Finite Group Databasebeta

← Group #10897666

Character table — Group #10897666

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888881212121212121212161616161616161616161616242424242424242424242424
order124422234444444612124466688881212121212121288121224242424242424248888888844881212121224242424222444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ511111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-11-1-11-1-1-111-1-1
χ611111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-111111111-11-11-1-111-1-111-1-11-1-11-1-1-1-111
χ711111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11-111-1111-1-111
χ811111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-111-11111-1-1
χ911111111-1-1-1-1111111-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111-1-11-1-111111-1-1
χ1011111111-1-1-1-1111111-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-11111-1-1-11-1-11-111-1-111
χ1111111111-1-1-1-1111111-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-11111-111-1-1-1-1-111
χ1211111111-1-1-1-1111111-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-11-111-11-1-111-1-1
χ1311111111-1-1-1-1111111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-11-1-11-1-1-1-11111
χ1411111111-1-1-1-1111111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1
χ1511111111-1-1-1-1111111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-111-11111-1-1-1-1
χ1611111111-1-1-1-1111111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1111111
χ172222222-12222222-1-1-122-1-1-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1000000000000
χ182222222-12222222-1-1-122-1-1-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-211111111000000000000
χ192222222-12222222-1-1-122-1-1-1-2-2-2-2-1-1-1-1-1-1-1-2-2-1-111111111000000002-22-2-1-111-1-111000000000000
χ202222222-12222222-1-1-122-1-1-1-2-2-2-2-1-1-1-1-1-1-1-2-2-1-11111111100000000-22-2211-1-111-1-1000000000000
χ212222222-1-2-2-2-2222-1-1-1-2-2-1-1-122221111-1-1-1-2-211-1-1-1-11111000000002-2-22-1-11111-1-1000000000000
χ222222222-1-2-2-2-2222-1-1-1-2-2-1-1-122221111-1-1-1-2-211-1-1-1-1111100000000-222-211-1-1-1-111000000000000
χ232222222-1-2-2-2-2222-1-1-1-2-2-1-1-1-2-2-2-21111-1-1-122111111-1-1-1-10000000022-2-2-1-1-1-11111000000000000
χ242222222-1-2-2-2-2222-1-1-1-2-2-1-1-1-2-2-2-21111-1-1-122111111-1-1-1-100000000-2-2221111-1-1-1-1000000000000
χ252222-2-2222222-2-22222-2-22-2-222-2-222222-2-22-2-2-222-2-222-2-200000000000000000000000000000000
χ262222-2-2222222-2-22222-2-22-2-2-2-22222222-2-2-22-2-2-2-222-2-22200000000000000000000000000000000
χ272222-2-222-2-2-2-2-2-22222222-2-222-2-2-2-2-2-22-2-2-222222-2-2-2-22200000000000000000000000000000000
χ282222-2-222-2-2-2-2-2-22222222-2-2-2-222-2-2-2-22-2-22-222-2-22222-2-200000000000000000000000000000000
χ292222-2-22-12222-2-22-1-1-1-2-2-11122-2-2-1-1-1-1-1112-211-1-111-1-1110000000000003−33−33−33−3000000000000
χ302222-2-22-12222-2-22-1-1-1-2-2-11122-2-2-1-1-1-1-1112-211-1-111-1-111000000000000−33−33−33−33000000000000
χ312222-2-22-12222-2-22-1-1-1-2-2-111-2-222-1-1-1-1-111-221111-1-111-1-10000000000003−3−333−3−33000000000000
χ322222-2-22-12222-2-22-1-1-1-2-2-111-2-222-1-1-1-1-111-221111-1-111-1-1000000000000−333−3−333−3000000000000
χ332222-2-22-1-2-2-2-2-2-22-1-1-122-11122-2-21111-111-22-1-1-1-11111-1-10000000000003−3−33−333−3000000000000
χ342222-2-22-1-2-2-2-2-2-22-1-1-122-11122-2-21111-111-22-1-1-1-11111-1-1000000000000−333−33−3−33000000000000
χ352222-2-22-1-2-2-2-2-2-22-1-1-122-111-2-2221111-1112-2-1-111-1-1-1-1110000000000003−33−3−33−33000000000000
χ362222-2-22-1-2-2-2-2-2-22-1-1-122-111-2-2221111-1112-2-1-111-1-1-1-111000000000000−33−333−33−3000000000000
χ3722-2-222220000-2-2-22-2-2002222i−2i2i−2i0000-2-2-200002i−2i2i−2i00002i2i−2i−2i00000000000000000000002-20000
χ3822-2-222220000-2-2-22-2-2002222i−2i2i−2i0000-2-2-200002i−2i2i−2i0000−2i−2i2i2i0000000000000000000000-220000
χ3922-2-222220000-2-2-22-2-200222−2i2i−2i2i0000-2-2-20000−2i2i−2i2i00002i2i−2i−2i0000000000000000000000-220000
χ4022-2-222220000-2-2-22-2-200222−2i2i−2i2i0000-2-2-20000−2i2i−2i2i0000−2i−2i2i2i00000000000000000000002-20000
χ4122-2-22-2-222i2i−2i−2i2-222-2-22i−2i-22-200002i2i−2i−2i22-2002i−2i00000000000000000000000000000200-20002i−2i00
χ4222-2-22-2-222i2i−2i−2i2-222-2-22i−2i-22-200002i2i−2i−2i22-2002i−2i00000000000000000000000000000-2002000−2i2i00
χ4322-2-22-2-22−2i−2i2i2i2-222-2-2−2i2i-22-20000−2i−2i2i2i22-200−2i2i00000000000000000000000000000200-2000−2i2i00
χ4422-2-22-2-22−2i−2i2i2i2-222-2-2−2i2i-22-20000−2i−2i2i2i22-200−2i2i00000000000000000000000000000-20020002i−2i00
χ4522-2-2-22-222i2i−2i−2i-2222-2-2−2i2i-2-2200002i2i−2i−2i2-2200−2i2i000000000000000000000000000000200-200002i−2i
χ4622-2-2-22-222i2i−2i−2i-2222-2-2−2i2i-2-2200002i2i−2i−2i2-2200−2i2i000000000000000000000000000000-20020000−2i2i
χ4722-2-2-22-22−2i−2i2i2i-2222-2-22i−2i-2-220000−2i−2i2i2i2-22002i−2i000000000000000000000000000000200-20000−2i2i
χ4822-2-2-22-22−2i−2i2i2i-2222-2-22i−2i-2-220000−2i−2i2i2i2-22002i−2i000000000000000000000000000000-200200002i−2i
χ4922-2-2-2-222000022-22-2-2002-2-22i−2i−2i2i0000-22200002i−2i−2i2i000000002i2i−2i−2i000000000000200-200000000
χ5022-2-2-2-222000022-22-2-2002-2-22i−2i−2i2i0000-22200002i−2i−2i2i00000000−2i−2i2i2i000000000000-200200000000
χ5122-2-2-2-222000022-22-2-2002-2-2−2i2i2i−2i0000-2220000−2i2i2i−2i000000002i2i−2i−2i000000000000-200200000000
χ5222-2-2-2-222000022-22-2-2002-2-2−2i2i2i−2i0000-2220000−2i2i2i−2i00000000−2i−2i2i2i000000000000200-200000000
χ5344444-4-440000-44-444400-44-400000000-4-4400000000000000000000000000000000000000000000
χ5444444-4-4-20000-44-4-2-2-2002-220000000022-20000000023−2323−2300000000000000000000000000000000
χ5544444-4-4-20000-44-4-2-2-2002-220000000022-200000000−2323−232300000000000000000000000000000000
χ564444-44-4400004-4-444400-4-4400000000-44-400000000000000000000000000000000000000000000
χ574444-44-4-200004-4-4-2-2-20022-2000000002-220000000023−23−232300000000000000000000000000000000
χ584444-44-4-200004-4-4-2-2-20022-2000000002-2200000000−232323−2300000000000000000000000000000000
χ5944-4-4444-20000-4-4-4-22200-2-2-24i−4i4i−4i00002220000−2i2i−2i2i000000000000000000000000000000000000
χ6044-4-4444-20000-4-4-4-22200-2-2-2−4i4i−4i4i000022200002i−2i2i−2i000000000000000000000000000000000000
χ6144-4-44-4-4-24i4i−4i−4i4-44-2224i−4i2-220000−2i−2i2i2i-2-2200−2i2i0000000000000000000000000000000000000000
χ6244-4-44-4-4-2−4i−4i4i4i4-44-222−4i4i2-2200002i2i−2i−2i-2-22002i−2i0000000000000000000000000000000000000000
χ6344-4-4-44-4-24i4i−4i−4i-444-222−4i4i22-20000−2i−2i2i2i-22-2002i−2i0000000000000000000000000000000000000000
χ6444-4-4-44-4-2−4i−4i4i4i-444-2224i−4i22-200002i2i−2i−2i-22-200−2i2i0000000000000000000000000000000000000000
χ6544-4-4-4-44-2000044-4-22200-2224i−4i−4i4i00002-2-20000−2i2i2i−2i000000000000000000000000000000000000
χ6644-4-4-4-44-2000044-4-22200-222−4i4i4i−4i00002-2-200002i−2i−2i2i000000000000000000000000000000000000
χ674-44i−4i00042+2i−2−2i2−2i−2+2i000-44i−4i0000000002+2i−2−2i2−2i−2+2i0000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ684-44i−4i00042+2i−2−2i2−2i−2+2i000-44i−4i0000000002+2i−2−2i2−2i−2+2i000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ694-44i−4i0004−2−2i2+2i−2+2i2−2i000-44i−4i000000000−2−2i2+2i−2+2i2−2i0000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ704-44i−4i0004−2−2i2+2i−2+2i2−2i000-44i−4i000000000−2−2i2+2i−2+2i2−2i000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ714-4−4i4i00042−2i−2+2i2+2i−2−2i000-4−4i4i0000000002−2i−2+2i2+2i−2−2i000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ724-4−4i4i00042−2i−2+2i2+2i−2−2i000-4−4i4i0000000002−2i−2+2i2+2i−2−2i0000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ734-4−4i4i0004−2+2i2−2i−2−2i2+2i000-4−4i4i000000000−2+2i2−2i−2−2i2+2i000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ744-4−4i4i0004−2+2i2−2i−2−2i2+2i000-4−4i4i000000000−2+2i2−2i−2−2i2+2i0000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ758-88i−8i000-44+4i−4−4i4−4i−4+4i0004−4i4i000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000000000000000000000000
χ768-88i−8i000-4−4−4i4+4i−4+4i4−4i0004−4i4i0000000002+2i−2−2i2−2i−2+2i00000000000000000000000000000000000000000000000
χ778-8−8i8i000-44−4i−4+4i4+4i−4−4i00044i−4i000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000000000000000000000000
χ788-8−8i8i000-4−4+4i4−4i−4−4i4+4i00044i−4i0000000002−2i−2+2i2+2i−2−2i00000000000000000000000000000000000000000000000

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