Finite Group Databasebeta

← Group #10897659

Character table — Group #10897659

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444466668888888888881212121212121212121216161616161616161616161616162424242424244848
order1244222344461212666888812121244442244448824242424448888888844661212121212121212242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-11-1-1-1-1-11111111111-1-1-1-11-11-11-111-1-1-1-1-1-1-1-111-1-11-1
χ31111111111111111111111111111-11-11-1-1-1-11111111111-1-1-1-1-11-11-11-1-111-1-1-1-1-1-1-1-111-11
χ41111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11-11-1-1-1-1-11111-1-1-1-1-1-111111-11-11-111-1-1-1-1-1-111-1-111-11
χ7111111111111111111111111-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-11111-11-11-11-1-111-1-1-1-11111-1-11-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ911111111111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1
χ1011111111111111111-1-1-1-111111111-11-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-11-1-1-11111-1-11111-1-1-11
χ1111111111111111111-1-1-1-11111111-11-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11-1111-1-111-1-111-1-1111-1
χ1211111111111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111
χ1311111111111111111-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1411111111111111111-1-1-1-1111-1-1-1-11-11-111-1-1-1-1-1-1-1-111111111-111-11-1-1-11111-1-1-1-1-1-1111-1
χ1511111111111111111-1-1-1-1111-1-1-1-1-11-1111-1-1-1-1-1-1-1-1111111111-1-11-1111-1-111-1-1-1-111-1-1-11
χ1611111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ172222222-1222-1-1-1-1-1-12222-1-1-1000022222222-1-1-1-1000000000022-1-1-1-1-1-1-1-1-1-1-1-100000000
χ182222222-1222-1-1-1-1-1-12222-1-1-100002-22-2-2-2-2-2-1-1-1-100000000002-2-11-11-1-111111100000000
χ192222222-1222-1-1-1-1-1-12222-1-1-10000-22-22-2-2-2-2-1-1-1-10000000000-221-11-111-1-1111100000000
χ202222222-1222-1-1-1-1-1-12222-1-1-10000-2-2-2-22222-1-1-1-10000000000-2-211111111-1-1-1-100000000
χ212222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-100002222-2-22211110000000000-2-2-1-1-1-1111111-1-100000000
χ222222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-100002-22-222-2-211110000000000-22-11-1111-1-1-1-11100000000
χ232222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-10000-22-2222-2-2111100000000002-21-11-1-1-111-1-11100000000
χ242222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-10000-2-2-2-2-2-22211110000000000221111-1-1-1-111-1-100000000
χ252222-2-2222-2-22222-2-20000-2-2222220000002-20000-2-2000022-2-20000000000002-200000000
χ262222-2-2222-2-22222-2-20000-2-222222000000-220000-2-20000-2-222000000000000-2200000000
χ272222-2-2222-2-22222-2-20000-2-22-2-2-2-20000002-20000220000-2-2220000000000002-200000000
χ282222-2-2222-2-22222-2-20000-2-22-2-2-2-2000000-22000022000022-2-2000000000000-2200000000
χ2922-2-22222-2-2-22-2-22220000-2-2-2000000002-2000000002i2i−2i−2i2i−2i2i−2i00000000002-20000000000
χ3022-2-22222-2-2-22-2-22220000-2-2-2000000002-200000000−2i−2i2i2i−2i2i−2i2i00000000002-20000000000
χ3122-2-22222-2-2-22-2-22220000-2-2-200000000-22000000002i2i−2i−2i−2i2i−2i2i0000000000-220000000000
χ3222-2-22222-2-2-22-2-22220000-2-2-200000000-2200000000−2i−2i2i2i2i−2i2i−2i0000000000-220000000000
χ3322-2-22-2-2222-22-2-2-22-200002-222i2i−2i−2i020-2000000002i−2i0000000000020-20000000000002i−2i00
χ3422-2-22-2-2222-22-2-2-22-200002-222i2i−2i−2i0-202000000002i−2i00000000000-202000000000000−2i2i00
χ3522-2-22-2-2222-22-2-2-22-200002-22−2i−2i2i2i020-200000000−2i2i0000000000020-2000000000000−2i2i00
χ3622-2-22-2-2222-22-2-2-22-200002-22−2i−2i2i2i0-20200000000−2i2i00000000000-2020000000000002i−2i00
χ3722-2-2-22-222-222-2-2-2-220000-2222i2i−2i−2i20-2000000000−2i2i000000000020-2000000000002i−2i0000
χ3822-2-2-22-222-222-2-2-2-220000-2222i2i−2i−2i-202000000000−2i2i0000000000-20200000000000−2i2i0000
χ3922-2-2-22-222-222-2-2-2-220000-222−2i−2i2i2i20-20000000002i−2i000000000020-200000000000−2i2i0000
χ4022-2-2-22-222-222-2-2-2-220000-222−2i−2i2i2i-2020000000002i−2i0000000000-202000000000002i−2i0000
χ4122-2-2-2-222-2222-2-22-2-22i2i−2i−2i22-20000000000002i2i−2i−2i0000002i−2i−2i2i000000000000002-2000000
χ4222-2-2-2-222-2222-2-22-2-22i2i−2i−2i22-20000000000002i2i−2i−2i000000−2i2i2i−2i00000000000000-22000000
χ4322-2-2-2-222-2222-2-22-2-2−2i−2i2i2i22-2000000000000−2i−2i2i2i0000002i−2i−2i2i00000000000000-22000000
χ4422-2-2-2-222-2222-2-22-2-2−2i−2i2i2i22-2000000000000−2i−2i2i2i000000−2i2i2i−2i000000000000002-2000000
χ4544444-4-44-4-44444-44-40000-44-4000000000000000000000000000000000000000000000000
χ4644444-4-4-2-4-44-2-2-22-2200002-220000000000000000000000000000000023−2300000000000000
χ4744444-4-4-2-4-44-2-2-22-2200002-2200000000000000000000000000000000−232300000000000000
χ484444-44-44-44-4444-4-4400004-4-4000000000000000000000000000000000000000000000000
χ494444-44-4-2-44-4-2-2-222-20000-222000000000000000000000000000000000023−23000000000000
χ504444-44-4-2-44-4-2-2-222-20000-2220000000000000000000000000000000000−2323000000000000
χ514444-4-44-24-4-4-2-2-2-222000022-200000000004-400000000000000000000000000-2200000000
χ524444-4-44-24-4-4-2-2-2-222000022-20000000000-44000000000000000000000000002-200000000
χ5344-4-4444-2-4-4-4-222-2-2-20000222000000004-400000000000000000000000000-220000000000
χ5444-4-4444-2-4-4-4-222-2-2-2000022200000000-44000000000000000000000000002-20000000000
χ5544-4-44-4-4-244-4-2222-220000-22-20000040-4000000000000000000000-2020000000000000000
χ5644-4-44-4-4-244-4-2222-220000-22-200000-40400000000000000000000020-20000000000000000
χ5744-4-4-44-4-24-44-22222-200002-2-2000040-4000000000000000000000-20200000000000000000
χ5844-4-4-44-4-24-44-22222-200002-2-20000-40400000000000000000000020-200000000000000000
χ5944-4-4-4-44-2-444-222-2224i4i−4i−4i-2-22000000000000−2i−2i2i2i00000000000000000000000000000000
χ6044-4-4-4-44-2-444-222-222−4i−4i4i4i-2-220000000000002i2i−2i−2i00000000000000000000000000000000
χ614-44i−4i0004000-44i−4i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130002+2i−2−2i2−2i−2+2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ624-44i−4i0004000-44i−4i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−2−2i2+2i−2+2i2−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ634-44i−4i0004000-44i−4i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130002+2i−2−2i2−2i−2+2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ644-44i−4i0004000-44i−4i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000−2−2i2+2i−2+2i2−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ654-4−4i4i0004000-4−4i4i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230002−2i−2+2i2+2i−2−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ664-4−4i4i0004000-4−4i4i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000−2+2i2−2i−2−2i2+2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ674-4−4i4i0004000-4−4i4i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230002−2i−2+2i2+2i−2−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ684-4−4i4i0004000-4−4i4i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000−2+2i2−2i−2−2i2+2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ698-88i−8i000-40004−4i4i0004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ708-88i−8i000-40004−4i4i000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ718-8−8i8i000-400044i−4i000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ728-8−8i8i000-400044i−4i0004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000

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