Finite Group Databasebeta

← Group #10706292

Character table — Group #10706292

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122234444446668888121212122224666666888888121212121212242424242424242424242424242424248888242424242424242416161616161616162444
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
χ5111111111-1-1111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1111-1-1111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1-1-11
χ6111111111-1-1111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1111-1-1111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1
χ7111111111-1-1111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1111-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-111-1
χ8111111111-1-1111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1111-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1-1-11
χ9111111-1-111111111111111-11-1-1-1-111-1-111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-111-1-111-1-1
χ10111111-1-111111111111111-11-1-1-1-111-1-111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1-1-111-1-111-1-111
χ11111111-1-111111111111111-11-1-1-1-111-1-111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-11111-1-111-1-1-1-111
χ12111111-1-111111111111111-11-1-1-1-111-1-111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111-1-11111-1-1
χ13111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1-11111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiiii−i−i−i−iii1-11-1
χ14111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1-11111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iii−i−iiiii−i−i-11-11
χ15111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1-11111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−iii−i−i−i−iii-11-11
χ16111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1-11111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−i−iiiii−i−i1-11-1
χ1722222222222222-2-2-2-222222222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ18222222222-2-22222222-2-2-2-22-2-2-222-2-2-2-2-2-2-2-222222-2-22-2-2-2-2-2-2-2-222222222000000000000000000000000
χ19222222-2-2222222-2-2-2-22222-22-2-2-2-222-2-2-2-222222-2-2-2-22-2-2-2-22222-2-2-2-22222000000000000000000000000
χ20222222-2-22-2-22222222-2-2-2-2-2-222-2-2-2-222-2-222-2-22-2-2222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2122222-222-22222200002222-2-22-2-2-2-2-222000000-222-2-2-200000000000000000000000000002−22−22−22−20000
χ2222222-222-22222200002222-2-22-2-2-2-2-222000000-222-2-2-20000000000000000000000000000−22−22−22−220000
χ2322222-222-2-2-22220000-2-2-2-2-22-22-2-222-2-2000000-22222-20000000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ2422222-222-2-2-22220000-2-2-2-2-22-22-2-222-2-2000000-22222-20000000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ2522222-2-2-2-222222000022222-2-2222-2-2-2-2000000-2-2-222-200000000000000000000000000002−2−222−2−220000
χ2622222-2-2-2-222222000022222-2-2222-2-2-2-2000000-2-2-222-20000000000000000000000000000−222−2−222−20000
χ2722222-2-2-2-2-2-22220000-2-2-2-2222-2222222000000-2-2-2-2-2-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ2822222-2-2-2-2-2-22220000-2-2-2-2222-2222222000000-2-2-2-2-2-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ292222-1222222-1-1-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ302222-1222222-1-1-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ312222-1222222-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ322222-1222222-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ332222-12222-2-2-1-1-1222211112-2-2-2-1-11111-2-2-2-222-1-1-111-111111111-1-1-1-1-1-1-1-100003−33−3−33−33000000000000
χ342222-12222-2-2-1-1-1222211112-2-2-2-1-11111-2-2-2-222-1-1-111-111111111-1-1-1-1-1-1-1-10000−33−333−33−3000000000000
χ352222-12222-2-2-1-1-1-2-2-2-211112-2-2-2-1-111112222-2-2-1-1-111-1-1-1-1-1-1-1-1-1111111112i2i−2i−2i−i−i−i−iiiii000000000000
χ362222-12222-2-2-1-1-1-2-2-2-211112-2-2-2-1-111112222-2-2-1-1-111-1-1-1-1-1-1-1-1-111111111−2i−2i2i2iiiii−i−i−i−i000000000000
χ372222-12-2-2222-1-1-12222-1-1-1-1-22-2-211-1-11122-2-2-2-2-11111-1-1-1-1-11111-1-1-1-111112-22-2-1-111-1-111000000000000
χ382222-12-2-2222-1-1-12222-1-1-1-1-22-2-211-1-11122-2-2-2-2-11111-1-1-1-1-11111-1-1-1-11111-22-2211-1-111-1-1000000000000
χ392222-12-2-2222-1-1-1-2-2-2-2-1-1-1-1-22-2-211-1-111-2-22222-11111-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ402222-12-2-2222-1-1-1-2-2-2-2-1-1-1-1-22-2-211-1-111-2-22222-11111-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ412222-12-2-22-2-2-1-1-122221111-2-2221111-1-1-2-222-2-2-111-1-1-11111-1-1-1-1-1-1-1-1111100003−3−33−333−3000000000000
χ422222-12-2-22-2-2-1-1-122221111-2-2221111-1-1-2-222-2-2-111-1-1-11111-1-1-1-1-1-1-1-111110000−333−33−3−33000000000000
χ432222-12-2-22-2-2-1-1-1-2-2-2-21111-2-2221111-1-122-2-222-111-1-1-1-1-1-1-111111111-1-1-1-12i−2i−2i2i−i−iiiii−i−i000000000000
χ442222-12-2-22-2-2-1-1-1-2-2-2-21111-2-2221111-1-122-2-222-111-1-1-1-1-1-1-111111111-1-1-1-1−2i2i2i−2iii−i−i−i−iii000000000000
χ454444-2-444-444-2-2-20000-2-2-2-2-4-44-42222-2-20000002-2-22220000000000000000000000000000000000000000
χ464444-2-444-4-4-4-2-2-200002222-44-4422-2-2220000002-2-2-2-220000000000000000000000000000000000000000
χ474444-2-4-4-4-444-2-2-20000-2-2-2-24-4-44-2-22222000000222-2-220000000000000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-200002222444-4-2-2-2-2-2-20000002222220000000000000000000000000000000000000000
χ4944-4-4400004i−4i4-4-4−2i2−2i22i22i24i4i−4i−4i000000000022−2200000000002222−22−220000−2i2−2i22i22i20000000000000000000000000000
χ5044-4-4400004i−4i4-4-42i22i2−2i2−2i24i4i−4i−4i0000000000−22220000000000−22−22222200002i22i2−2i2−2i20000000000000000000000000000
χ5144-4-440000−4i4i4-4-4−2i2−2i22i22i2−4i−4i4i4i0000000000−22220000000000−22−2222220000−2i2−2i22i22i20000000000000000000000000000
χ5244-4-440000−4i4i4-4-42i22i2−2i2−2i2−4i−4i4i4i000000000022−2200000000002222−22−2200002i22i2−2i2−2i20000000000000000000000000000
χ5344-4-4-200004i−4i-222−2i2−2i22i22i2−2i−2i2i2i0000−2i32i3000022−22000000023−230−2−222i6i6−i6−i6i2i2−i2−i266−6−6000000000000000000000000
χ5444-4-4-200004i−4i-222−2i2−2i22i22i2−2i−2i2i2i00002i3−2i3000022−220000000−23230−2−222−i6−i6i6i6i2i2−i2−i2−6−666000000000000000000000000
χ5544-4-4-200004i−4i-2222i22i2−2i2−2i2−2i−2i2i2i0000−2i32i30000−2222000000023−23022−2−2−i6−i6i6i6−i2−i2i2i2−6−666000000000000000000000000
χ5644-4-4-200004i−4i-2222i22i2−2i2−2i2−2i−2i2i2i00002i3−2i30000−22220000000−2323022−2−2i6i6−i6−i6−i2−i2i2i266−6−6000000000000000000000000
χ5744-4-4-20000−4i4i-222−2i2−2i22i22i22i2i−2i−2i0000−2i32i30000−22220000000−2323022−2−2−i6−i6i6i6i2i2−i2−i266−6−6000000000000000000000000
χ5844-4-4-20000−4i4i-222−2i2−2i22i22i22i2i−2i−2i00002i3−2i30000−2222000000023−23022−2−2i6i6−i6−i6i2i2−i2−i2−6−666000000000000000000000000
χ5944-4-4-20000−4i4i-2222i22i2−2i2−2i22i2i−2i−2i0000−2i32i3000022−220000000−23230−2−222i6i6−i6−i6−i2−i2i2i2−6−666000000000000000000000000
χ6044-4-4-20000−4i4i-2222i22i2−2i2−2i22i2i−2i−2i00002i3−2i3000022−22000000023−230−2−222−i6−i6i6i6−i2−i2i2i266−6−6000000000000000000000000
χ614-44-4404i−4i000-44-422−2222−22000000000000000000−2i22i204i−4i0000000000022−2222−22−2i22i2−2i22i2000000000000000000000000
χ624-44-4404i−4i000-44-4−2222−22220000000000000000002i2−2i204i−4i00000000000−2222−22222i2−2i22i2−2i2000000000000000000000000
χ634-44-440−4i4i000-44-422−2222−220000000000000000002i2−2i20−4i4i0000000000022−2222−222i2−2i22i2−2i2000000000000000000000000
χ644-44-440−4i4i000-44-4−2222−2222000000000000000000−2i22i20−4i4i00000000000−2222−2222−2i22i2−2i22i2000000000000000000000000
χ654-44-4-204i−4i0002-2222−2222−2223−2323−2300000000−2i32i30000−2i22i20−2i2i0006−66−6i6−i6i6−i6−22−22i2−i2i2−i2000000000000000000000000
χ664-44-4-204i−4i0002-2222−2222−22−2323−2323000000002i3−2i30000−2i22i20−2i2i000−66−66−i6i6−i6i6−22−22i2−i2i2−i2000000000000000000000000
χ674-44-4-204i−4i0002-22−2222−222223−2323−2300000000−2i32i300002i2−2i20−2i2i000−66−66−i6i6−i6i62−22−2−i2i2−i2i2000000000000000000000000
χ684-44-4-204i−4i0002-22−2222−2222−2323−2323000000002i3−2i300002i2−2i20−2i2i0006−66−6i6−i6i6−i62−22−2−i2i2−i2i2000000000000000000000000
χ694-44-4-20−4i4i0002-2222−2222−2223−2323−23000000002i3−2i300002i2−2i202i−2i0006−66−6−i6i6−i6i6−22−22−i2i2−i2i2000000000000000000000000
χ704-44-4-20−4i4i0002-2222−2222−22−2323−232300000000−2i32i300002i2−2i202i−2i000−66−66i6−i6i6−i6−22−22−i2i2−i2i2000000000000000000000000
χ714-44-4-20−4i4i0002-22−2222−222223−2323−23000000002i3−2i30000−2i22i202i−2i000−66−66i6−i6i6−i62−22−2i2−i2i2−i2000000000000000000000000
χ724-44-4-20−4i4i0002-22−2222−2222−2323−232300000000−2i32i30000−2i22i202i−2i0006−66−6−i6i6−i6i62−22−2i2−i2i2−i2000000000000000000000000
χ734-4-444400-400-4-444i−4i−4i4i0000000000000000000040000-4000000004i−4i−4i4i0000000000000000000000000000
χ744-4-444400-400-4-44−4i4i4i−4i0000000000000000000040000-400000000−4i4i4i−4i0000000000000000000000000000
χ754-4-444-400400-4-44000000000000000000004-400-40000400004-4-4400000000000000000000000000000000
χ764-4-444-400400-4-4400000000000000000000-4400-4000040000-444-400000000000000000000000000000000
χ774-4-44-2400-40022-24i−4i−4i4i−2i32i32i3−2i3000000−2i32i300000000-20000223−23−23230000−2i2i2i−2i0000000000000000000000000000
χ784-4-44-2400-40022-24i−4i−4i4i2i3−2i3−2i32i30000002i3−2i300000000-200002−232323−230000−2i2i2i−2i0000000000000000000000000000
χ794-4-44-2400-40022-2−4i4i4i−4i−2i32i32i3−2i3000000−2i32i300000000-200002−232323−2300002i−2i−2i2i0000000000000000000000000000
χ804-4-44-2400-40022-2−4i4i4i−4i2i3−2i3−2i32i30000002i3−2i300000000-20000223−23−232300002i−2i−2i2i0000000000000000000000000000
χ814-4-44-2-40040022-20000−2i32i32i3−2i30000002i3−2i300004-40020000-20000-222-200002i3−2i3−2i32i3000000000000000000000000
χ824-4-44-2-40040022-20000−2i32i32i3−2i30000002i3−2i30000-440020000-200002-2-220000−2i32i32i3−2i3000000000000000000000000
χ834-4-44-2-40040022-200002i3−2i3−2i32i3000000−2i32i300004-40020000-20000-222-20000−2i32i32i3−2i3000000000000000000000000
χ844-4-44-2-40040022-200002i3−2i3−2i32i3000000−2i32i30000-440020000-200002-2-2200002i3−2i3−2i32i3000000000000000000000000

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