Finite Group Databasebeta

← Group #13147295

Character table — Group #13147295

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222226666666666121212121212121212121212121212121212121212121212121818181824242424242424242424242424242424242424247272727272727272108108
order1222344666121212123446661212121223366666666666666121212121212121222443366666612121212121212121212121266661212121244
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211
χ41111111111111111111111111−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-1-1
χ51111111111111111111111111−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211
χ61111111111111111111111111−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-1-1
χ711111-1-1111-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11
χ811111-1-1111-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1
χ911111-1-1111-1-1-1-1111111-1-1-1-1-1−1−i32−1+i32-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11
χ1011111-1-1111-1-1-1-1111111-1-1-1-1-1−1−i32−1+i32-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1
χ1111111-1-1111-1-1-1-1111111-1-1-1-1-1−1+i32−1−i32-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11
χ1211111-1-1111-1-1-1-1111111-1-1-1-1-1−1+i32−1−i32-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-1
χ1322222222222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-122222222-1-1-1-1-1-10000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ1422222222222222-122-1-1-1-1-1-1-12−1−i3−1+i322-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-1-1-1-1-1-100001+i321−i321+i321+i321−i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i320000000000
χ1522222222222222-122-1-1-1-1-1-1-12−1+i3−1−i322-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322-1-1-1-1-1-100001−i321+i321−i321−i321+i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i320000000000
χ1622222-2-2222-2-2-2-2-122-1-1-11111-222-2-211111122222222-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ1722222-2-2222-2-2-2-2-122-1-1-11111-2−1−i3−1+i3-2-2111111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-1-1-1-1-1-100001+i321−i321+i321+i321−i321−i321+i321−i321+i31+i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320000000000
χ1822222-2-2222-2-2-2-2-122-1-1-11111-2−1+i3−1−i3-2-2111111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322-1-1-1-1-1-100001−i321+i321−i321−i321+i321+i321−i321+i321−i31−i31+i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320000000000
χ192-22-222i−2i2-2-22i2i−2i−2i2002-2-22i2i−2i−2i0-1-100000000-1-11111000000002-22i−2i-1-11-11-111i−ii−iii−i−iii−i−i1-11-1i−ii−i00
χ202-22-222i−2i2-2-22i2i−2i−2i2002-2-22i2i−2i−2i0-1-100000000-1-1111100000000-22−2i2i-1-11-11-111i−ii−iii−i−iii−i−i-11-11−ii−ii00
χ212-22-222i−2i2-2-22i2i−2i−2i2002-2-22i2i−2i−2i01+i321−i32000000001+i321−i32−1−i32−1+i32−1−i32−1+i32000000002-22i−2i1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7−1−i321+i32−1+i321−i32ζ11−ζ11ζ7−ζ700
χ222-22-222i−2i2-2-22i2i−2i−2i2002-2-22i2i−2i−2i01+i321−i32000000001+i321−i32−1−i32−1+i32−1−i32−1+i3200000000-22−2i2i1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ71+i32−1−i321−i32−1+i32−ζ11ζ11−ζ7ζ700
χ232-22-222i−2i2-2-22i2i−2i−2i2002-2-22i2i−2i−2i01−i321+i32000000001−i321+i32−1+i32−1−i32−1+i32−1−i32000000002-22i−2i1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11−1+i321−i32−1−i321+i32ζ7−ζ7ζ11−ζ1100
χ242-22-222i−2i2-2-22i2i−2i−2i2002-2-22i2i−2i−2i01−i321+i32000000001−i321+i32−1+i32−1−i32−1+i32−1−i3200000000-22−2i2i1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ111−i32−1+i321+i32−1−i32−ζ7ζ7−ζ11ζ1100
χ252-22-22−2i2i2-2-2−2i−2i2i2i2002-2-2−2i−2i2i2i0-1-100000000-1-11111000000002-2−2i2i-1-11-11-111−ii−ii−i−iii−i−iii1-11-1−ii−ii00
χ262-22-22−2i2i2-2-2−2i−2i2i2i2002-2-2−2i−2i2i2i0-1-100000000-1-1111100000000-222i−2i-1-11-11-111−ii−ii−i−iii−i−iii-11-11i−ii−i00
χ272-22-22−2i2i2-2-2−2i−2i2i2i2002-2-2−2i−2i2i2i01+i321−i32000000001+i321−i32−1−i32−1+i32−1−i32−1+i32000000002-2−2i2i1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−1−i321+i32−1+i321−i32−ζ11ζ11−ζ7ζ700
χ282-22-22−2i2i2-2-2−2i−2i2i2i2002-2-2−2i−2i2i2i01+i321−i32000000001+i321−i32−1−i32−1+i32−1−i32−1+i3200000000-222i−2i1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ71+i32−1−i321−i32−1+i32ζ11−ζ11ζ7−ζ700
χ292-22-22−2i2i2-2-2−2i−2i2i2i2002-2-2−2i−2i2i2i01−i321+i32000000001−i321+i32−1+i32−1−i32−1+i32−1−i32000000002-2−2i2i1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−1+i321−i32−1−i321+i32−ζ7ζ7−ζ11ζ1100
χ302-22-22−2i2i2-2-2−2i−2i2i2i2002-2-2−2i−2i2i2i01−i321+i32000000001−i321+i32−1+i32−1−i32−1+i32−1−i3200000000-222i−2i1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ111−i32−1+i321+i32−1−i32ζ7−ζ7ζ11−ζ1100
χ312-2-22200-2-22000022-2-2-22000002200000000-2-222-2-22-2222-2-2-2000022-2-2-2-2220000000000000000000000
χ322-2-22200-2-22000022-2-2-2200000−1−i3−1+i3000000001+i31−i3−1−i3−1+i31+i31−i32-2222-2-2-20000−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i30000000000000000000000
χ332-2-22200-2-22000022-2-2-2200000−1+i3−1−i3000000001−i31+i3−1+i3−1−i31−i31+i32-2222-2-2-20000−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i30000000000000000000000
χ342-2-22200-2-220000-12-211-1−i3i3−i3i302200−i3−i3−i3i3i3i3-2-222-2-22-2-1-1-11110000-1-11111-1-10000−i3i3−i3i3−i3i3−i3i30000000000
χ352-2-22200-2-220000-12-211-1−i3i3−i3i30−1−i3−1+i300−i3−i3−i3i3i3i31+i31−i3−1−i3−1+i31+i31−i32-2-1-1-111100001+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i320000−3+i323−i32−3+i323−i323+i32−3−i323+i32−3−i320000000000
χ362-2-22200-2-220000-12-211-1−i3i3−i3i30−1+i3−1−i300−i3−i3−i3i3i3i31−i31+i3−1+i3−1−i31−i31+i32-2-1-1-111100001−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i3200003+i32−3−i323+i32−3−i32−3+i323−i32−3+i323−i320000000000
χ372-2-22200-2-220000-12-211-1i3−i3i3−i302200i3i3i3−i3−i3−i3-2-222-2-22-2-1-1-11110000-1-11111-1-10000i3−i3i3−i3i3−i3i3−i30000000000
χ382-2-22200-2-220000-12-211-1i3−i3i3−i30−1−i3−1+i300i3i3i3−i3−i3−i31+i31−i3−1−i3−1+i31+i31−i32-2-1-1-111100001+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i3200003−i32−3+i323−i32−3+i32−3−i323+i32−3−i323+i320000000000
χ392-2-22200-2-220000-12-211-1i3−i3i3−i30−1+i3−1−i300i3i3i3−i3−i3−i31−i31+i3−1+i3−1−i31−i31+i32-2-1-1-111100001−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i320000−3−i323+i32−3−i323+i323−i32−3+i323−i32−3+i320000000000
χ40333333333333333-1-13333333-100-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-133330000000000000000000000000000-1-1
χ41333333333333333-1-13333333-100-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-3-3-3-3000000000000000000000000000011
χ4233333-3-3333-3-3-3-33-1-1333-3-3-3-310011111111000000-1-1-1-1-1-1-1-133-3-300000000000000000000000000001-1
χ4333333-3-3333-3-3-3-33-1-1333-3-3-3-310011111111000000-1-1-1-1-1-1-1-1-3-3330000000000000000000000000000-11
χ4444-4-4400-44-40000400-44-400000-2-2000000002222-2-2000000000000-2-2-22-22220000000000000000000000
χ4544-4-4400-44-40000400-44-4000001+i31−i300000000−1−i3−1+i3−1−i3−1+i31+i31−i30000000000001+i31−i31+i3−1−i31−i3−1+i3−1−i3−1+i30000000000000000000000
χ4644-4-4400-44-40000400-44-4000001−i31+i300000000−1+i3−1−i3−1+i3−1−i31−i31+i30000000000001−i31+i31−i3−1+i31+i3−1−i3−1+i3−1−i30000000000000000000000
χ4744-4-4400-44-40000-2002-2223−23−23230-2-2000000002222-2-2000000000000111-11-1-1-100003−3−333−3−330000000000
χ4844-4-4400-44-40000-2002-2223−23−232301+i31−i300000000−1−i3−1+i3−1−i3−1+i31+i31−i3000000000000−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i3200002ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ110000000000
χ4944-4-4400-44-40000-2002-2223−23−232301−i31+i300000000−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i320000−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ110000000000
χ5044-4-4400-44-40000-2002-22−232323−230-2-2000000002222-2-2000000000000111-11-1-1-10000−333−3−333−30000000000
χ5144-4-4400-44-40000-2002-22−232323−2301+i31−i300000000−1−i3−1+i3−1−i3−1+i31+i31−i3000000000000−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i320000−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ110000000000
χ5244-4-4400-44-40000-2002-22−232323−2301−i31+i300000000−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i320000ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ110000000000
χ534-44-444i−4i4-4-44i4i−4i−4i-200-222−2i−2i2i2i0-2-200000000-2-2222200000000000011-11-11-1-12i−2i2i−2i−i−iii−i−iii0000000000
χ544-44-444i−4i4-4-44i4i−4i−4i-200-222−2i−2i2i2i01+i31−i3000000001+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i322ζ11−2ζ112ζ7−2ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ70000000000
χ554-44-444i−4i4-4-44i4i−4i−4i-200-222−2i−2i2i2i01−i31+i3000000001−i31+i3−1+i3−1−i3−1+i3−1−i3000000000000−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i322ζ7−2ζ72ζ11−2ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ110000000000
χ564-44-44−4i4i4-4-4−4i−4i4i4i-200-2222i2i−2i−2i0-2-200000000-2-2222200000000000011-11-11-1-1−2i2i−2i2iii−i−iii−i−i0000000000
χ574-44-44−4i4i4-4-4−4i−4i4i4i-200-2222i2i−2i−2i01+i31−i3000000001+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i32−2ζ112ζ11−2ζ72ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ70000000000
χ584-44-44−4i4i4-4-4−4i−4i4i4i-200-2222i2i−2i−2i01−i31+i3000000001−i31+i3−1+i3−1−i3−1+i3−1−i3000000000000−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i32−2ζ72ζ7−2ζ112ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ110000000000
χ5966666666666666-3-2-2-3-3-3-3-3-3-3-200-2-2111111000000-2-21111110000000000000000000000000000000000
χ6066666-6-6666-6-6-6-6-3-2-2-3-3-3333320022-1-1-1-1-1-1000000-2-21111110000000000000000000000000000000000
χ616666-366-3-3-3-3-3-3-30660000000600-3-3000000000000-3-30000000000000000000000000000000000000000
χ626666-366-3-3-3-3-3-3-30-2-20000000-200114-2-24-2-2000000114-2-24-2-20000000000000000000000000000000000
χ636666-366-3-3-3-3-3-3-30-2-20000000-20011-24-2-24-200000011-24-2-24-20000000000000000000000000000000000
χ646666-366-3-3-3-3-3-3-30-2-20000000-20011-2-24-2-2400000011-2-24-2-240000000000000000000000000000000000
χ656666-3-6-6-3-3-333330660000000-60033000000000000-3-30000000000000000000000000000000000000000
χ666666-3-6-6-3-3-333330-2-20000000200-1-122-422-400000011-2-24-2-240000000000000000000000000000000000
χ676666-3-6-6-3-3-333330-2-20000000200-1-12-422-4200000011-24-2-24-20000000000000000000000000000000000
χ686666-3-6-6-3-3-333330-2-20000000200-1-1-422-422000000114-2-24-2-20000000000000000000000000000000000
χ696-6-66600-6-6600006-22-6-66000000000000000000000-22-2-2-22220000000000000000000000000000000000
χ706-6-66600-6-660000-3-2233-3−3i33i3−3i33i300000i3i3i3−i3−i3−i3000000-22111-1-1-10000000000000000000000000000000000
χ716-6-66600-6-660000-3-2233-33i3−3i33i3−3i300000−i3−i3−i3i3i3i3000000-22111-1-1-10000000000000000000000000000000000
χ726-6-66-30033-3−3i33i3−3i33i306-60000000000−3i33i3000000000000-330000000000000000000000000000000000000000
χ736-6-66-30033-3−3i33i3−3i33i30-220000000000i3−i30−2i32i302i3−2i30000001-14-2-2-4220000000000000000000000000000000000
χ746-6-66-30033-3−3i33i3−3i33i30-220000000000i3−i3−2i32i302i3−2i300000001-1-2-2422-40000000000000000000000000000000000
χ756-6-66-30033-3−3i33i3−3i33i30-220000000000i3−i32i30−2i3−2i302i30000001-1-24-22-420000000000000000000000000000000000
χ766-6-66-30033-33i3−3i33i3−3i306-600000000003i3−3i3000000000000-330000000000000000000000000000000000000000
χ776-6-66-30033-33i3−3i33i3−3i30-220000000000−i3i302i3−2i30−2i32i30000001-14-2-2-4220000000000000000000000000000000000
χ786-6-66-30033-33i3−3i33i3−3i30-220000000000−i3i3−2i302i32i30−2i30000001-1-24-22-420000000000000000000000000000000000
χ796-6-66-30033-33i3−3i33i3−3i30-220000000000−i3i32i3−2i30−2i32i300000001-1-2-2422-40000000000000000000000000000000000
χ801212-12-12-6006-6663−63−6363000000000000000000000000000000000000000000000000000000000000000000000
χ811212-12-12-6006-66−636363−63000000000000000000000000000000000000000000000000000000000000000000000
χ8212-1212-12-612i−12i-666−6i−6i6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-6−12i12i-6666i6i−6i−6i000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.