Finite Group Databasebeta

← Group #72010

Character table — Group #72010

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222222222222222224444444444444444444444444444444444121212121212121224242424
order122244442234466688881212121224242424242424242244666666888888121212121212242424242424242424242424444488882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ81111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ91111-1-1-1-1-1-1111111ii−i−i-1-1-1-1iiii−i−i−i−i11-1-1-1-11111i−iii−i−i11-1-1-1-1ii−i−iiiii−i−i−i−iii−i−i11-1-11-1i−i
χ101111-1-1-1-1-1-1111111ii−i−i-1-1-1-1iiii−i−i−i−i11-1-1-1-11111i−iii−i−i11-1-1-1-1ii−i−iiiii−i−i−i−i−i−iii-1-111-11−ii
χ111111-1-1-1-1-1-1111111ii−i−i-1-1-1-1iiii−i−i−i−i-1-111-1-1-1-1-1-1i−i−i−iii111111ii−i−i−i−i−i−iiiiiii−i−i11-1-1-11−ii
χ121111-1-1-1-1-1-1111111ii−i−i-1-1-1-1iiii−i−i−i−i-1-111-1-1-1-1-1-1i−i−i−iii111111ii−i−i−i−i−i−iiiii−i−iii-1-1111-1i−i
χ131111-1-1-1-1-1-1111111−i−iii-1-1-1-1−i−i−i−iiiii11-1-1-1-11111−ii−i−iii11-1-1-1-1−i−iii−i−i−i−iiiiiii−i−i-1-111-11i−i
χ141111-1-1-1-1-1-1111111−i−iii-1-1-1-1−i−i−i−iiiii11-1-1-1-11111−ii−i−iii11-1-1-1-1−i−iii−i−i−i−iiiii−i−iii11-1-11-1−ii
χ151111-1-1-1-1-1-1111111−i−iii-1-1-1-1−i−i−i−iiiii-1-111-1-1-1-1-1-1−iiii−i−i111111−i−iiiiiii−i−i−i−iii−i−i-1-1111-1−ii
χ161111-1-1-1-1-1-1111111−i−iii-1-1-1-1−i−i−i−iiiii-1-111-1-1-1-1-1-1−iiii−i−i111111−i−iiiiiii−i−i−i−i−i−iii11-1-1-11i−i
χ172222222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111122-2-2-2-2-1-11111-1-1-1-111111111000000000000
χ192222222222-122-1-1-1-2-2-2-2-1-1-1-1111111112222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000
χ202222222222-122-1-1-1-2-2-2-2-1-1-1-111111111-2-2-2-2-1-11111-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000
χ2122222222-2-22-2-222222222222222222220000-2-20000-2-20000-2-20000-2-2-2-200000000000000000000
χ2222222222-2-22-2-2222-2-2-2-22222-2-2-2-2-2-2-2-20000-2-20000220000-2-20000222200000000000000000000
χ2322222222-2-2-1-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000011−i3−i3i3i3-2-2000011−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i3000000000000
χ2422222222-2-2-1-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000011i3i3−i3−i3-2-2000011i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i3000000000000
χ2522222222-2-2-1-2-2-1-1-1-2-2-2-2-1-1-1-111111111000011−i3−i3i3i322000011−i3−i3i3i3-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000
χ2622222222-2-2-1-2-2-1-1-1-2-2-2-2-1-1-1-111111111000011i3i3−i3−i322000011i3i3−i3−i3-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000
χ272222-2-2-2-2222-2-22222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i0000220000−2i2i0000-2-20000−2i−2i2i2i00000000000000000000
χ282222-2-2-2-2222-2-2222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i00002200002i−2i0000-2-200002i2i−2i−2i00000000000000000000
χ292222-2-2-2-222-1-2-2-1-1-12i2i−2i−2i1111−i−i−i−iiiii0000-1-1−i3−i3i3i3−2i2i000011i3i3−i3−i3ii−i−i33−3−3−3−333000000000000
χ302222-2-2-2-222-1-2-2-1-1-12i2i−2i−2i1111−i−i−i−iiiii0000-1-1i3i3−i3−i3−2i2i000011−i3−i3i3i3ii−i−i−3−33333−3−3000000000000
χ312222-2-2-2-222-1-2-2-1-1-1−2i−2i2i2i1111iiii−i−i−i−i0000-1-1−i3−i3i3i32i−2i000011i3i3−i3−i3−i−iii−3−33333−3−3000000000000
χ322222-2-2-2-222-1-2-2-1-1-1−2i−2i2i2i1111iiii−i−i−i−i0000-1-1i3i3−i3−i32i−2i000011−i3−i3i3i3−i−iii33−3−3−3−333000000000000
χ332222-2-2-2-2-2-2-122-1-1-12i2i−2i−2i1111−i−i−i−iiiii22-2-211-1-1-1-12i−2i2i2i−2i−2i-1-11111−i−iii−i−i−i−iiiii000000000000
χ342222-2-2-2-2-2-2-122-1-1-12i2i−2i−2i1111−i−i−i−iiiii-2-2221111112i−2i−2i−2i2i2i-1-1-1-1-1-1−i−iiiiiii−i−i−i−i000000000000
χ352222-2-2-2-2-2-2-122-1-1-1−2i−2i2i2i1111iiii−i−i−i−i22-2-211-1-1-1-1−2i2i−2i−2i2i2i-1-11111ii−i−iiiii−i−i−i−i000000000000
χ362222-2-2-2-2-2-2-122-1-1-1−2i−2i2i2i1111iiii−i−i−i−i-2-222111111−2i2i2i2i−2i−2i-1-1-1-1-1-1ii−i−i−i−i−i−iiiii000000000000
χ3722-2-22i−2i2i−2i002002-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300000000000000000000000000000000001+i−1−i1−i−1+i2−2−i2i20000
χ3822-2-22i−2i2i−2i002002-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ130000000000000000000000000000000000−1−i1+i−1+i1−i−22i2−i20000
χ3922-2-22i−2i2i−2i002002-2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300000000000000000000000000000000001+i−1−i1−i−1+i−22i2−i20000
χ4022-2-22i−2i2i−2i002002-2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000000000000000000000000000000000−1−i1+i−1+i1−i2−2−i2i20000
χ4122-2-2−2i2i−2i2i002002-2-2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i2i−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000000000000000000000001−i−1+i1+i−1−i2−2i2−i20000
χ4222-2-2−2i2i−2i2i002002-2-2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i2i−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000000000000000000000000000000000−1+i1−i−1−i1+i−22−i2i20000
χ4322-2-2−2i2i−2i2i002002-2-22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i2i−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000000000000000000000001−i−1+i1+i−1−i−22−i2i20000
χ4422-2-2−2i2i−2i2i002002-2-22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i2i−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ230000000000000000000000000000000000−1+i1−i−1−i1+i2−2i2−i20000
χ452-2-2222-2-22-22-22-2-220000-2-222000000002-22-22-22-22-20000002-22-22-2000000000000000000000000
χ462-2-2222-2-22-22-22-2-220000-2-22200000000-22-222-2-22-220000002-2-22-22000000000000000000000000
χ472-2-2222-2-22-2-1-2211-1000011-1-1−i3i3−i3i3−i3i3−i3i32-22-2-11-11-11000000-11-11-11−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000
χ482-2-2222-2-22-2-1-2211-1000011-1-1−i3i3−i3i3−i3i3−i3i3-22-22-111-11-1000000-111-11-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3000000000000
χ492-2-2222-2-22-2-1-2211-1000011-1-1i3−i3i3−i3i3−i3i3−i32-22-2-11-11-11000000-11-11-11i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000
χ502-2-2222-2-22-2-1-2211-1000011-1-1i3−i3i3−i3i3−i3i3−i3-22-22-111-11-1000000-111-11-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3000000000000
χ512-2-2222-2-2-2222-2-2-220000-2-222000000000000-220000002-22-2-22000000002-2-222-2-22000000000000
χ522-2-2222-2-2-2222-2-2-220000-2-222000000000000-22000000-22-22-2200000000-222-2-222-2000000000000
χ532-2-2222-2-2-22-12-211-1000011-1-1−i3i3−i3i3−i3i3−i3i300001-1−i3i3i3−i3002-22-21-1−i3i3i3−i3i3−i3i3−i3-111-1-111-1000000000000
χ542-2-2222-2-2-22-12-211-1000011-1-1−i3i3−i3i3−i3i3−i3i300001-1i3−i3−i3i300-22-221-1i3−i3−i3i3i3−i3i3−i31-1-111-1-11000000000000
χ552-2-2222-2-2-22-12-211-1000011-1-1i3−i3i3−i3i3−i3i3−i300001-1−i3i3i3−i300-22-221-1−i3i3i3−i3−i3i3−i3i31-1-111-1-11000000000000
χ562-2-2222-2-2-22-12-211-1000011-1-1i3−i3i3−i3i3−i3i3−i300001-1i3−i3−i3i3002-22-21-1i3−i3−i3i3−i3i3−i3i3-111-1-111-1000000000000
χ572-2-22-2-2222-222-2-2-22000022-2-20000000000002-20000002i−2i−2i2i-22000000002i−2i−2i2i−2i2i2i−2i000000000000
χ582-2-22-2-2222-222-2-2-22000022-2-20000000000002-2000000−2i2i2i−2i-2200000000−2i2i2i−2i2i−2i−2i2i000000000000
χ592-2-22-2-2222-2-12-211-10000-1-1113−33−3−33−330000-11−i3i3i3−i3002i−2i−2i2i1-1i3−i3−i3i3−333−3−iii−ii−i−ii000000000000
χ602-2-22-2-2222-2-12-211-10000-1-1113−33−3−33−330000-11i3−i3−i3i300−2i2i2i−2i1-1−i3i3i3−i3−333−3i−i−ii−iii−i000000000000
χ612-2-22-2-2222-2-12-211-10000-1-111−33−333−33−30000-11−i3i3i3−i300−2i2i2i−2i1-1i3−i3−i3i33−3−33i−i−ii−iii−i000000000000
χ622-2-22-2-2222-2-12-211-10000-1-111−33−333−33−30000-11i3−i3−i3i3002i−2i−2i2i1-1−i3i3i3−i33−3−33−iii−ii−i−ii000000000000
χ632-2-22-2-222-222-22-2-22000022-2-2000000002-2-22-222-22-20000002-2-22-22000000000000000000000000
χ642-2-22-2-222-222-22-2-22000022-2-200000000-222-2-22-22-220000002-22-22-2000000000000000000000000
χ652-2-22-2-222-22-1-2211-10000-1-1113−33−3−33−332-2-221-1-11-11000000-111-11-13−3−333−33−3−33−33000000000000
χ662-2-22-2-222-22-1-2211-10000-1-1113−33−3−33−33-222-21-11-11-1000000-11-11-113−3−33−33−333−33−3000000000000
χ672-2-22-2-222-22-1-2211-10000-1-111−33−333−33−32-2-221-1-11-11000000-111-11-1−333−3−33−333−33−3000000000000
χ682-2-22-2-222-22-1-2211-10000-1-111−33−333−33−3-222-21-11-11-1000000-11-11-11−333−33−33−3−33−33000000000000
χ6944-4-44i−4i4i−4i00-200-2224ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13−2i2i−2i2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000000000000000000000000000000000000000000000
χ7044-4-44i−4i4i−4i00-200-222−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13−2i2i−2i2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ130000000000000000000000000000000000000000000000
χ7144-4-4−4i4i−4i4i00-200-222−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ232i−2i2i−2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ230000000000000000000000000000000000000000000000
χ7244-4-4−4i4i−4i4i00-200-2224ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ232i−2i2i−2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000000000000000000000000000000000000000000000
χ734-44-44i−4i−4i4i00400-44-40000−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ744-44-44i−4i−4i4i00-2002-2200002i−2i−2i2i−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000000000000000000000
χ754-44-44i−4i−4i4i00-2002-2200002i−2i−2i2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000000000000000000000
χ764-44-4−4i4i4i−4i00400-44-400004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ774-44-4−4i4i4i−4i00-2002-220000−2i2i2i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000000000000000000000
χ784-44-4−4i4i4i−4i00-2002-220000−2i2i2i−2i−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000000000000000000000

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