Finite Group Databasebeta

← Group #10909529

Character table — Group #10909529

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111222222222222444488888888888888888888881212121216161616161616161616242424242424242424244848
order1222222234444666666612121212244444668888121224242424242424242244441212121212121212444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111-11111-1-1-1-11111-1-1-1-1-1-11-1
χ41111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-1111111-11
χ51111111111111111111111111-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111-11-1-1-1-1111111-1-111-1-1-1-1-11
χ61111111111111111111111111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-111111-1
χ71111111111111111111111111-1-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ81111111111111111111111111-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ9111111111111111111111111-111-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-11-1-11111-1-11-1
χ10111111111111111111111111-111-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-11-111-1-1-1-111-11
χ11111111111111111111111111-111-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1111-1-1-1-111-11-1-1-1-1-1-11111
χ12111111111111111111111111-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1111-1-1-1-1111-1111111-1-1-1-1
χ13111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-11-1-1-11111-1-1-111111-1-111-1-1
χ14111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1111-1-1-11111-1-11-1-1-1-1-111-1-111
χ15111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1111-1-111-1-1-11
χ16111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1111-1-1-111-1-1111-1
χ17222222222-2-2-2-22222222-2-2-2-2200-200220000-2-20000000022-2-200000000002-20000000000
χ18222222222-2-2-2-22222222-2-2-2-2200-200220000-2-200000000-2-2220000000000-220000000000
χ19222222222-2-2-2-22222222-2-2-2-2-200200-2-20000220000000022220000000000-2-20000000000
χ20222222222-2-2-2-22222222-2-2-2-2-200200-2-200002200000000-2-2-2-20000000000220000000000
χ2122222222-12222-1-1-1-1-1-1-1-1-1-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1-1-1-1-12222-2-2-1-1-2-2-2-2-1-11111111100002-2-1-1-1-11111000000000000
χ2322222222-12222-1-1-1-1-1-1-1-1-1-1-12-2-2222-1-1-2-2-2-2-1-1111111110000-221111-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-1-1-1-1-12-2-22-2-2-1-12222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-222-2221122-2-211-1-1-1-111110000-2-2-1-111-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-222-2-2-211-2-222111111-1-1-1-10000-22-1-11111-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211-2-222111111-1-1-1-100002-211-1-1-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21122-2-211-1-1-1-1111100002211-1-111-1-1000000000000
χ2922-2-2-22-22222-2-222-2-2-22-22-22-202i−2i00000000000000000000000002i−2i00000000002-22i−2i0000
χ3022-2-2-22-22222-2-222-2-2-22-22-22-202i−2i00000000000000000000000002i−2i0000000000-22−2i2i0000
χ3122-2-2-22-22222-2-222-2-2-22-22-22-20−2i2i0000000000000000000000000−2i2i00000000002-2−2i2i0000
χ3222-2-2-22-22222-2-222-2-2-22-22-22-20−2i2i0000000000000000000000000−2i2i0000000000-222i−2i0000
χ332-2-22-2-2222-22-22-2-22-2-222-222-200002-2000000000000000000000000002-200002-200002-200
χ342-2-22-2-2222-22-22-2-22-2-222-222-200002-2000000000000000000000000002-20000-220000-2200
χ352-2-22-2-2222-22-22-2-22-2-222-222-20000-2200000000000000000000000000-2200002-20000-2200
χ362-2-22-2-2222-22-22-2-22-2-222-222-20000-2200000000000000000000000000-220000-2200002-200
χ3744444444-2-4-4-4-4-2-2-2-2-2-2-22222400-400-2-20000220000000000000000000000000000000000
χ3844444444-2-4-4-4-4-2-2-2-2-2-2-22222-400400220000-2-20000000000000000000000000000000000
χ394444-4-4-4-4400004-4-44-4-4400000000000022−2200002222−22−22000000000000000000000000000000
χ404444-4-4-4-4400004-4-44-4-44000000000000−22220000−22−222222000000000000000000000000000000
χ414444-4-4-4-4-20000-222-222-200000000000022−220023−23−2−22266−6−600000000000000000000000000
χ424444-4-4-4-4-20000-222-222-200000000000022−2200−2323−2−222−6−66600000000000000000000000000
χ434444-4-4-4-4-20000-222-222-2000000000000−22220023−2322−2−2−6−66600000000000000000000000000
χ444444-4-4-4-4-20000-222-222-2000000000000−222200−232322−2−266−6−600000000000000000000000000
χ4544-4-44-44-4400004-44-44-4-4000000000000000000000000004-4000000000000000000000000
χ4644-4-44-44-4400004-44-44-4-400000000000000000000000000-44000000000000000000000000
χ4744-4-4-44-444-4-44444-4-4-44-4-44-44000000000000000000000000000000000000000000000000
χ4844-4-4-44-44-244-4-4-2-2222-22-22-2204i−4i0000000000000000000000000−2i2i000000000000000000
χ4944-4-4-44-44-244-4-4-2-2222-22-22-220−4i4i00000000000000000000000002i−2i000000000000000000
χ5044-4-4-44-44-2-4-444-2-2222-222-22-200000000000000000000000000000023−230000000000000000
χ5144-4-4-44-44-2-4-444-2-2222-222-22-2000000000000000000000000000000−23230000000000000000
χ524-44-44-4-4444-4-44-4-4-4444-444-4-4000000000000000000000000000000000000000000000000
χ534-44-44-4-444-444-4-4-4-4444-4-4-444000000000000000000000000000000000000000000000000
χ544-44-44-4-44-24-4-44222-2-2-22-2-22200000000000000000023−2323−2300000000000000000000000000
χ554-44-44-4-44-24-4-44222-2-2-22-2-222000000000000000000−2323−232300000000000000000000000000
χ564-44-44-4-44-2-444-4222-2-2-2222-2-200000000000000−2i32i3−2i32i3000000000000000000000000000000
χ574-44-44-4-44-2-444-4222-2-2-2222-2-2000000000000002i3−2i32i3−2i3000000000000000000000000000000
χ584-44-4-444-440000-4444-4-4-40000000000000022−2200000022−22−222200000000000000000000000000
χ594-44-4-444-440000-4444-4-4-400000000000000−2222000000−222222−2200000000000000000000000000
χ604-44-4-444-4-200002-2-2-22220000000000−2i32i30022−2200i6−i6−i6i6−222−200000000000000000000000000
χ614-44-4-444-4-200002-2-2-22220000000000−2i32i300−222200−i6i6i6−i62−2−2200000000000000000000000000
χ624-44-4-444-4-200002-2-2-222200000000002i3−2i30022−2200−i6i6i6−i6−222−200000000000000000000000000
χ634-44-4-444-4-200002-2-2-222200000000002i3−2i300−222200i6−i6−i6i62−2−2200000000000000000000000000
χ644-4-4444-4-440000-44-4-44-4400000000000000000000000000004i−4i0000000000000000000000
χ654-4-4444-4-440000-44-4-44-440000000000000000000000000000−4i4i0000000000000000000000
χ664-4-44-4-44444-44-4-4-44-4-4444-4-44000000000000000000000000000000000000000000000000
χ674-4-44-4-444-24-44-422-222-2-2-222-20000000000000000000000000000000000−2i32i3000000000000
χ684-4-44-4-444-24-44-422-222-2-2-222-200000000000000000000000000000000002i3−2i3000000000000
χ694-4-44-4-444-2-44-4422-222-2-22-2-2200004-400000000000000000000000000-2200000000000000
χ704-4-44-4-444-2-44-4422-222-2-22-2-220000-44000000000000000000000000002-200000000000000
χ7188-8-88-88-8-40000-44-44-4440000000000000000000000000000000000000000000000000000
χ728-8-8888-8-8-400004-444-44-40000000000000000000000000000000000000000000000000000

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