Finite Group Databasebeta

← Group #71995

Character table — Group #71995

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111111111111222222222222222244444444444444444444444444444444444412121212121212121212121212121212
order1222222244444444366666661212121212121212224466668888888812121212242424242424242424242424242424244444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111110000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111110000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-10000000000000000
χ2122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-12i2i−2i−2i2i2i−2i−2i1111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ2222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-1−2i−2i2i2i−2i−2i2i2i1111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ2322222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-22211112i2i−2i−2i−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ2422222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2221111−2i−2i2i2i2i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ252222-2-2-2-22222-2-2-2-2222-2-2-2-222222-2-2-2-22-22-222-2-20000000022-2-200000000000000000000000000000000
χ262222-2-2-2-22222-2-2-2-2222-2-2-2-222222-2-2-2-2-22-22-2-22200000000-2-22200000000000000000000000000000000
χ272222-2-2-2-22222-2-2-2-2-1-1-11111-1-1-1-1-111112-22-2-1-11100000000-1-11133−3−333−3−333−3−333−3−30000000000000000
χ282222-2-2-2-22222-2-2-2-2-1-1-11111-1-1-1-1-111112-22-2-1-11100000000-1-111−3−333−3−333−3−333−3−3330000000000000000
χ292222-2-2-2-22222-2-2-2-2-1-1-11111-1-1-1-1-11111-22-2211-1-10000000011-1-133−3−333−3−3−3−333−3−3330000000000000000
χ302222-2-2-2-22222-2-2-2-2-1-1-11111-1-1-1-1-11111-22-2211-1-10000000011-1-1−3−333−3−33333−3−333−3−30000000000000000
χ312222-2-2-2-2-2-2-2-22222222-2-2-2-22-2-2-2-222222-2-2222-2-200000000-2-22200000000000000000000000000000000
χ322222-2-2-2-2-2-2-2-22222222-2-2-2-22-2-2-2-22222-222-2-2-2220000000022-2-200000000000000000000000000000000
χ332222-2-2-2-2-2-2-2-22222-1-1-11111-11111-1-1-1-12-2-22-1-1110000000011-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ342222-2-2-2-2-2-2-2-22222-1-1-11111-11111-1-1-1-12-2-22-1-1110000000011-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ352222-2-2-2-2-2-2-2-22222-1-1-11111-11111-1-1-1-1-222-211-1-100000000-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ362222-2-2-2-2-2-2-2-22222-1-1-11111-11111-1-1-1-1-222-211-1-100000000-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3722-2-222-2-22i2i−2i−2i2i−2i2i−2i22-222-2-2-22i2i−2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ3822-2-222-2-22i2i−2i−2i2i−2i2i−2i22-222-2-2-22i2i−2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ3922-2-222-2-2−2i−2i2i2i−2i2i−2i2i22-222-2-2-2−2i−2i2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ4022-2-222-2-2−2i−2i2i2i−2i2i−2i2i22-222-2-2-2−2i−2i2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ4122-2-2-2-2222i2i−2i−2i−2i2i−2i2i22-2-2-222-22i2i−2i−2i−2i2i−2i2i000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ4222-2-2-2-2222i2i−2i−2i−2i2i−2i2i22-2-2-222-22i2i−2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ4322-2-2-2-222−2i−2i2i2i2i−2i2i−2i22-2-2-222-2−2i−2i2i2i2i−2i2i−2i00000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ4422-2-2-2-222−2i−2i2i2i2i−2i2i−2i22-2-2-222-2−2i−2i2i2i2i−2i2i−2i000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ452-22-22-22-22i−2i2i−2i2i−2i−2i2i2-222-22-2-22i−2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000002i−2i2-200000000
χ462-22-22-22-22i−2i2i−2i2i−2i−2i2i2-222-22-2-22i−2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000−2i2i-2200000000
χ472-22-22-22-2−2i2i−2i2i−2i2i2i−2i2-222-22-2-2−2i2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000002i−2i-2200000000
χ482-22-22-22-2−2i2i−2i2i−2i2i2i−2i2-222-22-2-2−2i2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000−2i2i2-200000000
χ492-22-2-22-222i−2i2i−2i−2i2i2i−2i2-22-22-22-22i−2i2i−2i−2i2i2i−2i0000000000000000000000000000000000002-22i−2i000000000000
χ502-22-2-22-222i−2i2i−2i−2i2i2i−2i2-22-22-22-22i−2i2i−2i−2i2i2i−2i000000000000000000000000000000000000-22−2i2i000000000000
χ512-22-2-22-22−2i2i−2i2i2i−2i−2i2i2-22-22-22-2−2i2i−2i2i2i−2i−2i2i0000000000000000000000000000000000002-2−2i2i000000000000
χ522-22-2-22-22−2i2i−2i2i2i−2i−2i2i2-22-22-22-2−2i2i−2i2i2i−2i−2i2i000000000000000000000000000000000000-222i−2i000000000000
χ532-2-222-2-222-2-2222-2-22-2-22-2-2222-2-2222-2-2000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ542-2-222-2-222-2-2222-2-22-2-22-2-2222-2-2222-2-200000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ552-2-222-2-222-2-2222-2-2-111-111-1-1-111-1-1-1110000−i3i3−i3i32i−2i2i−2i0000−i3i3−i3i3−ii−ii−ii−ii3−33−33−33−30000000000000000
χ562-2-222-2-222-2-2222-2-2-111-111-1-1-111-1-1-1110000−i3i3−i3i3−2i2i−2i2i0000−i3i3−i3i3i−ii−ii−ii−i−33−33−33−330000000000000000
χ572-2-222-2-222-2-2222-2-2-111-111-1-1-111-1-1-1110000i3−i3i3−i32i−2i2i−2i0000i3−i3i3−i3−ii−ii−ii−ii−33−33−33−330000000000000000
χ582-2-222-2-222-2-2222-2-2-111-111-1-1-111-1-1-1110000i3−i3i3−i3−2i2i−2i2i0000i3−i3i3−i3i−ii−ii−ii−i3−33−33−33−30000000000000000
χ592-2-222-2-22-222-2-2-2222-2-22-2-222-222-2-2-222000000002-2-22000000002-22-2-22-22000000000000000000000000
χ602-2-222-2-22-222-2-2-2222-2-22-2-222-222-2-2-22200000000-222-200000000-22-222-22-2000000000000000000000000
χ612-2-222-2-22-222-2-2-222-111-111-1-11-1-1111-1-10000−i3i3−i3i32-2-220000i3−i3i3−i3-11-111-11-1−i3i3−i3i3i3−i3i3−i30000000000000000
χ622-2-222-2-22-222-2-2-222-111-111-1-11-1-1111-1-10000−i3i3−i3i3-222-20000i3−i3i3−i31-11-1-11-11i3−i3i3−i3−i3i3−i3i30000000000000000
χ632-2-222-2-22-222-2-2-222-111-111-1-11-1-1111-1-10000i3−i3i3−i32-2-220000−i3i3−i3i3-11-111-11-1i3−i3i3−i3−i3i3−i3i30000000000000000
χ642-2-222-2-22-222-2-2-222-111-111-1-11-1-1111-1-10000i3−i3i3−i3-222-20000−i3i3−i3i31-11-1-11-11−i3i3−i3i3i3−i3i3−i30000000000000000
χ652-2-22-222-22-2-22-2-2222-2-2-222-222-2-22-2-2220000000000002-22-20000000000002-2-222-2-220000000000000000
χ662-2-22-222-22-2-22-2-2222-2-2-222-222-2-22-2-222000000000000-22-22000000000000-222-2-222-20000000000000000
χ672-2-22-222-22-2-22-2-222-1111-1-11-1-111-111-1-10000−i3i3i3−i300002-22-2−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3-111-1-111-10000000000000000
χ682-2-22-222-22-2-22-2-222-1111-1-11-1-111-111-1-10000−i3i3i3−i30000-22-22−i3i3i3−i3i3−i3−i3i3i3−i3−i3i31-1-111-1-110000000000000000
χ692-2-22-222-22-2-22-2-222-1111-1-11-1-111-111-1-10000i3−i3−i3i300002-22-2i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3-111-1-111-10000000000000000
χ702-2-22-222-22-2-22-2-222-1111-1-11-1-111-111-1-10000i3−i3−i3i30000-22-22i3−i3−i3i3−i3i3i3−i3−i3i3i3−i31-1-111-1-110000000000000000
χ712-2-22-222-2-222-222-2-22-2-2-222-22-222-222-2-20000000000002i−2i−2i2i0000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ722-2-22-222-2-222-222-2-22-2-2-222-22-222-222-2-2000000000000−2i2i2i−2i000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ732-2-22-222-2-222-222-2-2-1111-1-11-11-1-11-1-1110000−i3i3i3−i300002i−2i−2i2ii3−i3−i3i33−3−33−333−3−iii−ii−i−ii0000000000000000
χ742-2-22-222-2-222-222-2-2-1111-1-11-11-1-11-1-1110000−i3i3i3−i30000−2i2i2i−2ii3−i3−i3i3−333−33−3−33i−i−ii−iii−i0000000000000000
χ752-2-22-222-2-222-222-2-2-1111-1-11-11-1-11-1-1110000i3−i3−i3i300002i−2i−2i2i−i3i3i3−i3−333−33−3−33−iii−ii−i−ii0000000000000000
χ762-2-22-222-2-222-222-2-2-1111-1-11-11-1-11-1-1110000i3−i3−i3i30000−2i2i2i−2i−i3i3i3−i33−3−33−333−3i−i−ii−iii−i0000000000000000
χ7744-4-444-4-44i4i−4i−4i4i−4i4i−4i-2-22-2-2222−2i−2i2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ7844-4-444-4-4−4i−4i4i4i−4i4i−4i4i-2-22-2-22222i2i−2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ7944-4-4-4-4444i4i−4i−4i−4i4i−4i4i-2-2222-2-22−2i−2i2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ8044-4-4-4-444−4i−4i4i4i4i−4i4i−4i-2-2222-2-222i2i−2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ814-44-44-44-44i−4i4i−4i4i−4i−4i4i-22-2-22-222−2i2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ824-44-44-44-4−4i4i−4i4i−4i4i4i−4i-22-2-22-2222i−2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ834-44-4-44-444i−4i4i−4i−4i4i4i−4i-22-22-22-22−2i2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ844-44-4-44-44−4i4i−4i4i4i−4i−4i4i-22-22-22-222i−2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000

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