Finite Group Databasebeta

← Group #10831116

Character table — Group #10831116

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444466668888888888881212121212121212121216161616161616161616161616162424242424244848
order1244222344461212444466612121288882244888812121212224488888866881212242424242424242422244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-11-1-1-1-1-11111-1-1-1-11111111-11-11-111-1-1-1-1-1-11-1-11-1-11-1
χ31111111111111111111111111111-11-11-1-1-1-11111-1-1-1-1111111-11-11-11-1-111-1-1-1-1-11-1-11-1-11
χ41111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-11-1-1
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11-11-1-1-1-1-111111111-1-1-1-1-1-11-11-11-111-1-1-1-1-1-1-111-111-11
χ7111111111111111111111111-1-1-1-1-11-11-1-1-1-111111111-1-1-1-1-1-1-11-11-11-1-111-1-1-1-11-111-111-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-111
χ911111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111-111-1-1-1
χ1011111111111111-1-1-1-111111111111-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-111-1-1111-111-11-11
χ1111111111111111-1-1-1-11111111111-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1111-1-1-1-111-111-1111-1
χ1211111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-111
χ1311111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-1-1-11-1-1111
χ1411111111111111-1-1-1-1111111-1-1-1-11-11-1-1-111-1-1-1-111111111-1-11-1-111-1-1-111-1-111-11-1-11-11-1
χ1511111111111111-1-1-1-1111111-1-1-1-1-11-11-1-111-1-1-1-111111111-1-1-111-1-1111-1-1-1-1111-1-11-1-1-11
χ1611111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1111111-1-1
χ172222222-1222-1-1-12222-1-1-1-1-1-1000022222222-1-1-1-10000000000-1-122-1-1-1-1-1-1-1-1-1-100000000
χ182222222-1222-1-1-12222-1-1-1-1-1-100002-22-2-2-2-2-2-1-1-1-10000000000-112-2-11-1-111111100000000
χ192222222-1222-1-1-12222-1-1-1-1-1-10000-22-22-2-2-2-2-1-1-1-100000000001-1-221-111-1-1111100000000
χ202222222-1222-1-1-12222-1-1-1-1-1-10000-2-2-2-22222-1-1-1-1000000000011-2-2111111-1-1-1-100000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-10000222222-2-211110000000000-1-1-2-2-1-11111-1-11100000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-100002-22-2-2-22211110000000000-11-22-1111-1-111-1-100000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-10000-22-22-2-222111100000000001-12-21-1-1-11111-1-100000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-10000-2-2-2-222-2-211110000000000112211-1-1-1-1-1-11100000000
χ252222-2-222-2-222220000-2-22-2-22222200002-20000002-22-20000-2-200000000002-20000000000
χ262222-2-222-2-222220000-2-22-2-2222220000-22000000-22-220000-2-20000000000-220000000000
χ272222-2-222-2-222220000-2-22-2-22-2-2-2-200002-2000000-22-2200002200000000002-20000000000
χ282222-2-222-2-222220000-2-22-2-22-2-2-2-20000-220000002-22-20000220000000000-220000000000
χ2922-2-22222-2-2-22-2-20000222-2-2-200000000002i−2i00002-2-222i2i−2i−2i000000000000002i−2i00000000
χ3022-2-22222-2-2-22-2-20000222-2-2-200000000002i−2i0000-222-2−2i−2i2i2i000000000000002i−2i00000000
χ3122-2-22222-2-2-22-2-20000222-2-2-20000000000−2i2i00002-2-22−2i−2i2i2i00000000000000−2i2i00000000
χ3222-2-22222-2-2-22-2-20000222-2-2-20000000000−2i2i0000-222-22i2i−2i−2i00000000000000−2i2i00000000
χ3322-2-22-2-222-222-2-200002-2-22-2222-2-2020-200000000000000002-202000-2000000000200-2000
χ3422-2-22-2-222-222-2-200002-2-22-2222-2-20-20200000000000000002-20-20002000000000-2002000
χ3522-2-22-2-222-222-2-200002-2-22-22-2-222020-20000000000000000-2202000-2000000000-2002000
χ3622-2-22-2-222-222-2-200002-2-22-22-2-2220-2020000000000000000-220-20002000000000200-2000
χ3722-2-2-22-22-2222-2-20000-22-2-22222-2-220-200000000000000000-222000-2000000000200-20000
χ3822-2-2-22-22-2222-2-20000-22-2-22222-2-2-20200000000000000000-22-20002000000000-20020000
χ3922-2-2-22-22-2222-2-20000-22-2-222-2-22220-2000000000000000002-22000-2000000000-20020000
χ4022-2-2-22-22-2222-2-20000-22-2-222-2-222-202000000000000000002-2-20002000000000200-20000
χ4122-2-2-2-22222-22-2-222-2-2-2-2222-200000000000022-2-222-2-20000000000000000000000200-200
χ4222-2-2-2-22222-22-2-222-2-2-2-2222-200000000000022-2-2-2-2220000000000000000000000-200200
χ4322-2-2-2-22222-22-2-2-2-222-2-2222-2000000000000-2-22222-2-20000000000000000000000-200200
χ4422-2-2-2-22222-22-2-2-2-222-2-2222-2000000000000-2-222-2-2220000000000000000000000200-200
χ4544444-4-44-44-444400004-4-4-44-4000000000000000000000000000000000000000000000000
χ4644444-4-4-2-44-4-2-2-20000-2222-220000000000000000000000000000000023−2300000000000000
χ4744444-4-4-2-44-4-2-2-20000-2222-2200000000000000000000000000000000−232300000000000000
χ484444-44-444-4-44440000-44-44-4-4000000000000000000000000000000000000000000000000
χ494444-44-4-24-4-4-2-2-200002-22-222000000000000000000000000000000000023−23000000000000
χ504444-44-4-24-4-4-2-2-200002-22-2220000000000000000000000000000000000−2323000000000000
χ514444-4-44-2-4-44-2-2-2000022-222-2000000004-400000000000000000000000000-220000000000
χ524444-4-44-2-4-44-2-2-2000022-222-200000000-44000000000000000000000000002-20000000000
χ5344-4-4444-2-4-4-4-2220000-2-2-222200000000004i−4i00000000000000000000000000−2i2i00000000
χ5444-4-4444-2-4-4-4-2220000-2-2-22220000000000−4i4i000000000000000000000000002i−2i00000000
χ5544-4-44-4-4-24-44-2220000-222-22-20000040-40000000000000000000-200020000000000000000
χ5644-4-44-4-4-24-44-2220000-222-22-200000-40400000000000000000002000-20000000000000000
χ5744-4-4-44-4-2-444-22200002-222-2-2000040-40000000000000000000-2000200000000000000000
χ5844-4-4-44-4-2-444-22200002-222-2-20000-40400000000000000000002000-200000000000000000
χ5944-4-4-4-44-244-4-22244-4-422-2-2-22000000000000-2-22200000000000000000000000000000000
χ6044-4-4-4-44-244-4-222-4-44422-2-2-2200000000000022-2-200000000000000000000000000000000
χ614-44i−4i0004000-44i−4i2-22i−2i00000022−22−2i22i2000000002-22i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ624-44i−4i0004000-44i−4i2-22i−2i000000−22222i2−2i2000000002-22i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ634-44i−4i0004000-44i−4i-22−2i2i00000022−22−2i22i200000000-22−2i2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ644-44i−4i0004000-44i−4i-22−2i2i000000−22222i2−2i200000000-22−2i2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ654-4−4i4i0004000-4−4i4i2-2−2i2i00000022−222i2−2i2000000002-2−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ664-4−4i4i0004000-4−4i4i2-2−2i2i000000−2222−2i22i2000000002-2−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ674-4−4i4i0004000-4−4i4i-222i−2i00000022−222i2−2i200000000-222i−2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ684-4−4i4i0004000-4−4i4i-222i−2i000000−2222−2i22i200000000-222i−2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ698-88i−8i000-40004−4i4i4-44i−4i000000000000000000-22−2i2i00000000000000000000000000000000
χ708-88i−8i000-40004−4i4i-44−4i4i0000000000000000002-22i−2i00000000000000000000000000000000
χ718-8−8i8i000-400044i−4i4-4−4i4i000000000000000000-222i−2i00000000000000000000000000000000
χ728-8−8i8i000-400044i−4i-444i−4i0000000000000000002-2−2i2i00000000000000000000000000000000

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