Finite Group Databasebeta

← Group #10829887

Character table — Group #10829887

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222234444666444466121212121212121222224444666612121212121244446688121224242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ61111111111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1111111-1-1
χ911111111111111-1-1-1-111111-1-1-1-111-1111-1-1-11111-1-1-1-1-1-111111-11-11-111-1-11-1-1-11-111-1-11-1
χ1011111111111111-1-1-1-111111-1-1-1-111-1111-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-11-111-1-1-1111-11-1-111-11
χ1111111111111111-1-1-1-111111-1-1-1-111-1-1-11-111-1-1-1-1-1-1111111111-1-111-1-1-1111-1-1-11-1-1-111-11
χ1211111111111111-1-1-1-111111-1-1-1-111-1-1-11-111-1-1-1-1-1-11111-1-1-1-11-1-111-1-1-111-1111-1111-1-11-1
χ1311111111111111-1-1-1-111111-1-1-1-11-1111-11-1-11111-1-1-1-1-1-11111-11-11-11-1-111-11-1-1-1111-1-1-11
χ1411111111111111-1-1-1-111111-1-1-1-11-1111-11-1-11111-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1111-1111-1-1-1111-1
χ1511111111111111-1-1-1-111111-1-1-1-11-11-1-1-1111-1-1-1-1-1-111111111-111-1-1111-1-1-11-1-1-11-1-1111-1
χ1611111111111111-1-1-1-111111-1-1-1-11-11-1-1-1111-1-1-1-1-1-11111-1-1-1-1-111-1-1111-1-11-1111-111-1-1-11
χ172222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-200000000000022000022-2-20000000000002-200000000
χ182222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-2000000000000220000-2-222000000000000-2200000000
χ192222222-2-2-2-2222-2-22222-2-2-22222-2000000000000-2-2000022-2-2000000000000-2200000000
χ202222222-2-2-2-2222-2-22222-2-2-22222-2000000000000-2-20000-2-2220000000000002-200000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000-1-122-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122-2-222-2-21111-1-111110000-1-1-2-2-1-11111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1-1-1-1-1-1-1000011-2-2111111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-111110000112211-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-1-1-1-11111-12-2222-2-2-2-1-1-1-11111110000-112-2-11-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-1-1-1-11111-12-2-2-22-222111111-1-1-1-10000-11-22-1111-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-1-1-11111-1-2222-22-2-2-1-1-1-111111100001-1-221-111-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-1-1-11111-1-22-2-2-2222111111-1-1-1-100001-12-21-1-1-111000000000000
χ292222-2-222-22-22222-22-2-2-22-2-222-2-222200-2-20000002-2000000002200-2-20000000000000000
χ302222-2-222-22-22222-22-2-2-22-2-222-2-22-2-200220000002-200000000-2-200220000000000000000
χ312222-2-222-22-2222-22-22-2-22-2-2-2-22222-200-22000000-22000000002-200-220000000000000000
χ322222-2-222-22-2222-22-22-2-22-2-2-2-2222-22002-2000000-2200000000-22002-20000000000000000
χ332222-2-22-22-222222-2-22-2-2-222-2-222-20000000000002-20000000000000000002200-2-2000000
χ342222-2-22-22-222222-2-22-2-2-222-2-222-20000000000002-2000000000000000000-2-20022000000
χ352222-2-22-22-22222-222-2-2-2-22222-2-2-2000000000000-220000000000000000002-200-22000000
χ362222-2-22-22-22222-222-2-2-2-22222-2-2-2000000000000-22000000000000000000-22002-2000000
χ372222-2-2-12-22-2-1-1-12-22-211-111-1-111-12200-2-200−i3−i3i3i3-11−i3−i3i3i30000-1-10011−i3i3−i3i3000000000000
χ382222-2-2-12-22-2-1-1-12-22-211-111-1-111-12200-2-200i3i3−i3−i3-11i3i3−i3−i30000-1-10011i3−i3i3−i3000000000000
χ392222-2-2-12-22-2-1-1-12-22-211-111-1-111-1-2-2002200−i3−i3i3i3-11−i3−i3i3i300001100-1-1i3−i3i3−i3000000000000
χ402222-2-2-12-22-2-1-1-12-22-211-111-1-111-1-2-2002200i3i3−i3−i3-11i3i3−i3−i300001100-1-1−i3i3−i3i3000000000000
χ412222-2-2-12-22-2-1-1-1-22-2211-11111-1-1-12-200-2200−i3−i3i3i31-1i3i3−i3−i30000-11001-1−i3i3i3−i3000000000000
χ422222-2-2-12-22-2-1-1-1-22-2211-11111-1-1-12-200-2200i3i3−i3−i31-1−i3−i3i3i30000-11001-1i3−i3−i3i3000000000000
χ432222-2-2-12-22-2-1-1-1-22-2211-11111-1-1-1-22002-200−i3−i3i3i31-1i3i3−i3−i300001-100-11i3−i3−i3i3000000000000
χ442222-2-2-12-22-2-1-1-1-22-2211-11111-1-1-1-22002-200i3i3−i3−i31-1−i3−i3i3i300001-100-11−i3i3i3−i3000000000000
χ452-22-22-222-2-22-22-200002-222-20000-20000002i−2i0000002i−2i2i−2i2i−2i2i−2i0000000000000000002-200
χ462-22-22-222-2-22-22-200002-222-20000-20000002i−2i0000002i−2i2i−2i−2i2i−2i2i000000000000000000-2200
χ472-22-22-222-2-22-22-200002-222-20000-2000000−2i2i000000−2i2i−2i2i2i−2i2i−2i000000000000000000-2200
χ482-22-22-222-2-22-22-200002-222-20000-2000000−2i2i000000−2i2i−2i2i−2i2i−2i2i0000000000000000002-200
χ492-22-22-22-222-2-22-200002-2-2-2200002002-200002-22-20000002i−2i−2i2i00000000000000002i−2i0000
χ502-22-22-22-222-2-22-200002-2-2-2200002002-200002-22-2000000−2i2i2i−2i0000000000000000−2i2i0000
χ512-22-22-22-222-2-22-200002-2-2-220000200-220000-22-220000002i−2i−2i2i0000000000000000−2i2i0000
χ522-22-22-22-222-2-22-200002-2-2-220000200-220000-22-22000000−2i2i2i−2i00000000000000002i−2i0000
χ53444444-2-4-4-4-4-2-2-244-4-4-2-222222222000000000000-2-2000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-444-2-2222-2-2-2-2200000000000022000000000000000000000000000000
χ554444-4-4-2-44-44-2-2-24-4-44222-2-222-2-22000000000000-22000000000000000000000000000000
χ564444-4-4-2-44-44-2-2-2-444-4222-2-2-2-22220000000000002-2000000000000000000000000000000
χ574-44-44-4-24-4-442-220000-22-2-22000020000004i−4i000000−2i2i−2i2i00000000000000000000000000
χ584-44-44-4-24-4-442-220000-22-2-2200002000000−4i4i0000002i−2i2i−2i00000000000000000000000000
χ594-44-44-4-2-444-42-220000-2222-20000-2004-40000-22-2200000000000000000000000000000000
χ604-44-44-4-2-444-42-220000-2222-20000-200-4400002-22-200000000000000000000000000000000
χ614-44-4-44444-4-4-44-40000-444-440000-400000000000000000000000000000000000000000000
χ624-44-4-444-4-444-44-40000-44-44-40000400000000000000000000000000000000000000000000
χ634-44-4-44-244-4-42-2200002-2-22-2000020000000000000023−23−232300000000000000000000000000
χ644-44-4-44-244-4-42-2200002-2-22-20000200000000000000−232323−2300000000000000000000000000
χ654-44-4-44-2-4-4442-2200002-22-220000-200000000−2i32i32i3−2i300000000000000000000000000000000
χ664-44-4-44-2-4-4442-2200002-22-220000-2000000002i3−2i3−2i32i300000000000000000000000000000000
χ6788-8-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-4440000000000043−43000000000000000000000000000000000000000000000
χ6988-8-800-40000-44400000000000−4343000000000000000000000000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-4000000000−4i34i300000000000000000000000000000000000000000000000
χ728-8-8800-4000044-40000000004i3−4i300000000000000000000000000000000000000000000000

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