Finite Group Databasebeta

← Group #10831096

Character table — Group #10831096

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444466668888888888881212121212121212121216161616161616161616161616162424242424244848
order12442223444612122244666121212888822446688881212224488888844661212121212122424242422444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-11-111-1-1-1-111-1-1-1-11111111-11-11-111-1-1-1-1-1-11-11-1-1-11-1
χ31111111111111111111111111111-11-1111-1-1-1-111-1-1-1-1111111-11-11-11-1-111-1-1-1-1-11-11-1-1-11
χ41111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11-11-111-1-1-1-1111111-1-1-1-1-1-11-11-11-111-1-1-1-1-1-1-11-1111-11
χ7111111111111111111111111-1-1-1-1-11-1111-1-1-1-1111111-1-1-1-1-1-1-11-11-11-1-111-1-1-1-11-11-1111-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ911111111111111-1-1-1-111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ1011111111111111-1-1-1-111111111111-11-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-111-11-1-1-11111-1-11-11-111-11
χ1111111111111111-1-1-1-11111111111-11-11-1-111-1-1-1-1-1-1-1-111-1-1-1-11-1-11-1111-1-111-1-1-11-11111-1
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111
χ1311111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-11111
χ1411111111111111-1-1-1-1111111-1-1-1-11-11-1-1-111-1-1-1-11111-1-11111-111-11-1-1-11111-1-1-11-11-1-11-1
χ1511111111111111-1-1-1-1111111-1-1-1-1-11-11-1-111-1-1-1-11111-1-111111-1-11-1111-1-111-1-11-11-1-1-1-11
χ1611111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111111111-1-1
χ172222222-1222-1-1-12222-1-1-1-1-1-100002222-1-12222-1-1000000000022-1-1-1-1-1-1-1-1-1-1-1-100000000
χ182222222-1222-1-1-12222-1-1-1-1-1-100002-22-2-1-1-2-2-2-2-1-100000000002-2-11-11-1-111111100000000
χ192222222-1222-1-1-12222-1-1-1-1-1-10000-22-22-1-1-2-2-2-2-1-10000000000-221-11-111-1-1111100000000
χ202222222-1222-1-1-12222-1-1-1-1-1-10000-2-2-2-2-1-12222-1-10000000000-2-211111111-1-1-1-100000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-10000222211-2-222110000000000-2-2-1-1-1-1111111-1-100000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-100002-22-21122-2-2110000000000-22-11-1111-1-1-1-11100000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-10000-22-221122-2-21100000000002-21-11-1-1-111-1-11100000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-10000-2-2-2-211-2-222110000000000221111-1-1-1-111-1-100000000
χ2522222-2-22-2-2222200002-2-2-2-222222000000002-2002-22-2-2-200000000000000002-200000000
χ2622222-2-22-2-2222200002-2-2-2-22222200000000-2200-22-22-2-20000000000000000-2200000000
χ2722222-2-22-2-2222200002-2-2-2-22-2-2-2-2000000002-200-22-222200000000000000002-200000000
χ2822222-2-22-2-2222200002-2-2-2-22-2-2-2-200000000-22002-22-2220000000000000000-2200000000
χ2922-2-22222-2-2-22-2-222-2-2222-2-2-200000000220000-2-22-2-220000000000000000000000002-200
χ3022-2-22222-2-2-22-2-222-2-2222-2-2-200000000220000-2-2-222-2000000000000000000000000-2200
χ3122-2-22222-2-2-22-2-2-2-222222-2-2-200000000-2-20000222-2-22000000000000000000000000-2200
χ3222-2-22222-2-2-22-2-2-2-222222-2-2-200000000-2-2000022-222-20000000000000000000000002-200
χ3322-2-22-2-2222-22-2-200002-2-222-200000000002i−2i000022-2-2002i2i−2i−2i00000000002i−2i0000000000
χ3422-2-22-2-2222-22-2-200002-2-222-200000000002i−2i0000-2-22200−2i−2i2i2i00000000002i−2i0000000000
χ3522-2-22-2-2222-22-2-200002-2-222-20000000000−2i2i000022-2-200−2i−2i2i2i0000000000−2i2i0000000000
χ3622-2-22-2-2222-22-2-200002-2-222-20000000000−2i2i0000-2-222002i2i−2i−2i0000000000−2i2i0000000000
χ3722-2-2-22-222-222-2-20000-22-22-2222-2-2020-20000000000002-2000000020-200000000020-20000
χ3822-2-2-22-222-222-2-20000-22-22-2222-2-20-2020000000000002-20000000-202000000000-2020000
χ3922-2-2-22-222-222-2-20000-22-22-22-2-222020-2000000000000-22000000020-2000000000-2020000
χ4022-2-2-22-222-222-2-20000-22-22-22-2-2220-202000000000000-220000000-20200000000020-20000
χ4122-2-2-2-222-2222-2-20000-2-22-22222-2-220-20000000000000-2200000020-200000000020-200000
χ4222-2-2-2-222-2222-2-20000-2-22-22222-2-2-2020000000000000-22000000-202000000000-20200000
χ4322-2-2-2-222-2222-2-20000-2-22-222-2-22220-200000000000002-200000020-2000000000-20200000
χ4422-2-2-2-222-2222-2-20000-2-22-222-2-222-20200000000000002-2000000-20200000000020-200000
χ4544444-4-4-2-4-44-2-2-20000-22222-20000000000004-4000000000000000000000000-2200000000
χ4644444-4-4-2-4-44-2-2-20000-22222-2000000000000-440000000000000000000000002-200000000
χ474444-44-44-44-44440000-44-4-44-4000000000000000000000000000000000000000000000000
χ484444-44-4-2-44-4-2-2-200002-222-220000000000000000000000000000000000−2i32i3000000000000
χ494444-44-4-2-44-4-2-2-200002-222-2200000000000000000000000000000000002i3−2i3000000000000
χ504444-4-4444-4-44440000-4-444-4-4000000000000000000000000000000000000000000000000
χ514444-4-44-24-4-4-2-2-2000022-2-22200000000000000000000000000000000−2i32i300000000000000
χ524444-4-44-24-4-4-2-2-2000022-2-222000000000000000000000000000000002i3−2i300000000000000
χ5344-4-4444-2-4-4-4-22244-4-4-2-2-222200000000-2-200002200000000000000000000000000000000
χ5444-4-4444-2-4-4-4-222-4-444-2-2-222200000000220000-2-200000000000000000000000000000000
χ5544-4-44-4-4-244-4-2220000-222-2-2200000000004i−4i000000000000000000000000−2i2i0000000000
χ5644-4-44-4-4-244-4-2220000-222-2-220000000000−4i4i0000000000000000000000002i−2i0000000000
χ5744-4-4-44-4-24-44-22200002-22-22-20000040-4000000000000000000000-2020000000000000000
χ5844-4-4-44-4-24-44-22200002-22-22-200000-40400000000000000000000020-20000000000000000
χ5944-4-4-4-44-2-444-222000022-22-2-2000040-4000000000000000000000-20200000000000000000
χ6044-4-4-4-44-2-444-222000022-22-2-20000-40400000000000000000000020-200000000000000000
χ614-44i−4i0004000-44i−4i2-22i−2i00000022−22−2i22i200002-200002i−2i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ624-44i−4i0004000-44i−4i2-22i−2i000000−22222i2−2i200002-200002i−2i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ634-44i−4i0004000-44i−4i-22−2i2i00000022−22−2i22i20000-220000−2i2i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ644-44i−4i0004000-44i−4i-22−2i2i000000−22222i2−2i20000-220000−2i2i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ654-4−4i4i0004000-4−4i4i2-2−2i2i00000022−222i2−2i200002-20000−2i2i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ664-4−4i4i0004000-4−4i4i2-2−2i2i000000−2222−2i22i200002-20000−2i2i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ674-4−4i4i0004000-4−4i4i-222i−2i00000022−222i2−2i20000-2200002i−2i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ684-4−4i4i0004000-4−4i4i-222i−2i000000−2222−2i22i20000-2200002i−2i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ698-88i−8i000-40004−4i4i4-44i−4i00000000000000-220000−2i2i00000000000000000000000000000000
χ708-88i−8i000-40004−4i4i-44−4i4i000000000000002-200002i−2i00000000000000000000000000000000
χ718-8−8i8i000-400044i−4i4-4−4i4i00000000000000-2200002i−2i00000000000000000000000000000000
χ728-8−8i8i000-400044i−4i-444i−4i000000000000002-20000−2i2i00000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.