Finite Group Databasebeta

← Group #10768794

Character table — Group #10768794

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881616161616161616161624242424242424242424242424242424
order1222222234466624446666121212121212244468888122424242424242424688121212242424242444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ71111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-111-1-1-1111111-1-11-1-11-1-1-1-11111
χ81111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-111-11111-1-1-1-1
χ911111-1-111-1-1111-1-11111-1-1-1-111111-1-11-111-1-1-11111-1-1-1-111-11-1-111-1-11111-11-1-11-1-1-111-1-1
χ1011111-1-111-1-1111-1-11111-1-1-1-111111-1-11-111-1-1-11111-1-1-1-111-11-1-111-1-1-1-1-1-11-111-1111-1-111
χ1111111-1-111-1-1111-1-11111-1-1-1-111111-1-11-1-1-111-1-1-1-1-111111-111-1-1-1-11111-1-1-11-1-11-111-1-111
χ1211111-1-111-1-1111-1-11111-1-1-1-111111-1-11-1-1-111-1-1-1-1-111111-111-1-1-1-111-1-1111-111-11-1-111-1-1
χ1311111-1-111-1-1111-1-11111-1-1-1-11111-111-1-111-1-1-11111-1-1-1-1-1-11-111-1-1111111-1-11-1-11-1-1-1-111
χ1411111-1-111-1-1111-1-11111-1-1-1-11111-111-1-111-1-1-11111-1-1-1-1-1-11-111-1-111-1-1-1-111-111-11111-1-1
χ1511111-1-111-1-1111-1-11111-1-1-1-11111-111-1-1-1-111-1-1-1-1-11111-11-1-11111-1-111-1-1-1-11-1-111111-1-1
χ1611111-1-111-1-1111-1-11111-1-1-1-11111-111-1-1-1-111-1-1-1-1-11111-11-1-11111-1-1-1-11111-111-1-1-1-1-111
χ17222222222-2-22222-2-2-22222-2-2-2-2-2-22-22-220000-200000000200-2-2200000000000000000000
χ18222222222-2-22222-2-2-22222-2-2-2-2-2-2-22-2220000-200000000-20022-200000000000000000000
χ1922222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-10000000000000000
χ2022222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-111111111-1-2-2-1-1-111110000000000000000
χ2122222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-11-2-211111110000000000000000
χ2222222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-2-2-2-2-111111111122111-1-1-1-10000000000000000
χ2322222222-1-2-2-1-1-12-2-2-2-1-1-1-11111112-22-2-10000133−3−333−3−3-10011-13−33−30000000000000000
χ2422222222-1-2-2-1-1-12-2-2-2-1-1-1-11111112-22-2-100001−3−333−3−333-10011-1−33−330000000000000000
χ2522222222-1-2-2-1-1-12-2-2-2-1-1-1-1111111-22-22-10000133−3−333−3−3100-1-11−33−330000000000000000
χ2622222222-1-2-2-1-1-12-2-2-2-1-1-1-1111111-22-22-100001−3−333−3−333100-1-113−33−30000000000000000
χ2722222-2-22222222-22-2-222-2-222-2-2-2-222-2-2-20000200000000200-22-200000000000000000000
χ2822222-2-22222222-22-2-222-2-222-2-2-2-2-2-222-20000200000000-2002-2200000000000000000000
χ2922222-2-22-122-1-1-1-22-2-2-1-111-1-1111122-2-210000-133−3−3−3−333-1001-113−3−330000000000000000
χ3022222-2-22-122-1-1-1-22-2-2-1-111-1-1111122-2-210000-1−3−33333−3−3-1001-11−333−30000000000000000
χ3122222-2-22-122-1-1-1-22-2-2-1-111-1-11111-2-22210000-133−3−3−3−333100-11-1−333−30000000000000000
χ3222222-2-22-122-1-1-1-22-2-2-1-111-1-11111-2-22210000-1−3−33333−3−3100-11-13−3−330000000000000000
χ3322222-2-22-1-2-2-1-1-1-2-222-1-11111-1-1-1-12-2-22122-2-21-1-1-1-11111-12-2-111-1-1110000000000000000
χ3422222-2-22-1-2-2-1-1-1-2-222-1-11111-1-1-1-12-2-221-2-22211111-1-1-1-1-1-22-11111-1-10000000000000000
χ3522222-2-22-1-2-2-1-1-1-2-222-1-11111-1-1-1-1-222-2122-2-21-1-1-1-111111-221-1-111-1-10000000000000000
χ3622222-2-22-1-2-2-1-1-1-2-222-1-11111-1-1-1-1-222-21-2-22211111-1-1-1-112-21-1-1-1-1110000000000000000
χ372222-222-2222222-2-22-2-2-2222222-2-20000-20000-20000000000000000002-200200-200000000
χ382222-222-2222222-2-22-2-2-2222222-2-20000-20000-2000000000000000000-2200-200200000000
χ392222-222-22-2-2222-22-22-2-222-2-2-2-2220000-20000200000000000000000000000220-2-2000000
χ402222-222-22-2-2222-22-22-2-222-2-2-2-2220000-20000200000000000000000000000-2-2022000000
χ412222-2-2-2-22222222-2-22-2-2-2-222-2-222000020000-2000000000000000000000002-20-22000000
χ422222-2-2-2-22222222-2-22-2-2-2-222-2-222000020000-200000000000000000000000-2202-2000000
χ432222-2-2-2-22-2-2222222-2-2-2-2-2-2-222-2-200002000020000000000000000002-200-200200000000
χ442222-2-2-2-22-2-2222222-2-2-2-2-2-2-222-2-20000200002000000000000000000-2200200-200000000
χ454444-444-4-244-2-2-2-4-44-422-2-2-2-2-2-22200002000020000000000000000000000000000000000
χ464444-444-4-2-4-4-2-2-2-44-4422-2-22222-2-2000020000-20000000000000000000000000000000000
χ474444-4-4-4-4-244-2-2-24-4-442222-2-222-2-20000-2000020000000000000000000000000000000000
χ484444-4-4-4-4-2-4-4-2-2-2444-4222222-2-2220000-20000-20000000000000000000000000000000000
χ4944-4-4400-44004-4-400004-4000000000000022−2200022−2222−22000000000000000000000000000000
χ5044-4-4400-44004-4-400004-40000000000000−2222000−2222−2222000000000000000000000000000000
χ5144-4-4400-4-200-2220000-22000023−2323−230000022−220002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000000000
χ5244-4-4400-4-200-2220000-22000023−2323−2300000−2222000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000000000
χ5344-4-4400-4-200-2220000-220000−2323−23230000022−220002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000
χ5444-4-4400-4-200-2220000-220000−2323−232300000−2222000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000
χ5544-4-4-40044004-4-40000-44000000000000000−2i22i200000−2i22i2−2i22i200000000000000000000000000
χ5644-4-4-40044004-4-40000-440000000000000002i2−2i2000002i2−2i22i2−2i200000000000000000000000000
χ5744-4-4-4004-200-22200002-2000023−23−23230000000−2i22i2000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000
χ5844-4-4-4004-200-22200002-2000023−23−232300000002i2−2i200000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000
χ5944-4-4-4004-200-22200002-20000−232323−230000000−2i22i2000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000
χ6044-4-4-4004-200-22200002-20000−232323−2300000002i2−2i200000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000
χ614-44-404-40400-4-440000004-40000000000000000000000000000000000002i−2i0000002i−2i0000
χ624-44-404-40400-4-440000004-4000000000000000000000000000000000000−2i2i000000−2i2i0000
χ634-44-40-440400-4-44000000-440000000000000000000000000000000000002i−2i000000−2i2i0000
χ644-44-40-440400-4-44000000-44000000000000000000000000000000000000−2i2i0000002i−2i0000
χ654-4-44000044i−4i-44-4000000004i−4i000000000000000000000000000000000000000000002i−2i2-2
χ664-4-44000044i−4i-44-4000000004i−4i00000000000000000000000000000000000000000000−2i2i-22
χ674-4-4400004−4i4i-44-400000000−4i4i000000000000000000000000000000000000000000002i−2i-22
χ684-4-4400004−4i4i-44-400000000−4i4i00000000000000000000000000000000000000000000−2i2i2-2
χ698-88-808-80-40044-4000000-4400000000000000000000000000000000000000000000000000
χ708-88-80-880-40044-40000004-400000000000000000000000000000000000000000000000000
χ718-8-880000-48i−8i4-4400000000−4i4i000000000000000000000000000000000000000000000000
χ728-8-880000-4−8i8i4-44000000004i−4i000000000000000000000000000000000000000000000000

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