Finite Group Databasebeta

← Group #70546

Character table — Group #70546

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222444444444444444444448888888888121212121212121224242424
order1244222344466612121212668888888812122424242424242424441212121224242424224488884488
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ911-1-11111-1-1-1111-1-1-1-111ii−i−iii−i−i-1-1iiii−i−i−i−i1-111-1-1ii−i−i1-11-1ii−i−i1-1i−i
χ1011-1-11111-1-1-1111-1-1-1-111ii−i−iii−i−i-1-1iiii−i−i−i−i1-111-1-1ii−i−i-11-11−i−iii-11−ii
χ1111-1-11111-1-1-1111-1-1-1-111ii−i−i−i−iii-1-1iiii−i−i−i−i-11-1-111−i−iii1-11-1−i−iii-11i−i
χ1211-1-11111-1-1-1111-1-1-1-111ii−i−i−i−iii-1-1iiii−i−i−i−i-11-1-111−i−iii-11-11ii−i−i1-1−ii
χ1311-1-11111-1-1-1111-1-1-1-111−i−iiiii−i−i-1-1−i−i−i−iiiii-11-1-111ii−i−i1-11-1ii−i−i-11−ii
χ1411-1-11111-1-1-1111-1-1-1-111−i−iiiii−i−i-1-1−i−i−i−iiiii-11-1-111ii−i−i-11-11−i−iii1-1i−i
χ1511-1-11111-1-1-1111-1-1-1-111−i−iii−i−iii-1-1−i−i−i−iiiii1-111-1-1−i−iii1-11-1−i−iii1-1−ii
χ1611-1-11111-1-1-1111-1-1-1-111−i−iii−i−iii-1-1−i−i−i−iiiii1-111-1-1−i−iii-11-11ii−i−i-11i−i
χ172222222-1222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-211111111000000000000
χ192222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-2-21111-1-1-1-1000000000000
χ202222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111122-1-1-1-11111000000000000
χ2122222-2-22-2-222-2-2-2-2222-2000000002-20000000000000000002-2-2200000000
χ2222222-2-22-2-222-2-2-2-2222-2000000002-2000000000000000000-222-200000000
χ232222-22-222-2-22222222-2-200002-22-2-2-2000000000000002-22-2000000000000
χ242222-22-222-2-22222222-2-20000-22-22-2-200000000000000-22-22000000000000
χ252222-22-2-12-2-2-1-1-1-1-1-1-11100002-22-211−i3−i3i3i3−i3−i3i3i300−i3i3−i3i3-11-11000000000000
χ262222-22-2-12-2-2-1-1-1-1-1-1-11100002-22-211i3i3−i3−i3i3i3−i3−i300i3−i3i3−i3-11-11000000000000
χ272222-22-2-12-2-2-1-1-1-1-1-1-1110000-22-2211−i3−i3i3i3−i3−i3i3i300i3−i3i3−i31-11-1000000000000
χ282222-22-2-12-2-2-1-1-1-1-1-1-1110000-22-2211i3i3−i3−i3i3i3−i3−i300−i3i3−i3i31-11-1000000000000
χ292222-2-222-22-22-2-2-2-222-2200000000-2200000000000000000000002-22-20000
χ302222-2-222-22-22-2-2-2-222-2200000000-220000000000000000000000-22-220000
χ3122-2-2222-1-2-2-2-1-1-11111-1-12i2i−2i−2i2i2i−2i−2i11−i−i−i−iiiii2-2-1-111−i−iii000000000000
χ3222-2-2222-1-2-2-2-1-1-11111-1-12i2i−2i−2i−2i−2i2i2i11−i−i−i−iiiii-2211-1-1ii−i−i000000000000
χ3322-2-2222-1-2-2-2-1-1-11111-1-1−2i−2i2i2i2i2i−2i−2i11iiii−i−i−i−i-2211-1-1−i−iii000000000000
χ3422-2-2222-1-2-2-2-1-1-11111-1-1−2i−2i2i2i−2i−2i2i2i11iiii−i−i−i−i2-2-1-111ii−i−i000000000000
χ3522-2-22-2-2222-22-2-222-2-22-200000000-2200000000000000000022-2-200000000
χ3622-2-22-2-2222-22-2-222-2-22-200000000-22000000000000000000-2-22200000000
χ3722-2-2-22-22-222222-2-2-2-2-2-200002i−2i−2i2i22000000000000002i−2i−2i2i000000000000
χ3822-2-2-22-22-222222-2-2-2-2-2-20000−2i2i2i−2i2200000000000000−2i2i2i−2i000000000000
χ3922-2-2-22-2-1-222-1-1-111111100002i−2i−2i2i-1-133−3−3−3−33300−i3i3i3−i3−iii−i000000000000
χ4022-2-2-22-2-1-222-1-1-111111100002i−2i−2i2i-1-1−3−33333−3−300i3−i3−i3i3−iii−i000000000000
χ4122-2-2-22-2-1-222-1-1-11111110000−2i2i2i−2i-1-133−3−3−3−33300i3−i3−i3i3i−i−ii000000000000
χ4222-2-2-22-2-1-222-1-1-11111110000−2i2i2i−2i-1-1−3−33333−3−300−i3i3i3−i3i−i−ii000000000000
χ4322-2-2-2-2222-222-2-222-2-2-22000000002-200000000000000000000002i−2i−2i2i0000
χ4422-2-2-2-2222-222-2-222-2-2-22000000002-20000000000000000000000−2i2i2i−2i0000
χ4544444-4-4-2-4-44-22222-2-2-2200000000-22000000000000000000000000000000
χ464444-4-44-2-44-4-22222-2-22-2000000002-2000000000000000000000000000000
χ4744-4-44-4-4-244-4-222-2-222-22000000002-2000000000000000000000000000000
χ4844-4-4-4-44-24-44-222-2-2222-200000000-22000000000000000000000000000000
χ494-44i−4i0004000-400004i−4i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ504-44i−4i0004000-400004i−4i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ514-44i−4i000-20002−2i32i323−23−2i2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ50000000000000000000000
χ524-44i−4i000-20002−2i32i323−23−2i2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000002ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ50000000000000000000000
χ534-44i−4i000-200022i3−2i3−2323−2i2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ130000000000000000000000
χ544-44i−4i000-200022i3−2i3−2323−2i2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000002ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ130000000000000000000000
χ554-4−4i4i0004000-40000−4i4i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ564-4−4i4i0004000-40000−4i4i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ574-4−4i4i000-20002−2i32i3−23232i−2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000002ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ230000000000000000000000
χ584-4−4i4i000-20002−2i32i3−23232i−2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ230000000000000000000000
χ594-4−4i4i000-200022i3−2i323−232i−2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000002ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ70000000000000000000000
χ604-4−4i4i000-200022i3−2i323−232i−2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ70000000000000000000000

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