Finite Group Databasebeta

← Group #70296

Character table — Group #70296

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222222244444444444444448888888888882424242424242424
order12442223444666121212126688881212242424242424242424446612121212121224444488
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111
χ611111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-1
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-1
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
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
χ112222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-11111-1-100000000
χ122222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-22211-1-1-1-11100000000
χ1322222-2-222-2-22222222-2-20000-2-200000000000000000000002i−2i0000
χ1422222-2-222-2-22222222-2-20000-2-20000000000000000000000−2i2i0000
χ152222-22-22-22-2-2-2222-2-22-200002-200000000002i−2i002i2i−2i−2i0000000000
χ162222-22-22-22-2-2-2222-2-22-200002-20000000000−2i2i00−2i−2i2i2i0000000000
χ172222-22-2-1-22-211-1-1-111-110000-113333−3−3−3−3002i−2i−i3i3−i−iii−i3i300000000
χ182222-22-2-1-22-211-1-1-111-110000-113333−3−3−3−300−2i2ii3−i3ii−i−ii3−i300000000
χ192222-22-2-1-22-211-1-1-111-110000-11−3−3−3−33333002i−2ii3−i3−i−iiii3−i300000000
χ202222-22-2-1-22-211-1-1-111-110000-11−3−3−3−3333300−2i2i−i3i3ii−i−i−i3i300000000
χ212222-2-222-2-22-2-2222-2-2-220000-22000000000000000000000000002-2
χ222222-2-222-2-22-2-2222-2-2-220000-2200000000000000000000000000-22
χ2322-2-22222-2-2-2222-2-2-2-2220000-2-20000000000000000000000002-200
χ2422-2-22222-2-2-2222-2-2-2-2220000-2-2000000000000000000000000-2200
χ2522-2-22-2-22-222222-2-2-2-2-2-2000022000000002-200220000-2-200000000
χ2622-2-22-2-22-222222-2-2-2-2-2-200002200000000-2200-2-200002200000000
χ2722-2-22-2-2-1-222-1-1-11111110000-1-1−i3−i3i3i3−i3−i3i3i32-200-1-1−i3i3−i3i31100000000
χ2822-2-22-2-2-1-222-1-1-11111110000-1-1−i3−i3i3i3−i3−i3i3i3-220011i3−i3i3−i3-1-100000000
χ2922-2-22-2-2-1-222-1-1-11111110000-1-1i3i3−i3−i3i3i3−i3−i32-200-1-1i3−i3i3−i31100000000
χ3022-2-22-2-2-1-222-1-1-11111110000-1-1i3i3−i3−i3i3i3−i3−i3-220011−i3i3−i3i3-1-100000000
χ3122-2-2-22-222-22-2-22-2-2222-20000-22000000000000000000002-2000000
χ3222-2-2-22-222-22-2-22-2-2222-20000-2200000000000000000000-22000000
χ3322-2-2-2-22222-2-2-22-2-222-222i2i−2i−2i2-22i2i−2i−2i−2i−2i2i2i00000000000000000000
χ3422-2-2-2-22222-2-2-22-2-222-22−2i−2i2i2i2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ3522-2-2-2-22-122-211-111-1-11-12i2i−2i−2i-11−i−iiiii−i−i0000−i3i33−3−33i3−i300000000
χ3622-2-2-2-22-122-211-111-1-11-12i2i−2i−2i-11−i−iiiii−i−i0000i3−i3−333−3−i3i300000000
χ3722-2-2-2-22-122-211-111-1-11-1−2i−2i2i2i-11ii−i−i−i−iii0000−i3i3−333−3i3−i300000000
χ3822-2-2-2-22-122-211-111-1-11-1−2i−2i2i2i-11ii−i−i−i−iii0000i3−i33−3−33−i3i300000000
χ3944444-4-4-24-4-4-2-2-2-2-2-2-2220000220000000000000000000000000000
χ404444-4-44-2-4-4422-2-2-2222-200002-20000000000000000000000000000
χ4144-4-4444-2-4-4-4-2-2-22222-2-20000220000000000000000000000000000
χ4244-4-4-44-4-24-4422-222-2-2-2200002-20000000000000000000000000000
χ434-44i−4i000400000-44i−4i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ444-44i−4i000400000-44i−4i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ454-44i−4i000-2000−2i32i32−2i2i23−23002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ2300000000000000000000
χ464-44i−4i000-2000−2i32i32−2i2i23−2300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ2300000000000000000000
χ474-44i−4i000-20002i3−2i32−2i2i−2323002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ2300000000000000000000
χ484-44i−4i000-20002i3−2i32−2i2i−232300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ2300000000000000000000
χ494-4−4i4i000400000-4−4i4i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ504-4−4i4i000400000-4−4i4i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ514-4−4i4i000-2000−2i32i322i−2i−232300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ2300000000000000000000
χ524-4−4i4i000-2000−2i32i322i−2i−2323002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ2300000000000000000000
χ534-4−4i4i000-20002i3−2i322i−2i23−2300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ2300000000000000000000
χ544-4−4i4i000-20002i3−2i322i−2i23−23002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ2300000000000000000000

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