Finite Group Databasebeta

← Group #10706163

Character table — Group #10706163

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122234444446668888121212122444668888881212121212121212121224242424242424242424242424242424224466661212121216161616161616168888
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
χ5111111111-1-1111-1-1-1-11111-11-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1iiii−i−i−i−iii−i−i
χ6111111111-1-1111-1-1-1-11111-11-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1−i−i−i−iiiii−i−iii
χ7111111111-1-1111-1-1-1-11111-11-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111iiii−i−i−i−i−i−iii
χ8111111111-1-1111-1-1-1-11111-11-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111−i−i−i−iiiiiii−i−i
χ911111-1-111111111111-1-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-11111-1-111-1-11-11-1
χ1011111-1-111111111111-1-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111-1-111-1-111-11-11
χ1111111-1-111111111111-1-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-1-11111-1-111-1-111-1-1-11-11
χ1211111-1-111111111111-1-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-1-11111-1-1-1-111-1-1111-11-1
χ1311111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1ii−i−i−i−iiii−i−ii
χ1411111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1−i−iiiii−i−i−iii−i
χ1511111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111ii−i−i−i−iii−iii−i
χ1611111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111−i−iiiii−i−ii−i−ii
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
χ18222222222-2-222222222222-22-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ192222222-2-22222200002222-2-22-2-2-2000000-2-22222-2-2-2-200000000000000000000000000002−22−22−22−20000
χ202222222-2-22222200002222-2-22-2-2-2000000-2-22222-2-2-2-20000000000000000000000000000−22−22−22−220000
χ212222222-2-2-2-2222000022222-2-2222000000-2-2-2-2-2-222-2-20000000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ222222222-2-2-2-2222000022222-2-2222000000-2-2-2-2-2-222-2-20000000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ2322222-2-22222222-2-2-2-2-2-2-2-22-2-2-222-2-22222-2-222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ2422222-2-222-2-22222222-2-2-2-2-2-222-2-2-2-222-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2522222-2-2-2-2222220000-2-2-2-2-22-22-2-20000002222-2-222-2-200000000000000000000000000002−2−222−2−220000
χ2622222-2-2-2-2222220000-2-2-2-2-22-22-2-20000002222-2-222-2-20000000000000000000000000000−222−2−222−20000
χ2722222-2-2-2-2-2-22220000-2-2-2-2222-22200000022-2-222-2-2-2-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ2822222-2-2-2-2-2-22220000-2-2-2-2222-22200000022-2-222-2-2-2-20000000000000000000000000000i2−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
χ332222-12222-2-2-1-1-12222-1-1-1-1-22-2-211-2-2-2-222-1-1111111-1-111111111-1-1-1-1-1-1-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ342222-12222-2-2-1-1-12222-1-1-1-1-22-2-211-2-2-2-222-1-1111111-1-111111111-1-1-1-1-1-1-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ352222-12222-2-2-1-1-1-2-2-2-2-1-1-1-1-22-2-2112222-2-2-1-1111111-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-111000000000000
χ362222-12222-2-2-1-1-1-2-2-2-2-1-1-1-1-22-2-2112222-2-2-1-1111111-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-1000000000000
χ372222-1-2-22222-1-1-1222211112-2-2-2-1-122-2-2-2-211-1-11111-1-1-1-1-1-11111-1-1-1-111112-2-22-1-11111-1-1000000000000
χ382222-1-2-22222-1-1-1222211112-2-2-2-1-122-2-2-2-211-1-11111-1-1-1-1-1-11111-1-1-1-11111-222-211-1-1-1-111000000000000
χ392222-1-2-22222-1-1-1-2-2-2-211112-2-2-2-1-1-2-2222211-1-11111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3i3−i3−i3i3000000000000
χ402222-1-2-22222-1-1-1-2-2-2-211112-2-2-2-1-1-2-2222211-1-11111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3−i3i3i3−i3000000000000
χ412222-1-2-222-2-2-1-1-122221111-2-22211-2-222-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000−i3i3−i3i3i3−i3i3−i3000000000000
χ422222-1-2-222-2-2-1-1-122221111-2-22211-2-222-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000i3−i3i3−i3−i3i3−i3i3000000000000
χ432222-1-2-222-2-2-1-1-1-2-2-2-21111-2-2221122-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-122-2-2-1-1-1-11111000000000000
χ442222-1-2-222-2-2-1-1-1-2-2-2-21111-2-2221122-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-2-2221111-1-1-1-1000000000000
χ454444-244-4-444-2-2-20000-2-2-2-2-4-44-42200000022-2-2-2-222220000000000000000000000000000000000000000
χ464444-244-4-4-4-4-2-2-20000-2-2-2-24-4-44-2-2000000222222-2-2220000000000000000000000000000000000000000
χ474444-2-4-4-4-444-2-2-200002222-44-4422000000-2-2-2-222-2-2220000000000000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-200002222444-4-2-2000000-2-222-2-222220000000000000000000000000000000000000000
χ4944-4-4400004i−4i4-4-4−2i2−2i22i22i2000000000022−220000004i−4i0000002222−22−220000−2i2−2i22i22i20000000000000000000000000000
χ5044-4-4400004i−4i4-4-42i22i2−2i2−2i20000000000−22220000004i−4i000000−22−22222200002i22i2−2i2−2i20000000000000000000000000000
χ5144-4-440000−4i4i4-4-4−2i2−2i22i22i20000000000−2222000000−4i4i000000−22−2222220000−2i2−2i22i22i20000000000000000000000000000
χ5244-4-440000−4i4i4-4-42i22i2−2i2−2i2000000000022−22000000−4i4i0000002222−22−2200002i22i2−2i2−2i20000000000000000000000000000
χ5344-4-4-200004i−4i-222−2i2−2i22i22i22323−23−2300000022−22000000−2i2i−2i32i30000−2−22266−6−6i2i2−i2−i2i6i6−i6−i6000000000000000000000000
χ5444-4-4-200004i−4i-222−2i2−2i22i22i2−23−23232300000022−22000000−2i2i2i3−2i30000−2−222−6−666i2i2−i2−i2−i6−i6i6i6000000000000000000000000
χ5544-4-4-200004i−4i-2222i22i2−2i2−2i22323−23−23000000−2222000000−2i2i−2i32i3000022−2−2−6−666−i2−i2i2i2−i6−i6i6i6000000000000000000000000
χ5644-4-4-200004i−4i-2222i22i2−2i2−2i2−23−232323000000−2222000000−2i2i2i3−2i3000022−2−266−6−6−i2−i2i2i2i6i6−i6−i6000000000000000000000000
χ5744-4-4-20000−4i4i-222−2i2−2i22i22i22323−23−23000000−22220000002i−2i2i3−2i3000022−2−2−6−666i2i2−i2−i2i6i6−i6−i6000000000000000000000000
χ5844-4-4-20000−4i4i-222−2i2−2i22i22i2−23−232323000000−22220000002i−2i−2i32i3000022−2−266−6−6i2i2−i2−i2−i6−i6i6i6000000000000000000000000
χ5944-4-4-20000−4i4i-2222i22i2−2i2−2i22323−23−2300000022−220000002i−2i2i3−2i30000−2−22266−6−6−i2−i2i2i2−i6−i6i6i6000000000000000000000000
χ6044-4-4-20000−4i4i-2222i22i2−2i2−2i2−23−23232300000022−220000002i−2i−2i32i30000−2−222−6−666−i2−i2i2i2i6i6−i6−i6000000000000000000000000
χ614-44-44004-400-44-400000000000000004i−4i00000000004-400004i−4i4i−4i00000000000000000000000000000000
χ624-44-44004-400-44-40000000000000000−4i4i00000000004-40000−4i4i−4i4i00000000000000000000000000000000
χ634-44-4400-4400-44-44i−4i4i−4i000000000000000000000000-44000000004i−4i4i−4i0000000000000000000000000000
χ644-44-4400-4400-44-4−4i4i−4i4i000000000000000000000000-4400000000−4i4i−4i4i0000000000000000000000000000
χ654-44-4-2004-4002-22000023−2323−23000000004i−4i0023−23000000-22−2i32i3−2i32i3−2i2i−2i2i00000000000000000000000000000000
χ664-44-4-2004-4002-22000023−2323−2300000000−4i4i0023−23000000-222i3−2i32i3−2i32i−2i2i−2i00000000000000000000000000000000
χ674-44-4-2004-4002-220000−2323−2323000000004i−4i00−2323000000-222i3−2i32i3−2i3−2i2i−2i2i00000000000000000000000000000000
χ684-44-4-2004-4002-220000−2323−232300000000−4i4i00−2323000000-22−2i32i3−2i32i32i−2i2i−2i00000000000000000000000000000000
χ694-44-4-200-44002-224i−4i4i−4i23−2323−23000000000000−23230000002-200000000−2i2i−2i2i−2i32i3−2i32i3000000000000000000000000
χ704-44-4-200-44002-224i−4i4i−4i−2323−232300000000000023−230000002-200000000−2i2i−2i2i2i3−2i32i3−2i3000000000000000000000000
χ714-44-4-200-44002-22−4i4i−4i4i23−2323−23000000000000−23230000002-2000000002i−2i2i−2i2i3−2i32i3−2i3000000000000000000000000
χ724-44-4-200-44002-22−4i4i−4i4i−2323−232300000000000023−230000002-2000000002i−2i2i−2i−2i32i3−2i32i3000000000000000000000000
χ734-4-4444-40000-4-4422−22−22224-4-44000000000022−2200000000000000000022−22−222222−22−2222000000000000000000000000
χ744-4-4444-40000-4-44−222222−224-4-440000000000−2222000000000000000000−222222−22−222222−22000000000000000000000000
χ754-4-444-440000-4-4422−22−2222-444-40000000000−222200000000000000000022−22−2222−222222−22000000000000000000000000
χ764-4-444-440000-4-44−222222−22-444-4000000000022−22000000000000000000−222222−2222−22−2222000000000000000000000000
χ774-4-44-24-4000022-222−22−2222-222-20000−2i32i3000022−22000000−2i32i300i6−i6−i6i6i6−i6−i6i6−222−2−222−2000000000000000000000000
χ784-4-44-24-4000022-222−22−2222-222-200002i3−2i3000022−220000002i3−2i300−i6i6i6−i6−i6i6i6−i6−222−2−222−2000000000000000000000000
χ794-4-44-24-4000022-2−222222−22-222-20000−2i32i30000−2222000000−2i32i300−i6i6i6−i6−i6i6i6−i62−2−222−2−22000000000000000000000000
χ804-4-44-24-4000022-2−222222−22-222-200002i3−2i30000−22220000002i3−2i300i6−i6−i6i6i6−i6−i6i62−2−222−2−22000000000000000000000000
χ814-4-44-2-44000022-222−22−22222-2-220000−2i32i30000−22220000002i3−2i300i6−i6−i6i6−i6i6i6−i6−222−22−2−22000000000000000000000000
χ824-4-44-2-44000022-222−22−22222-2-2200002i3−2i30000−2222000000−2i32i300−i6i6i6−i6i6−i6−i6i6−222−22−2−22000000000000000000000000
χ834-4-44-2-44000022-2−222222−222-2-220000−2i32i3000022−220000002i3−2i300−i6i6i6−i6i6−i6−i6i62−2−22−222−2000000000000000000000000
χ844-4-44-2-44000022-2−222222−222-2-2200002i3−2i3000022−22000000−2i32i300i6−i6−i6i6−i6i6i6−i62−2−22−222−2000000000000000000000000

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