Finite Group Databasebeta

← Group #70534

Character table — Group #70534

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order1222444422344666888812121212668812122424242424242424448812121212242424244444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ81111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ91111-1-1-1-1-1-1111111ii−i−i-1-1-1-1-1-1i−i11iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-1-1-1111111ii−i−i-1-1-1-1-1-1i−i11iiii−i−i−i−i1-1i−i11-1-1ii−i−i-1-111−i−iii−i−iii-1-111
χ111111-1-1-1-1-1-1111111ii−i−i-1-1-1-1-1-1i−i11iiii−i−i−i−i-11−ii-1-111−i−iii11-1-1−i−iiiii−i−i-1-111
χ121111-1-1-1-1-1-1111111ii−i−i-1-1-1-1-1-1i−i11iiii−i−i−i−i-11−ii-1-111−i−iii-1-111ii−i−i−i−iii11-1-1
χ131111-1-1-1-1-1-1111111−i−iii-1-1-1-1-1-1−ii11−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-1−i−iii−i−iii11-1-1
χ141111-1-1-1-1-1-1111111−i−iii-1-1-1-1-1-1−ii11−i−i−i−iiiii1-1−ii11-1-1−i−iii-1-111ii−i−iii−i−i-1-111
χ151111-1-1-1-1-1-1111111−i−iii-1-1-1-1-1-1−ii11−i−i−i−iiiii-11i−i-1-111ii−i−i11-1-1ii−i−i−i−iii-1-111
χ161111-1-1-1-1-1-1111111−i−iii-1-1-1-1-1-1−ii11−i−i−i−iiiii-11i−i-1-111ii−i−i-1-111−i−iiiii−i−i11-1-1
χ172222222222-122-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ182222222222-122-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ192222222222-122-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2-1-11111111122-2-2-1-1-1-111110000000000000000
χ202222222222-122-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2-1-111111111-2-2221111-1-1-1-10000000000000000
χ2122222222-2-22-2-222222222222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000
χ2222222222-2-22-2-2222-2-2-2-22222-2-222-2-2-2-222-2-2220000000000000000000000000000
χ2322222222-2-2-1-2-2-1-1-12222-1-1-1-111-2-211-1-111-1-1110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2422222222-2-2-1-2-2-1-1-12222-1-1-1-111-2-211-1-111-1-1110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2522222222-2-2-1-2-2-1-1-1-2-2-2-2-1-1-1-111221111-1-111-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2622222222-2-2-1-2-2-1-1-1-2-2-2-2-1-1-1-111221111-1-111-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ272222-2-2-2-2222-2-22222i2i−2i−2i-2-2-2-222−2i2i-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ282222-2-2-2-2222-2-2222−2i−2i2i2i-2-2-2-2222i−2i-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ292222-2-2-2-222-1-2-2-1-1-12i2i−2i−2i1111-1-1−2i2i11−i−iiiii−i−i0000−i3i3i3−i33−3−330000000000000000
χ302222-2-2-2-222-1-2-2-1-1-12i2i−2i−2i1111-1-1−2i2i11−i−iiiii−i−i0000i3−i3−i3i3−333−30000000000000000
χ312222-2-2-2-222-1-2-2-1-1-1−2i−2i2i2i1111-1-12i−2i11ii−i−i−i−iii0000−i3i3i3−i3−333−30000000000000000
χ322222-2-2-2-222-1-2-2-1-1-1−2i−2i2i2i1111-1-12i−2i11ii−i−i−i−iii0000i3−i3−i3i33−3−330000000000000000
χ332222-2-2-2-2-2-2-122-1-1-12i2i−2i−2i1111112i−2i-1-1−i−i−i−iiiii2-22i−2i-1-111−i−iii0000000000000000
χ342222-2-2-2-2-2-2-122-1-1-12i2i−2i−2i1111112i−2i-1-1−i−i−i−iiiii-22−2i2i11-1-1ii−i−i0000000000000000
χ352222-2-2-2-2-2-2-122-1-1-1−2i−2i2i2i111111−2i2i-1-1iiii−i−i−i−i2-2−2i2i-1-111ii−i−i0000000000000000
χ362222-2-2-2-2-2-2-122-1-1-1−2i−2i2i2i111111−2i2i-1-1iiii−i−i−i−i-222i−2i11-1-1−i−iii0000000000000000
χ3722-2-222-2-22-22-222-2-20000-2-2222-2002-2000000000000000000002i−2i2i−2i000000000000
χ3822-2-222-2-22-22-222-2-20000-2-2222-2002-200000000000000000000−2i2i−2i2i000000000000
χ3922-2-222-2-2-2222-22-2-20000-2-222-2200-2200000000000000000000000000002i−2i2i−2i0000
χ4022-2-222-2-2-2222-22-2-20000-2-222-2200-220000000000000000000000000000−2i2i−2i2i0000
χ4122-2-2-2-2222-222-22-2-2000022-2-22-200-2200000000000000000000000000002-2-220000
χ4222-2-2-2-2222-222-22-2-2000022-2-22-200-220000000000000000000000000000-222-20000
χ4322-2-2-2-222-222-222-2-2000022-2-2-22002-2000000000000000000002i−2i−2i2i000000000000
χ4422-2-2-2-222-222-222-2-2000022-2-2-22002-200000000000000000000−2i2i2i−2i000000000000
χ452-22-22i−2i2i−2i00200-22-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000000000001+i−1−i1−i−1+i00002−2−i2i2
χ462-22-22i−2i2i−2i00200-22-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000−1−i1+i−1+i1−i0000−22i2−i2
χ472-22-22i−2i2i−2i00200-22-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000000000001+i−1−i1−i−1+i0000−22i2−i2
χ482-22-22i−2i2i−2i00200-22-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000−1−i1+i−1+i1−i00002−2−i2i2
χ492-22-2−2i2i−2i2i00200-22-2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i2i−2i2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000000000001−i−1+i1+i−1−i00002−2i2−i2
χ502-22-2−2i2i−2i2i00200-22-2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i2i−2i2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000−1+i1−i−1−i1+i0000−22−i2i2
χ512-22-2−2i2i−2i2i00200-22-22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i2i−2i2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000000000001−i−1+i1+i−1−i0000−22−i2i2
χ522-22-2−2i2i−2i2i00200-22-22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i2i−2i2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000−1+i1−i−1−i1+i00002−2i2−i2
χ5344-4-444-4-44-4-2-44-222000022-2-2-2200-22000000000000000000000000000000000000
χ5444-4-444-4-4-44-24-4-222000022-2-22-2002-2000000000000000000000000000000000000
χ5544-4-4-4-4444-4-24-4-2220000-2-222-22002-2000000000000000000000000000000000000
χ5644-4-4-4-444-44-2-44-2220000-2-2222-200-22000000000000000000000000000000000000
χ574-44-44i−4i4i−4i00-2002-224ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13−2i2i−2i2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000000000
χ584-44-44i−4i4i−4i00-2002-22−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13−2i2i−2i2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000000
χ594-44-4−4i4i−4i4i00-2002-22−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ232i−2i2i−2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000000
χ604-44-4−4i4i−4i4i00-2002-224ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ232i−2i2i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000
χ614-4-444i−4i−4i4i00400-4-440000−4i4i4i−4i000000000000000000000000000000000000000000
χ624-4-444i−4i−4i4i00-20022-200002i−2i−2i2i000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000
χ634-4-444i−4i−4i4i00-20022-200002i−2i−2i2i00000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000
χ644-4-44−4i4i4i−4i00400-4-4400004i−4i−4i4i000000000000000000000000000000000000000000
χ654-4-44−4i4i4i−4i00-20022-20000−2i2i2i−2i00000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000
χ664-4-44−4i4i4i−4i00-20022-20000−2i2i2i−2i000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000

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