Finite Group Databasebeta

← Group #70549

Character table — Group #70549

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222222244444444444444448888888888882424242424242424
order1244222344466612121212668888121224242424242424244488121212122424242424448888
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1
χ611111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ92222222-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ102222222-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ112222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000
χ122222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000
χ1322222-2-22-2-222-2-2-2-2222-200002-2000000000000000000000000002-2
χ1422222-2-22-2-222-2-2-2-2222-200002-200000000000000000000000000-22
χ152222-22-222-2-22222222-2-20000-2-2000000002-20022-2-2000000000000
χ162222-22-222-2-22222222-2-20000-2-200000000-2200-2-222000000000000
χ172222-22-2-12-2-2-1-1-1-1-1-1-111000011−i3−i3−i3−i3i3i3i3i32-200-1-111−i3−i3i3i300000000
χ182222-22-2-12-2-2-1-1-1-1-1-1-111000011−i3−i3−i3−i3i3i3i3i3-220011-1-1i3i3−i3−i300000000
χ192222-22-2-12-2-2-1-1-1-1-1-1-111000011i3i3i3i3−i3−i3−i3−i32-200-1-111i3i3−i3−i300000000
χ202222-22-2-12-2-2-1-1-1-1-1-1-111000011i3i3i3i3−i3−i3−i3−i3-220011-1-1−i3−i3i3i300000000
χ212222-2-222-22-22-2-2-2-222-220000-2200000000000000000000002-20000
χ222222-2-222-22-22-2-2-2-222-220000-220000000000000000000000-220000
χ2322-2-22222-2-2-2222-2-2-2-2222i2i−2i−2i-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2422-2-22222-2-2-2222-2-2-2-222−2i−2i2i2i-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2522-2-2222-1-2-2-2-1-1-11111-1-12i2i−2i−2i11−i−iii−i−iii0000−i3i3−i3i33−33−300000000
χ2622-2-2222-1-2-2-2-1-1-11111-1-12i2i−2i−2i11−i−iii−i−iii0000i3−i3i3−i3−33−3300000000
χ2722-2-2222-1-2-2-2-1-1-11111-1-1−2i−2i2i2i11ii−i−iii−i−i0000−i3i3−i3i3−33−3300000000
χ2822-2-2222-1-2-2-2-1-1-11111-1-1−2i−2i2i2i11ii−i−iii−i−i0000i3−i3i3−i33−33−300000000
χ2922-2-22-2-2222-22-2-222-2-22-20000-22000000000000000000002-2000000
χ3022-2-22-2-2222-22-2-222-2-22-20000-2200000000000000000000-22000000
χ3122-2-2-22-22-222222-2-2-2-2-2-200002200000000002i−2i00002i−2i−2i2i00000000
χ3222-2-2-22-22-222222-2-2-2-2-2-20000220000000000−2i2i0000−2i2i2i−2i00000000
χ3322-2-2-22-2-1-222-1-1-11111110000-1-133−3−3−3−333002i−2i−i3i3i3−i3−iii−i00000000
χ3422-2-2-22-2-1-222-1-1-11111110000-1-133−3−3−3−33300−2i2ii3−i3−i3i3i−i−ii00000000
χ3522-2-2-22-2-1-222-1-1-11111110000-1-1−3−33333−3−3002i−2ii3−i3−i3i3−iii−i00000000
χ3622-2-2-22-2-1-222-1-1-11111110000-1-1−3−33333−3−300−2i2i−i3i3i3−i3i−i−ii00000000
χ3722-2-2-2-2222-222-2-222-2-2-2200002-20000000000000000000000002i−2i00
χ3822-2-2-2-2222-222-2-222-2-2-2200002-2000000000000000000000000−2i2i00
χ3944444-4-4-2-4-44-22222-2-2-220000-220000000000000000000000000000
χ404444-4-44-2-44-4-22222-2-22-200002-20000000000000000000000000000
χ4144-4-44-4-4-244-4-222-2-222-2200002-20000000000000000000000000000
χ4244-4-4-4-44-24-44-222-2-2222-20000-220000000000000000000000000000
χ434-44i−4i0004000-400004i−4i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ444-44i−4i0004000-400004i−4i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ454-44i−4i000-20002−2i32i323−23−2i2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ72ζ72ζ13−2ζ13−2ζ232ζ232ζ5−2ζ500000000000000000000
χ464-44i−4i000-20002−2i32i323−23−2i2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ7−2ζ7−2ζ132ζ132ζ23−2ζ23−2ζ52ζ500000000000000000000
χ474-44i−4i000-200022i3−2i3−2323−2i2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ232ζ232ζ5−2ζ5−2ζ72ζ72ζ13−2ζ1300000000000000000000
χ484-44i−4i000-200022i3−2i3−2323−2i2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ23−2ζ23−2ζ52ζ52ζ7−2ζ7−2ζ132ζ1300000000000000000000
χ494-4−4i4i0004000-40000−4i4i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ504-4−4i4i0004000-40000−4i4i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ514-4−4i4i000-20002−2i32i3−23232i−2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ13−2ζ13−2ζ72ζ72ζ5−2ζ5−2ζ232ζ2300000000000000000000
χ524-4−4i4i000-20002−2i32i3−23232i−2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ132ζ132ζ7−2ζ7−2ζ52ζ52ζ23−2ζ2300000000000000000000
χ534-4−4i4i000-200022i3−2i323−232i−2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ5−2ζ5−2ζ232ζ232ζ13−2ζ13−2ζ72ζ700000000000000000000
χ544-4−4i4i000-200022i3−2i323−232i−2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ52ζ52ζ23−2ζ23−2ζ132ζ132ζ7−2ζ700000000000000000000

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