Finite Group Databasebeta

← Group #10840274

Character table — Group #10840274

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order1244222344444446121244666121212121212128888244444668812121212121212128888884812121212242424242244448848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1
χ31111111111111111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1111111-1-111-1-111-1-1-11-11-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-111-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-1
χ9111111111-1-1-1-111111-1-11111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-11-11111-1-1-1-11-11-1-1-1111-1
χ10111111111-1-1-1-111111-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-11-1-1-1-111111111-1-1-1-1-11
χ11111111111-1-1-1-111111-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-1-1-111-1-1-1-11111-11
χ12111111111-1-1-1-111111-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11-1-1-11111-1-1-11-1111-1-11-1
χ13111111111-1-1-1-111111-1-11111-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111111-11111-1-1-1-1-11-1111-1-1-11
χ14111111111-1-1-1-111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-111111-1
χ15111111111-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1111-1-1-1-1111111-1-1-1-11-1
χ16111111111-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111-1-1-11111-1-11-11-1-1-111-11
χ172222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-10000222222-1-122-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ182222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-1000022-2-222-1-1-2-2-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ192222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-222-2-2112211-1-11111000000-2-2-1-111-1-1110000000000
χ202222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-2-211-2-211-1-111110000002211-1-111-1-10000000000
χ212222222-12-2-2-2-222-1-1-1-2-2-1-1-1-11111-1-100002222-2-2-1-1-2-2-1-11111110000002-2-1-1-1-111110000000000
χ222222222-12-2-2-2-222-1-1-1-2-2-1-1-1-11111-1-1000022-2-2-2-2-1-122-1-1111111000000-221111-1-1-1-10000000000
χ232222222-12-2-2-2-222-1-1-1-2-2-1-1-1-11111-1-10000-2-2222211-2-21111-1-1-1-1000000-22-1-11111-1-10000000000
χ242222222-12-2-2-2-222-1-1-1-2-2-1-1-1-11111-1-10000-2-2-2-22211221111-1-1-1-10000002-211-1-1-1-1110000000000
χ2522222-2-22-200002-2222002-2-2-200002-2222200002i−2i000000002i2i−2i−2i-2-20000000000000000002i−2i0000
χ2622222-2-22-200002-2222002-2-2-200002-222220000−2i2i00000000−2i−2i2i2i-2-2000000000000000000−2i2i0000
χ2722222-2-22-200002-2222002-2-2-200002-2-2-2-2-200002i−2i000000002i2i−2i−2i22000000000000000000−2i2i0000
χ2822222-2-22-200002-2222002-2-2-200002-2-2-2-2-20000−2i2i00000000−2i−2i2i2i220000000000000000002i−2i0000
χ292222-2-22222222-2-2222-2-2-2-2222222-2-20000002i−2i00002i−2i00-2-20000000000002i−2i002i−2i000000000000
χ302222-2-22222222-2-2222-2-2-2-2222222-2-2000000−2i2i0000−2i2i00-2-2000000000000−2i2i00−2i2i000000000000
χ312222-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2-2-20000002i−2i0000−2i2i00220000000000002i−2i00−2i2i000000000000
χ322222-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2-2-2000000−2i2i00002i−2i0022000000000000−2i2i002i−2i000000000000
χ332222-2-22-122222-2-2-1-1-1-2-211-1-1-1-1-1-1110000002i−2i00−i3i32i−2i−i3i311−i3i3−i3i300000000−ii3−3−ii3−30000000000
χ342222-2-22-122222-2-2-1-1-1-2-211-1-1-1-1-1-1110000002i−2i00i3−i32i−2ii3−i311i3−i3i3−i300000000−ii−33−ii−330000000000
χ352222-2-22-122222-2-2-1-1-1-2-211-1-1-1-1-1-111000000−2i2i00−i3i3−2i2i−i3i311−i3i3−i3i300000000i−i−33i−i−330000000000
χ362222-2-22-122222-2-2-1-1-1-2-211-1-1-1-1-1-111000000−2i2i00i3−i3−2i2ii3−i311i3−i3i3−i300000000i−i3−3i−i3−30000000000
χ372222-2-22-12-2-2-2-2-2-2-1-1-12211-1-11111110000002i−2i00−i3i3−2i2i−i3i3-1-1i3−i3i3−i300000000−ii3−3i−i−330000000000
χ382222-2-22-12-2-2-2-2-2-2-1-1-12211-1-11111110000002i−2i00i3−i3−2i2ii3−i3-1-1−i3i3−i3i300000000−ii−33i−i3−30000000000
χ392222-2-22-12-2-2-2-2-2-2-1-1-12211-1-1111111000000−2i2i00−i3i32i−2i−i3i3-1-1i3−i3i3−i300000000i−i−33−ii3−30000000000
χ402222-2-22-12-2-2-2-2-2-2-1-1-12211-1-1111111000000−2i2i00i3−i32i−2ii3−i3-1-1−i3i3−i3i300000000i−i3−3−ii−330000000000
χ4122-2-22-2-2222i2i−2i−2i-222-2-22i−2i2-2-222i2i−2i−2i-2200000000000000002i−2i00000000000000000000020-2002i−2i00
χ4222-2-22-2-2222i2i−2i−2i-222-2-22i−2i2-2-222i2i−2i−2i-2200000000000000002i−2i000000000000000000000-20200−2i2i00
χ4322-2-22-2-222−2i−2i2i2i-222-2-2−2i2i2-2-22−2i−2i2i2i-220000000000000000−2i2i00000000000000000000020-200−2i2i00
χ4422-2-22-2-222−2i−2i2i2i-222-2-2−2i2i2-2-22−2i−2i2i2i-220000000000000000−2i2i000000000000000000000-202002i−2i00
χ4522-2-2-22-2222i2i−2i−2i2-22-2-2−2i2i-22-222i2i−2i−2i2-222-2-2000000000000−2i2i00002-22i2i−2i−2i00000000000000000000
χ4622-2-2-22-2222i2i−2i−2i2-22-2-2−2i2i-22-222i2i−2i−2i2-2-2-222000000000000−2i2i0000-22−2i−2i2i2i00000000000000000000
χ4722-2-2-22-222−2i−2i2i2i2-22-2-22i−2i-22-22−2i−2i2i2i2-222-2-20000000000002i−2i00002-2−2i−2i2i2i00000000000000000000
χ4822-2-2-22-222−2i−2i2i2i2-22-2-22i−2i-22-22−2i−2i2i2i2-2-2-2220000000000002i−2i0000-222i2i−2i−2i00000000000000000000
χ4922-2-2-2-222-20000222-2-200-2-22-200002222-2-22-200002200-2-2000000-220000000000000020-20000000
χ5022-2-2-2-222-20000222-2-200-2-22-200002222-2-2-220000-2-20022000000-2200000000000000-2020000000
χ5122-2-2-2-222-20000222-2-200-2-22-2000022-2-2222-200002200-2-20000002-200000000000000-2020000000
χ5222-2-2-2-222-20000222-2-200-2-22-2000022-2-222-220000-2-200220000002-20000000000000020-20000000
χ5344444-4-4-2-400004-4-2-2-200-22220000-22000000004i−4i00000000−2i−2i2i2i00000000000000000000000000
χ5444444-4-4-2-400004-4-2-2-200-22220000-2200000000−4i4i000000002i2i−2i−2i00000000000000000000000000
χ554444-44-44-40000-4444400-44-4-40000-44000000000000000000000000000000000000000000000000
χ564444-44-4-2-40000-44-2-2-2002-22200002-200000000000000000023−23−232300000000000000000000000000
χ574444-44-4-2-40000-44-2-2-2002-22200002-2000000000000000000−232323−2300000000000000000000000000
χ5844-4-44444-40000-4-44-4-400444-40000-4-4000000000000000000000000000000000000000000000000
χ5944-4-4444-2-40000-4-4-22200-2-2-220000220000000000−2i32i3002i3−2i300000000000000000000000000000000
χ6044-4-4444-2-40000-4-4-22200-2-2-2200002200000000002i3−2i300−2i32i300000000000000000000000000000000
χ6144-4-44-4-4-244i4i−4i−4i-44-2224i−4i-222-2−2i−2i2i2i2-20000000000000000−2i2i000000000000000000000000000000
χ6244-4-44-4-4-24−4i−4i4i4i-44-222−4i4i-222-22i2i−2i−2i2-200000000000000002i−2i000000000000000000000000000000
χ6344-4-4-44-4-244i4i−4i−4i4-4-222−4i4i2-22-2−2i−2i2i2i-2200000000000000002i−2i000000000000000000000000000000
χ6444-4-4-44-4-24−4i−4i4i4i4-4-2224i−4i2-22-22i2i−2i−2i-220000000000000000−2i2i000000000000000000000000000000
χ6544-4-4-4-44-2-4000044-2220022-220000-2-200004-40000-2-2002200000000000000000000000000000000
χ6644-4-4-4-44-2-4000044-2220022-220000-2-20000-4400002200-2-200000000000000000000000000000000
χ674-44i−4i000402+2i−2−2i2−2i−2+2i00-44i−4i0000002+2i−2−2i2−2i−2+2i0022−22−2i22i2000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ684-44i−4i000402+2i−2−2i2−2i−2+2i00-44i−4i0000002+2i−2−2i2−2i−2+2i00−22222i2−2i200000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ694-44i−4i00040−2−2i2+2i−2+2i2−2i00-44i−4i000000−2−2i2+2i−2+2i2−2i0022−22−2i22i200000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ704-44i−4i00040−2−2i2+2i−2+2i2−2i00-44i−4i000000−2−2i2+2i−2+2i2−2i00−22222i2−2i2000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ714-4−4i4i000402−2i−2+2i2+2i−2−2i00-4−4i4i0000002−2i−2+2i2+2i−2−2i0022−222i2−2i200000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ724-4−4i4i000402−2i−2+2i2+2i−2−2i00-4−4i4i0000002−2i−2+2i2+2i−2−2i00−2222−2i22i2000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ734-4−4i4i00040−2+2i2−2i−2−2i2+2i00-4−4i4i000000−2+2i2−2i−2−2i2+2i0022−222i2−2i2000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ744-4−4i4i00040−2+2i2−2i−2−2i2+2i00-4−4i4i000000−2+2i2−2i−2−2i2+2i00−2222−2i22i200000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ758-88i−8i000-404+4i−4−4i4−4i−4+4i004−4i4i000000−2−2i2+2i−2+2i2−2i00000000000000000000000000000000000000000000000000
χ768-88i−8i000-40−4−4i4+4i−4+4i4−4i004−4i4i0000002+2i−2−2i2−2i−2+2i00000000000000000000000000000000000000000000000000
χ778-8−8i8i000-404−4i−4+4i4+4i−4−4i0044i−4i000000−2+2i2−2i−2−2i2+2i00000000000000000000000000000000000000000000000000
χ788-8−8i8i000-40−4+4i4−4i−4−4i4+4i0044i−4i0000002−2i−2+2i2+2i−2−2i00000000000000000000000000000000000000000000000000

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