i2i−2i00000000000000002i−2i00-222i3−2i32i3−2i30000000023−2323−23000000000000000000000000
χ714-44-400-2−4i4i-44004i−4i2-222i−2i2i−2i0000000000000000−2i2i002-20000−2i32i3−2i32i3−2323−23230000000000000000000000000000
χ724-44-400-2−4i4i-44004i−4i2-222i−2i2i−2i0000000000000000−2i2i002-200002i3−2i32i3−2i323−2323−230000000000000000000000000000
χ734-4-444-4400000000-4-440000004-422−220022−2200000000000022−22−2222000022−22−22220000000000000000000000000000
χ744-4-444-4400000000-4-440000004-4−222200−2222000000000000−222222−220000−222222−220000000000000000000000000000
χ754-4-444-4-20000000022-2−2i32i32i3−2i300-2222−220022−2200000000−2i32i300−222−2−i6i6i6−i6−222−2−i6i6i6−i6000000000000000000000000
χ764-4-444-4-20000000022-2−2i32i32i3−2i300-22−222200−222200000000−2i32i3002−2−22i6−i6−i6i62−2−22i6−i6−i6i6000000000000000000000000
χ774-4-444-4-20000000022-22i3−2i3−2i32i300-2222−220022−22000000002i3−2i300−222−2i6−i6−i6i6−222−2i6−i6−i6i6000000000000000000000000
χ784-4-444-4-20000000022-22i3−2i3−2i32i300-22−222200−2222000000002i3−2i3002−2−22−i6i6i6−i62−2−22−i6i6i6−i6000000000000000000000000
χ794-4-44-44400000000-4-44000000-4422−2200−222200000000000022−22−22220000−222222−220000000000000000000000000000
χ804-4-44-44400000000-4-44000000-44−22220022−22000000000000−222222−22000022−22−22220000000000000000000000000000
χ814-4-44-44-20000000022-2−2i32i32i3−2i3002-222−2200−2222000000002i3−2i300−222−2i6−i6−i6i62−2−22−i6i6i6−i6000000000000000000000000
χ824-4-44-44-20000000022-2−2i32i32i3−2i3002-2−22220022−22000000002i3−2i3002−2−22−i6i6i6−i6−222−2i6−i6−i6i6000000000000000000000000
χ834-4-44-44-20000000022-22i3−2i3−2i32i3002-222−2200−222200000000−2i32i300−222−2−i6i6i6−i62−2−22i6−i6−i6i6000000000000000000000000
χ844-4-44-44-20000000022-22i3−2i3−2i32i3002-2−22220022−2200000000−2i32i3002−2−22i6−i6−i6i6−222−2−i6i6i6−i6000000000000000000000000

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