Finite Group Databasebeta

← Group #70002

Character table — Group #70002

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222444444444444444444448888888888121212121212121224242424
order12442223444666121212122244668888121224242424242424246688121224242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ911-1-11111-1-1-1111-1-1-1-11-11-111ii−i−i-1-1iiii−i−i−i−i1-1i−i1-1ii−i−iii−i−iii−i−i1-11-1
χ1011-1-11111-1-1-1111-1-1-1-11-11-111ii−i−i-1-1iiii−i−i−i−i1-1i−i1-1ii−i−i−i−iii−i−iii-11-11
χ1111-1-11111-1-1-1111-1-1-1-11-11-111−i−iii-1-1−i−i−i−iiiii1-1−ii1-1−i−iiiii−i−iii−i−i-11-11
χ1211-1-11111-1-1-1111-1-1-1-11-11-111−i−iii-1-1−i−i−i−iiiii1-1−ii1-1−i−iii−i−iii−i−iii1-11-1
χ1311-1-11111-1-1-1111-1-1-1-1-11-1111ii−i−i-1-1iiii−i−i−i−i-11−ii-11−i−iiiii−i−i−i−iii1-1-11
χ1411-1-11111-1-1-1111-1-1-1-1-11-1111ii−i−i-1-1iiii−i−i−i−i-11−ii-11−i−iii−i−iiiii−i−i-111-1
χ1511-1-11111-1-1-1111-1-1-1-1-11-1111−i−iii-1-1−i−i−i−iiiii-11i−i-11ii−i−iii−i−i−i−iii-111-1
χ1611-1-11111-1-1-1111-1-1-1-1-11-1111−i−iii-1-1−i−i−i−iiiii-11i−i-11ii−i−i−i−iiiii−i−i1-1-11
χ172222222-1222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-111111111-1-1-2-2-1-11111000000000000
χ192222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-111-2-2111111000000000000
χ202222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-111111111112211-1-1-1-1000000000000
χ2122222-2-22-2-2222222222-2-22-2-20000-2-2000000002-200-220000000000000000
χ2222222-2-22-2-222222222-222-2-2-20000-2-200000000-22002-20000000000000000
χ2322222-2-2-1-2-22-1-1-1-1-1-1-12-2-2211000011−i3−i3i3i3−i3−i3i3i3-11001-1−i3i3−i3i3000000000000
χ2422222-2-2-1-2-22-1-1-1-1-1-1-12-2-2211000011i3i3−i3−i3i3i3−i3−i3-11001-1i3−i3i3−i3000000000000
χ2522222-2-2-1-2-22-1-1-1-1-1-1-1-222-211000011−i3−i3i3i3−i3−i3i3i31-100-11i3−i3i3−i3000000000000
χ2622222-2-2-1-2-22-1-1-1-1-1-1-1-222-211000011i3i3−i3−i3i3i3−i3−i31-100-11−i3i3−i3i3000000000000
χ272222-22-222-2-2-2-2222-2-200002-200002-200000000000000000000002-22-20000
χ282222-22-222-2-2-2-2222-2-200002-200002-20000000000000000000000-22-220000
χ292222-2-222-22-2-2-2222-2-20000-220000-220000000000000000002-22-200000000
χ302222-2-222-22-2-2-2222-2-20000-220000-22000000000000000000-22-2200000000
χ3122-2-2222-1-2-2-2-1-1-111112-22-2-1-12i2i−2i−2i11−i−i−i−iiiii-112i−2i-11−i−iii000000000000
χ3222-2-2222-1-2-2-2-1-1-111112-22-2-1-1−2i−2i2i2i11iiii−i−i−i−i-11−2i2i-11ii−i−i000000000000
χ3322-2-2222-1-2-2-2-1-1-11111-22-22-1-12i2i−2i−2i11−i−i−i−iiiii1-1−2i2i1-1ii−i−i000000000000
χ3422-2-2222-1-2-2-2-1-1-11111-22-22-1-1−2i−2i2i2i11iiii−i−i−i−i1-12i−2i1-1−i−iii000000000000
χ3522-2-22-2-2222-2222-2-2-2-222-2-2-2-2000022000000002200-2-20000000000000000
χ3622-2-22-2-2222-2222-2-2-2-2-2-222-2-200002200000000-2-200220000000000000000
χ3722-2-22-2-2-122-2-1-1-1111122-2-2110000-1-133−3−3−3−333-1-100113−3−33000000000000
χ3822-2-22-2-2-122-2-1-1-1111122-2-2110000-1-1−3−33333−3−3-1-10011−333−3000000000000
χ3922-2-22-2-2-122-2-1-1-11111-2-222110000-1-133−3−3−3−3331100-1-1−333−3000000000000
χ4022-2-22-2-2-122-2-1-1-11111-2-222110000-1-1−3−33333−3−31100-1-13−3−33000000000000
χ4122-2-2-22-22-222-2-22-2-22200002-20000-2200000000000000000000002i−2i−2i2i0000
χ4222-2-2-22-22-222-2-22-2-22200002-20000-220000000000000000000000−2i2i2i−2i0000
χ4322-2-2-2-2222-22-2-22-2-2220000-2200002-20000000000000000002i−2i−2i2i00000000
χ4422-2-2-2-2222-22-2-22-2-2220000-2200002-2000000000000000000−2i2i2i−2i00000000
χ454444-44-4-24-4-422-2-2-2220000-220000-22000000000000000000000000000000
χ464444-4-44-2-44-422-2-2-22200002-200002-2000000000000000000000000000000
χ4744-4-4-44-4-2-44422-222-2-20000-2200002-2000000000000000000000000000000
χ4844-4-4-4-44-24-4422-222-2-200002-20000-22000000000000000000000000000000
χ494-44i−4i000400000-44i−4i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ504-44i−4i000400000-44i−4i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ514-44i−4i000-2000−2i32i32−2i2i23−230000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ50000000000000000000000
χ524-44i−4i000-2000−2i32i32−2i2i23−23000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ50000000000000000000000
χ534-44i−4i000-20002i3−2i32−2i2i−23230000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ130000000000000000000000
χ544-44i−4i000-20002i3−2i32−2i2i−2323000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ130000000000000000000000
χ554-4−4i4i000400000-4−4i4i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ564-4−4i4i000400000-4−4i4i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ574-4−4i4i000-2000−2i32i322i−2i−2323000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ230000000000000000000000
χ584-4−4i4i000-2000−2i32i322i−2i−23230000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ230000000000000000000000
χ594-4−4i4i000-20002i3−2i322i−2i23−23000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ70000000000000000000000
χ604-4−4i4i000-20002i3−2i322i−2i23−230000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ70000000000000000000000

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