Finite Group Databasebeta

← Group #72001

Character table — Group #72001

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222222222222222224444444444444444444444444444444444121212121212121224242424
order1222444422223444466666661212121212121212246666888888881212121224242424242424242424242424242424888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-11-1-11111-1-1-1-1111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111-1-11-1-11111-1-1-1-1111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111-1-11-1-11111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111-1-11-1-11111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-1-1ii−i−iii−i−i1111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1i−ii−i
χ101111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-1-1ii−i−iii−i−i1111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−ii−ii
χ111111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-1-1−i−iii−i−iii1111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−ii−ii
χ121111-1-1-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-1-1−i−iii−i−iii1111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111i−ii−i
χ131111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-11111-1-11-1-1-111ii−i−i−i−iii11-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111i−i−ii
χ141111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-11111-1-11-1-1-111ii−i−i−i−iii11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−iii−i
χ151111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-11111-1-11-1-1-111−i−iiiii−i−i11-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−iii−i
χ161111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-11111-1-11-1-1-111−i−iiiii−i−i11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1i−i−ii
χ17222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ18222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111000000000000
χ192222222222-2-2-1-2-222-1-11111-1-1-11111-1-1-2-2-1-1112222-2-2-2-2-1-111-1-1-1-1-1-1-1-111111111000000000000
χ202222222222-2-2-1-2-222-1-11111-1-1-11111-1-1-2-2-1-111-2-2-2-22222-1-11111111111-1-1-1-1-1-1-1-1000000000000
χ2122222222-2-222222-2-2222222222222222-2-2-2-2-2-200000000-2-2-2-20000000000000000000000000000
χ2222222222-2-222-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111000000001111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ2322222222-2-222-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111000000001111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ2422222222-2-2-2-22-2-2-2-222-2-2-2-2222-2-2-2-22222-2-22200000000-2-2220000000000000000000000000000
χ2522222222-2-2-2-2-1-2-2-2-2-1-11111-1-1-11111-1-12211-1-10000000011-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000
χ2622222222-2-2-2-2-1-2-2-2-2-1-11111-1-1-11111-1-12211-1-10000000011-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000
χ272222-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-22-2222200000000-2-2-2-20000000000000000000000000000
χ282222-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1111111112-2-1-1-1-100000000111133−3−3−3−33333−3−3−3−333000000000000
χ292222-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1111111112-2-1-1-1-1000000001111−3−33333−3−3−3−33333−3−3000000000000
χ302222-2-2-2-222-2-2222-2-222-2-2-2-22-2-22222-2-2-2222-2-200000000-2-2220000000000000000000000000000
χ312222-2-2-2-222-2-2-122-2-2-1-11111-111-1-1-1-111-22-1-1110000000011-1-133−3−3−3−333−3−33333−3−3000000000000
χ322222-2-2-2-222-2-2-122-2-2-1-11111-111-1-1-1-111-22-1-1110000000011-1-1−3−33333−3−333−3−3−3−333000000000000
χ332222-2-2-2-2-2-222-1-2-222-1-1-1-1-1-1-111111111-2211112i2i−2i−2i2i2i−2i−2i-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii000000000000
χ342222-2-2-2-2-2-222-1-2-222-1-1-1-1-1-1-111111111-221111−2i−2i2i2i−2i−2i2i2i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i000000000000
χ352222-2-2-2-2-2-2-2-2-12222-1-11111-111-1-1-1-1112-211-1-12i2i−2i−2i−2i−2i2i2i-1-111−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ362222-2-2-2-2-2-2-2-2-12222-1-11111-111-1-1-1-1112-211-1-1−2i−2i2i2i2i2i−2i−2i-1-111iiii−i−i−i−i−i−i−i−iiiii000000000000
χ3722-2-22i−2i2i−2i002-222i−2i002-222-2-2-22i−2i2i2i−2i−2i2i−2i00000000000000000000000000000000002−2−i2i22−2−i2i20000
χ3822-2-22i−2i2i−2i002-222i−2i002-222-2-2-22i−2i2i2i−2i−2i2i−2i0000000000000000000000000000000000−22i2−i2−22i2−i20000
χ3922-2-22i−2i2i−2i00-222−2i2i002-2-2-222-22i−2i−2i−2i2i2i2i−2i00000000000000000000000000000000002−2−i2i2−22i2−i20000
χ4022-2-22i−2i2i−2i00-222−2i2i002-2-2-222-22i−2i−2i−2i2i2i2i−2i0000000000000000000000000000000000−22i2−i22−2−i2i20000
χ4122-2-2−2i2i−2i2i002-22−2i2i002-222-2-2-2−2i2i−2i−2i2i2i−2i2i00000000000000000000000000000000002−2i2−i22−2i2−i20000
χ4222-2-2−2i2i−2i2i002-22−2i2i002-222-2-2-2−2i2i−2i−2i2i2i−2i2i0000000000000000000000000000000000−22−i2i2−22−i2i20000
χ4322-2-2−2i2i−2i2i00-2222i−2i002-2-2-222-2−2i2i2i2i−2i−2i−2i2i00000000000000000000000000000000002−2i2−i2−22−i2i20000
χ4422-2-2−2i2i−2i2i00-2222i−2i002-2-2-222-2−2i2i2i2i−2i−2i−2i2i0000000000000000000000000000000000−22−i2i22−2i2−i20000
χ452-2-2222-2-22-2002002-2-2-200002220000-2-2002-20000002i−2i2i−2i2-200000000002i−2i2i−2i2i−2i2i−2i000000000000
χ462-2-2222-2-22-2002002-2-2-200002220000-2-2002-2000000−2i2i−2i2i2-20000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ472-2-2222-2-22-200-1002-211−i3i3−i3i3-1-1-1−i3i3−i3i31100-11−i3i300002i−2i2i−2i-11−i3i33−33−33−33−3−ii−ii−ii−ii000000000000
χ482-2-2222-2-22-200-1002-211−i3i3−i3i3-1-1-1−i3i3−i3i31100-11−i3i30000−2i2i−2i2i-11−i3i3−33−33−33−33i−ii−ii−ii−i000000000000
χ492-2-2222-2-22-200-1002-211i3−i3i3−i3-1-1-1i3−i3i3−i31100-11i3−i300002i−2i2i−2i-11i3−i3−33−33−33−33−ii−ii−ii−ii000000000000
χ502-2-2222-2-22-200-1002-211i3−i3i3−i3-1-1-1i3−i3i3−i31100-11i3−i30000−2i2i−2i2i-11i3−i33−33−33−33−3i−ii−ii−ii−i000000000000
χ512-2-2222-2-2-2200200-22-2-200002220000-2-200-22002i−2i2i−2i0000-22002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ522-2-2222-2-2-2200200-22-2-200002220000-2-200-2200−2i2i−2i2i0000-2200−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ532-2-2222-2-2-2200-100-2211−i3i3−i3i3-1-1-1−i3i3−i3i311001-1i3−i32i−2i2i−2i00001-1i3−i3−iii−i−iii−i3−3−333−3−33000000000000
χ542-2-2222-2-2-2200-100-2211−i3i3−i3i3-1-1-1−i3i3−i3i311001-1i3−i3−2i2i−2i2i00001-1i3−i3i−i−iii−i−ii−333−3−333−3000000000000
χ552-2-2222-2-2-2200-100-2211i3−i3i3−i3-1-1-1i3−i3i3−i311001-1−i3i32i−2i2i−2i00001-1−i3i3−iii−i−iii−i−333−3−333−3000000000000
χ562-2-2222-2-2-2200-100-2211i3−i3i3−i3-1-1-1i3−i3i3−i311001-1−i3i3−2i2i−2i2i00001-1−i3i3i−i−iii−i−ii3−3−333−3−33000000000000
χ572-2-22-2-2222-200200-22-2-200002-2-2000022002-2002-2-220000-22002-2-22-222-200000000000000000000
χ582-2-22-2-2222-200200-22-2-200002-2-2000022002-200-222-20000-2200-222-22-2-2200000000000000000000
χ592-2-22-2-2222-200-100-2211−i3i3−i3i3-111i3−i3i3−i3-1-100-11−i3i32-2-2200001-1i3−i3-111-11-1-11−i3i3i3−i3i3−i3−i3i3000000000000
χ602-2-22-2-2222-200-100-2211−i3i3−i3i3-111i3−i3i3−i3-1-100-11−i3i3-222-200001-1i3−i31-1-11-111-1i3−i3−i3i3−i3i3i3−i3000000000000
χ612-2-22-2-2222-200-100-2211i3−i3i3−i3-111−i3i3−i3i3-1-100-11i3−i32-2-2200001-1−i3i3-111-11-1-11i3−i3−i3i3−i3i3i3−i3000000000000
χ622-2-22-2-2222-200-100-2211i3−i3i3−i3-111−i3i3−i3i3-1-100-11i3−i3-222-200001-1−i3i31-1-11-111-1−i3i3i3−i3i3−i3−i3i3000000000000
χ632-2-22-2-222-22002002-2-2-200002-2-200002200-220000002-2-222-200000000002-22-2-22-22000000000000
χ642-2-22-2-222-22002002-2-2-200002-2-200002200-22000000-222-22-20000000000-22-222-22-2000000000000
χ652-2-22-2-222-2200-1002-211−i3i3−i3i3-111i3−i3i3−i3-1-1001-1i3−i300002-2-22-11−i3i3−i3i3−i3i3i3−i3i3−i3-11-111-11-1000000000000
χ662-2-22-2-222-2200-1002-211−i3i3−i3i3-111i3−i3i3−i3-1-1001-1i3−i30000-222-2-11−i3i3i3−i3i3−i3−i3i3−i3i31-11-1-11-11000000000000
χ672-2-22-2-222-2200-1002-211i3−i3i3−i3-111−i3i3−i3i3-1-1001-1−i3i300002-2-22-11i3−i3i3−i3i3−i3−i3i3−i3i3-11-111-11-1000000000000
χ682-2-22-2-222-2200-1002-211i3−i3i3−i3-111−i3i3−i3i3-1-1001-1−i3i30000-222-2-11i3−i3−i3i3−i3i3i3−i3i3−i31-11-1-11-11000000000000
χ6944-4-44i−4i4i−4i004-4-24i−4i00-22-2-2222−2i2i−2i−2i2i2i−2i2i0000000000000000000000000000000000000000000000
χ7044-4-44i−4i4i−4i00-44-2−4i4i00-2222-2-22−2i2i2i2i−2i−2i−2i2i0000000000000000000000000000000000000000000000
χ7144-4-4−4i4i−4i4i004-4-2−4i4i00-22-2-22222i−2i2i2i−2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7244-4-4−4i4i−4i4i00-44-24i−4i00-2222-2-222i−2i−2i−2i2i2i2i−2i0000000000000000000000000000000000000000000000
χ734-44-44i−4i−4i4i000040000-440000-44i−4i0000−4i4i0000000000000000000000000000000000000000000000
χ744-44-44i−4i−4i4i0000-200002-2−2i32i32i3−2i32−2i2i23−23−23232i−2i0000000000000000000000000000000000000000000000
χ754-44-44i−4i−4i4i0000-200002-22i3−2i3−2i32i32−2i2i−232323−232i−2i0000000000000000000000000000000000000000000000
χ764-44-4−4i4i4i−4i000040000-440000-4−4i4i00004i−4i0000000000000000000000000000000000000000000000
χ774-44-4−4i4i4i−4i0000-200002-2−2i32i32i3−2i322i−2i−232323−23−2i2i0000000000000000000000000000000000000000000000
χ784-44-4−4i4i4i−4i0000-200002-22i3−2i3−2i32i322i−2i23−23−2323−2i2i0000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).