Finite Group Databasebeta

← Group #10840268

Character table — Group #10840268

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444446666666688888888888812121212161616161616161616161616161624242424242424244848
order1244222344461212666888812121244448888224444442424242444884668121212121212121224242444888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-11-111-1-111111111-11-1-11-111-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111-11-11-1-11111111111-1-11-1-11-1-111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1-11-1-11-111-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-1111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1111111111111-1-1
χ911111111111111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1-1-111-1-11111-1-11-1
χ1011111111111111111-1-1-1-11111111-1-1-1-11-11-1-1-111-1-1-1-111-1-111-1-11-1-1-11111-1-111-1-111-1-1-11
χ1111111111111111111-1-1-1-11111111-1-1-1-1-11-1111-1-1-1-1-1-111-1-11-11-1-1111-1-111-1-1-1-111-1-111-11
χ1211111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-11-1-11111-1-11111-1-1-1-1111-1
χ1311111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-1-1-11111-1-1-1-111-11
χ1411111111111111111-1-1-1-1111-1-1-1-111111-11-1-1-111-1-1-1-1-1-11111-1-11-1-1-11111-1-1-1-111-1-1111-1
χ1511111111111111111-1-1-1-1111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1111-11-1-1111-1-111-1-111-1-111-1-11-1
χ1611111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-11-1-11111-1-111-1-11111-1-1-11
χ172222222-1222-1-1-1-1-1-12222-1-1-10000000022222222-1-1-1-100002-1-12-1-1-1-1-1-1-1-1-1-10000000000
χ182222222-1222-1-1-1-1-1-12222-1-1-1000000002-22-222-2-2-1-1-1-10000-2-11-2-11-1-11111110000000000
χ192222222-1222-1-1-1-1-1-12222-1-1-100000000-22-22-2-222-1-1-1-10000-21-1-21-111-1-111110000000000
χ202222222-1222-1-1-1-1-1-12222-1-1-100000000-2-2-2-2-2-2-2-2-1-1-1-100002112111111-1-1-1-10000000000
χ212222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-1000000002222-2-2-2-211110000-2-1-12-1-1111111-1-10000000000
χ222222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-1000000002-22-2-2-222111100002-11-2-1111-1-1-1-1110000000000
χ232222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-100000000-22-2222-2-21111000021-1-21-1-1-111-1-1110000000000
χ242222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-100000000-2-2-2-2222211110000-211211-1-1-1-111-1-10000000000
χ2522222-2-22-2-222222-2-200002-2-2000022220000002i−2i000000-2-2000000002i−2i0000002i−2i000000
χ2622222-2-22-2-222222-2-200002-2-200002222000000−2i2i000000-2-200000000−2i2i000000−2i2i000000
χ2722222-2-22-2-222222-2-200002-2-20000-2-2-2-20000002i−2i00000022000000002i−2i000000−2i2i000000
χ2822222-2-22-2-222222-2-200002-2-20000-2-2-2-2000000−2i2i0000002200000000−2i2i0000002i−2i000000
χ292222-2-2222-2-2222-22-20000-22-22222000000002i−2i000000-2-2000000002i−2i0000000000002i−2i00
χ302222-2-2222-2-2222-22-20000-22-2222200000000−2i2i000000-2-200000000−2i2i000000000000−2i2i00
χ312222-2-2222-2-2222-22-20000-22-2-2-2-2-2000000002i−2i00000022000000002i−2i000000000000−2i2i00
χ322222-2-2222-2-2222-22-20000-22-2-2-2-2-200000000−2i2i0000002200000000−2i2i0000000000002i−2i00
χ3322-2-22-2-2222-22-2-22-2-20000-2222i2i−2i−2i000020-20000000002i−2i000200-200000000000002i−2i0000
χ3422-2-22-2-2222-22-2-22-2-20000-2222i2i−2i−2i0000-2020000000002i−2i000-20020000000000000−2i2i0000
χ3522-2-22-2-2222-22-2-22-2-20000-222−2i−2i2i2i000020-2000000000−2i2i000200-20000000000000−2i2i0000
χ3622-2-22-2-2222-22-2-22-2-20000-222−2i−2i2i2i0000-202000000000−2i2i000-200200000000000002i−2i0000
χ3722-2-2-22-222-222-2-2-2-222i2i−2i−2i22-22i2i−2i−2i22-2-2000000002i2i−2i−2i−2i2i2-2000000000000000000000000
χ3822-2-2-22-222-222-2-2-2-222i2i−2i−2i22-2−2i−2i2i2i-2-222000000002i2i−2i−2i2i−2i-22000000000000000000000000
χ3922-2-2-22-222-222-2-2-2-22−2i−2i2i2i22-22i2i−2i−2i-2-22200000000−2i−2i2i2i−2i2i-22000000000000000000000000
χ4022-2-2-22-222-222-2-2-2-22−2i−2i2i2i22-2−2i−2i2i2i22-2-200000000−2i−2i2i2i2i−2i2-2000000000000000000000000
χ4122-2-2-2-222-2222-2-2-22-200002-22000022-2-2020-20000000000-2200200-2000000002-200000000
χ4222-2-2-2-222-2222-2-2-22-200002-22000022-2-20-2020000000000-2200-200200000000-2200000000
χ4322-2-2-2-222-2222-2-2-22-200002-220000-2-222020-200000000002-200200-200000000-2200000000
χ4422-2-2-2-222-2222-2-2-22-200002-220000-2-2220-20200000000002-200-2002000000002-200000000
χ4544444-4-4-2-4-44-2-2-2-2220000-222000000000000004i−4i0000000000000000−2i2i00000000000000
χ4644444-4-4-2-4-44-2-2-2-2220000-22200000000000000−4i4i00000000000000002i−2i00000000000000
χ474444-44-44-44-4444-4-440000-4-44000000000000000000000000000000000000000000000000
χ484444-44-4-2-44-4-2-2-222-2000022-2000000000000000000000000000000000000−2i32i30000000000
χ494444-44-4-2-44-4-2-2-222-2000022-20000000000000000000000000000000000002i3−2i30000000000
χ504444-4-44-24-4-4-2-2-22-2200002-220000000000004i−4i0000000000000000−2i2i0000000000000000
χ514444-4-44-24-4-4-2-2-22-2200002-22000000000000−4i4i00000000000000002i−2i0000000000000000
χ5244-4-44444-4-4-44-4-44440000-4-4-4000000000000000000000000000000000000000000000000
χ5344-4-4444-2-4-4-4-222-2-2-200002220000000000000000000000000000000000−2i32i3000000000000
χ5444-4-4444-2-4-4-4-222-2-2-2000022200000000000000000000000000000000002i3−2i3000000000000
χ5544-4-44-4-4-244-4-222-22200002-2-20000000040-400000000000000-20020000000000000000000
χ5644-4-44-4-4-244-4-222-22200002-2-200000000-40400000000000000200-20000000000000000000
χ5744-4-4-44-4-24-44-22222-24i4i−4i−4i-2-220000000000000000−2i−2i2i2i0000000000000000000000000000
χ5844-4-4-44-4-24-44-22222-2−4i−4i4i4i-2-2200000000000000002i2i−2i−2i0000000000000000000000000000
χ5944-4-4-4-44-2-444-2222-220000-22-200000000040-400000000000000-2002000000000000000000
χ6044-4-4-4-44-2-444-2222-220000-22-2000000000-40400000000000000200-2000000000000000000
χ614-44i−4i0004000-44i−4i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130002+2i−2−2i2−2i−2+2i22−22−2i22i2000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000
χ624-44i−4i0004000-44i−4i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−2−2i2+2i−2+2i2−2i−22222i2−2i2000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000
χ634-44i−4i0004000-44i−4i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130002+2i−2−2i2−2i−2+2i−22222i2−2i200000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000
χ644-44i−4i0004000-44i−4i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000−2−2i2+2i−2+2i2−2i22−22−2i22i200000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000
χ654-4−4i4i0004000-4−4i4i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230002−2i−2+2i2+2i−2−2i22−222i2−2i200000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000
χ664-4−4i4i0004000-4−4i4i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000−2+2i2−2i−2−2i2+2i−2222−2i22i200000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000
χ674-4−4i4i0004000-4−4i4i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230002−2i−2+2i2+2i−2−2i−2222−2i22i2000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000
χ684-4−4i4i0004000-4−4i4i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000−2+2i2−2i−2−2i2+2i22−222i2−2i2000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000
χ698-88i−8i000-40004−4i4i0004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ130000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000
χ708-88i−8i000-40004−4i4i000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ1300000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000
χ718-8−8i8i000-400044i−4i000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ2300000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000
χ728-8−8i8i000-400044i−4i0004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000

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