Finite Group Databasebeta

← Group #10855116

Character table — Group #10855116

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666644444412121212121212122444466888812121212121212122424242424242424224444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ911111111111111111111-1-1111111-1-1-1-111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111-111-1-1-1-111-111-1-111-1
χ1011111111111111111111-1-1111111-1-1-1-111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-111-1-11-1-111-1-11
χ1111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1111-1-111-1-111-1-1-111-1-11
χ1211111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11-1-11111-1-1111-1-111-1
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-111-1-111-1-1-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-1111-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1111-1-11111-1-1-1-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-11-1-111-1-11111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-22222-2-2-20000-2-20000000000000000000022-2-2-2-200000000020000000
χ18222222222-2-2-2-22222222220000-2-22222-2-2-20000-2-200000000000000000000-2-22222000000000-20000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-22000022000000000000000000002222-2-2000000000-20000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200002200000000000000000000-2-2-2-22200000000020000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-222-1-1-2-2-2-211111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-2-1-1222211111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-22211-2-2221111-1-1-1-1-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2-2-21122-2-21111-1-1-1-11111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222221122-2-2-1-1-1-111111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-211-2-222-1-1-1-11111-1-1-1-11111000000211-1-1000000000000
χ2922-222-2-2-22-2-22222-2-2-22-2002i2i−2i−2i2-200002-20000000000000002i2i−2i−2i0000000000000000000000002i−2i002-20
χ3022-222-2-2-22-2-22222-2-2-22-2002i2i−2i−2i2-200002-20000000000000002i2i−2i−2i000000000000000000000000−2i2i00-220
χ3122-222-2-2-22-2-22222-2-2-22-200−2i−2i2i2i2-200002-2000000000000000−2i−2i2i2i0000000000000000000000002i−2i00-220
χ3222-222-2-2-22-2-22222-2-2-22-200−2i−2i2i2i2-200002-2000000000000000−2i−2i2i2i000000000000000000000000−2i2i002-20
χ332-22-22-22-222-2-22-2-222-22-2002i−2i2i−2i-2200002-20000000000000002i−2i2i−2i000000002-2002-200000002i−2i00000000
χ342-22-22-22-222-2-22-2-222-22-2002i−2i2i−2i-2200002-20000000000000002i−2i2i−2i00000000-2200-220000000−2i2i00000000
χ352-22-22-22-222-2-22-2-222-22-200−2i2i−2i2i-2200002-2000000000000000−2i2i−2i2i000000002-2002-20000000−2i2i00000000
χ362-22-22-22-222-2-22-2-222-22-200−2i2i−2i2i-2200002-2000000000000000−2i2i−2i2i00000000-2200-2200000002i−2i00000000
χ372-22-22-22-22-222-2-2-222-22-20000002-20000-2202i−2i000000002i2i−2i−2i0000000000002-200-22000002i−2i0000000000
χ382-22-22-22-22-222-2-2-222-22-20000002-20000-2202i−2i000000002i2i−2i−2i000000000000-22002-200000−2i2i0000000000
χ392-22-22-22-22-222-2-2-222-22-20000002-20000-220−2i2i00000000−2i−2i2i2i0000000000002-200-2200000−2i2i0000000000
χ402-22-22-22-22-222-2-2-222-22-20000002-20000-220−2i2i00000000−2i−2i2i2i000000000000-22002-2000002i−2i0000000000
χ412-2-2-222-222-22-22-2-2-2-2222002-2-22-2-20000220002-200002-200002-2-2222-2-2000000000002-200000000000000
χ422-2-2-222-222-22-22-2-2-2-2222002-2-22-2-2000022000-220000-2200002-2-22-2-22200000000000-2200000000000000
χ432-2-2-222-222-22-22-2-2-2-222200-222-2-2-20000220002-20000-220000-222-2-2-222000000000002-200000000000000
χ442-2-2-222-222-22-22-2-2-2-222200-222-2-2-2000022000-2200002-20000-222-222-2-200000000000-2200000000000000
χ452-2-2-222-22-1-22-221111-1-1-1002-2-2211−i3−i3i3i3-1-10002-2−i3i3002-2−i3i3−i3i3-111-1-1-111−i3−i3i3i30000000-11−i3i3000000000000
χ462-2-2-222-22-1-22-221111-1-1-1002-2-2211−i3−i3i3i3-1-1000-22−i3i300-22−i3i3−i3i3-111-111-1-1i3i3−i3−i300000001-1i3−i3000000000000
χ472-2-2-222-22-1-22-221111-1-1-1002-2-2211i3i3−i3−i3-1-10002-2i3−i3002-2i3−i3i3−i3-111-1-1-111i3i3−i3−i30000000-11i3−i3000000000000
χ482-2-2-222-22-1-22-221111-1-1-1002-2-2211i3i3−i3−i3-1-1000-22i3−i300-22i3−i3i3−i3-111-111-1-1−i3−i3i3i300000001-1−i3i3000000000000
χ492-2-2-222-22-1-22-221111-1-1-100-222-211−i3−i3i3i3-1-10002-2−i3i300-22i3−i3i3−i31-1-1111-1-1i3i3−i3−i30000000-11−i3i3000000000000
χ502-2-2-222-22-1-22-221111-1-1-100-222-211−i3−i3i3i3-1-1000-22−i3i3002-2i3−i3i3−i31-1-11-1-111−i3−i3i3i300000001-1i3−i3000000000000
χ512-2-2-222-22-1-22-221111-1-1-100-222-211i3i3−i3−i3-1-10002-2i3−i300-22−i3i3−i3i31-1-1111-1-1−i3−i3i3i30000000-11i3−i3000000000000
χ522-2-2-222-22-1-22-221111-1-1-100-222-211i3i3−i3−i3-1-1000-22i3−i3002-2−i3i3−i3i31-1-11-1-111i3i3−i3−i300000001-1−i3i3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022-2-2-2-222-40000220000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222222240000-2-20000000000000000000000000000000000000000000
χ55444-4-44-4-4400004-44-44-4-400000000000000000000000000000000000000000004-40000000000000000000
χ56444-4-44-4-4400004-44-44-4-40000000000000000000000000000000000000000000-440000000000000000000
χ5744-444-4-4-4444-4-444-4-4-44-4000000-440000-4400000000000000000000000000000000000000000000000000
χ5844-444-4-4-4-244-4-4-2-2222-220000002-200002-20000000000023−23−232300000000000000000000000000000000000
χ5944-444-4-4-4-244-4-4-2-2222-220000002-200002-200000000000−232323−2300000000000000000000000000000000000
χ6044-444-4-4-4-2-4-444-2-2222-22004i4i−4i−4i-220000-22000000000000000−2i−2i2i2i0000000000000000000000000000000
χ6144-444-4-4-4-2-4-444-2-2222-2200−4i−4i4i4i-220000-220000000000000002i2i−2i−2i0000000000000000000000000000000
χ6244-4-4-4-444400004-4-44-4-44000000000000000000000−2i22i200000000000000−2i22i2−2i22i200000000000000000000000
χ6344-4-4-4-444400004-4-44-4-440000000000000000000002i2−2i2000000000000002i2−2i22i2−2i200000000000000000000000
χ6444-4-4-4-444-20000-222-222-20000000023−2323−23000000000−2i22i20000000000i6−i6i6−i6i2−i2i2−i200000000000000000000000
χ6544-4-4-4-444-20000-222-222-20000000023−2323−230000000002i2−2i20000000000−i6i6−i6i6−i2i2−i2i200000000000000000000000
χ6644-4-4-4-444-20000-222-222-200000000−2323−2323000000000−2i22i20000000000−i6i6−i6i6i2−i2i2−i200000000000000000000000
χ6744-4-4-4-444-20000-222-222-200000000−2323−23230000000002i2−2i20000000000i6−i6i6−i6−i2i2−i2i200000000000000000000000
χ684-444-4-4-4440000-444-4-4-444i−4i0000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ694-444-4-4-4440000-444-4-4-44−4i4i000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ704-444-4-4-44-200002-2-2222-24i−4i000000−2i2i2i−2i000000000000000000000i6−i6−i6i6−666−600000000000000000000000
χ714-444-4-4-44-200002-2-2222-24i−4i000000−2i2i2i−2i000000000000000000000−i6i6i6−i66−6−6600000000000000000000000
χ724-444-4-4-44-200002-2-2222-2−4i4i0000002i−2i−2i2i000000000000000000000i6−i6−i6i66−6−6600000000000000000000000
χ734-444-4-4-44-200002-2-2222-2−4i4i0000002i−2i−2i2i000000000000000000000−i6i6i6−i6−666−600000000000000000000000
χ744-44-44-44-4-24-4-4422-2-22-22004i−4i4i−4i2-20000-22000000000000000−2i2i−2i2i0000000000000000000000000000000
χ754-44-44-44-4-24-4-4422-2-22-2200−4i4i−4i4i2-20000-220000000000000002i−2i2i−2i0000000000000000000000000000000
χ764-44-44-44-4-2-444-422-2-22-22000000-2200002-204i−4i00000000−2i−2i2i2i00000000000000000000000000000000000
χ774-44-44-44-4-2-444-422-2-22-22000000-2200002-20−4i4i000000002i2i−2i−2i00000000000000000000000000000000000
χ784-4-44-444-440000-44-444-4-400000000000000000000000000000000000000000000000000000000000−2i22i2000
χ794-4-44-444-440000-44-444-4-4000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ804-4-4-444-4444-44-4-4-4-4-4444000000440000-4-400000000000000000000000000000000000000000000000000
χ814-4-4-444-44-24-44-42222-2-2-2000000-2-2−2i3−2i32i32i322000002i3−2i30000000000000000000000000000000000000000000
χ824-4-4-444-44-24-44-42222-2-2-2000000-2-22i32i3−2i3−2i32200000−2i32i30000000000000000000000000000000000000000000
χ83888-8-88-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000

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