Finite Group Databasebeta

← Group #13147281

Character table — Group #13147281

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222226666666666121212121212121212121212121212121212121212121212121818181824242424242424242424242424242424242424247272727272727272108108
order12222236666666344666666633466666612121212121212121212121212121212444433666666666666666666121212121212121224
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111111111−1−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
χ4111111111111111111111111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111111111-1-1-1-1−1−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
χ5111111111111111111111111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111111111−1+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
χ6111111111111111111111111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111111111-1-1-1-1−1+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
χ71111-1-1111-1-1-1-1111111-1-1-1-1111-111111111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-111-1-1-11
χ81111-1-1111-1-1-1-1111111-1-1-1-1111-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-111-1-1111-1
χ91111-1-1111-1-1-1-1111111-1-1-1-11−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1111111-1-1-1-1-1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11
χ101111-1-1111-1-1-1-1111111-1-1-1-11−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1111111-1-1-1-1-1-1-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1
χ111111-1-1111-1-1-1-1111111-1-1-1-11−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1111111-1-1-1-1-1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11
χ121111-1-1111-1-1-1-1111111-1-1-1-11−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1111111-1-1-1-1-1-1-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1
χ1322222222222222-122-1-1-1-1-1-1-12222222222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ1422222222222222-122-1-1-1-1-1-1-1−1−i3−1+i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i32222-1-1-1-1-1-1-1-1-1-1-1-100001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i320000000000
χ1522222222222222-122-1-1-1-1-1-1-1−1+i3−1−i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i32222-1-1-1-1-1-1-1-1-1-1-1-100001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i320000000000
χ162222-2-2222-2-2-2-22-122-1-11111-122-222222222-2-2-1-1-1-1-1-11111110000-1-1-2-2-2-2-1-1-11111-1-1-111110000000000
χ172222-2-2222-2-2-2-22-122-1-11111-1−1−i3−1+i3-2−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322-2-2-1-1-1-1-1-111111100001+i321−i321+i31+i31−i31−i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i320000000000
χ182222-2-2222-2-2-2-22-122-1-11111-1−1+i3−1−i3-2−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322-2-2-1-1-1-1-1-111111100001−i321+i321−i31−i31+i31+i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i320000000000
χ192-22-2002-2-20000222-2-2-200002220-2-22-22-22-200222-2-2-200000000002200002-2-200002-2-200000000000000
χ202-22-2002-2-20000222-2-2-200002−1−i3−1+i301+i31−i3−1−i31+i3−1+i31−i32-200222-2-2-20000000000−1−i3−1+i30000−1−i31+i31+i30000−1+i31−i31−i300000000000000
χ212-22-2002-2-20000222-2-2-200002−1+i3−1−i301−i31+i3−1+i31−i3−1−i31+i32-200222-2-2-20000000000−1+i3−1−i30000−1+i31−i31−i30000−1−i31+i31+i300000000000000
χ222-22-2002-2-200002-12-211−i3−i3i3i3-1220-2-22-22-22-200-1-1-1111−i3−i3−i3i3i3i30000-1-10000-111−i3−i3i3i3-111−i3−i3i3i30000000000
χ232-22-2002-2-200002-12-211−i3−i3i3i3-1−1−i3−1+i301+i31−i3−1−i31+i3−1+i31−i32-200-1-1-1111−i3−i3−i3i3i3i300001+i321−i3200001+i32−1−i32−1−i32−3+i32−3+i323−i323−i321−i32−1+i32−1+i323+i323+i32−3−i32−3−i320000000000
χ242-22-2002-2-200002-12-211−i3−i3i3i3-1−1+i3−1−i301−i31+i3−1+i31−i3−1−i31+i32-200-1-1-1111−i3−i3−i3i3i3i300001−i321+i3200001−i32−1+i32−1+i323+i323+i32−3−i32−3−i321+i32−1−i32−1−i32−3+i32−3+i323−i323−i320000000000
χ252-22-2002-2-200002-12-211i3i3−i3−i3-1220-2-22-22-22-200-1-1-1111i3i3i3−i3−i3−i30000-1-10000-111i3i3−i3−i3-111i3i3−i3−i30000000000
χ262-22-2002-2-200002-12-211i3i3−i3−i3-1−1−i3−1+i301+i31−i3−1−i31+i3−1+i31−i32-200-1-1-1111i3i3i3−i3−i3−i300001+i321−i3200001+i32−1−i32−1−i323−i323−i32−3+i32−3+i321−i32−1+i32−1+i32−3−i32−3−i323+i323+i320000000000
χ272-22-2002-2-200002-12-211i3i3−i3−i3-1−1+i3−1−i301−i31+i3−1+i31−i3−1−i31+i32-200-1-1-1111i3i3i3−i3−i3−i300001−i321+i3200001−i32−1+i32−1+i32−3−i32−3−i323+i323+i321+i32−1−i32−1−i323−i323−i32−3+i32−3+i320000000000
χ282-2-222-222-222-2-2-22002-22-22-2-2-1-10-1-1111100000000000000002i−2i2i−2i-1-11-11-111-11-11-111-11-11-1i−ii−ii−ii−i00
χ292-2-222-222-222-2-2-22002-22-22-2-2-1-10-1-111110000000000000000−2i2i−2i2i-1-11-11-111-11-11-111-11-11-1−ii−ii−ii−ii00
χ302-2-222-222-222-2-2-22002-22-22-2-21+i321−i3201+i321−i32−1−i32−1−i32−1+i32−1+i3200000000000000002i−2i2i−2i1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ700
χ312-2-222-222-222-2-2-22002-22-22-2-21+i321−i3201+i321−i32−1−i32−1−i32−1+i32−1+i320000000000000000−2i2i−2i2i1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ700
χ322-2-222-222-222-2-2-22002-22-22-2-21−i321+i3201−i321+i32−1+i32−1+i32−1−i32−1−i3200000000000000002i−2i2i−2i1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ1100
χ332-2-222-222-222-2-2-22002-22-22-2-21−i321+i3201−i321+i32−1+i32−1+i32−1−i32−1−i320000000000000000−2i2i−2i2i1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ1100
χ342-2-22-2222-2-2-222-22002-2-22-22-2-1-10-1-1111100000000000000002i−2i−2i2i-1-1-11-1111-1-11-1111-1-11-11i−i−iii−i−ii00
χ352-2-22-2222-2-2-222-22002-2-22-22-2-1-10-1-111110000000000000000−2i2i2i−2i-1-1-11-1111-1-11-1111-1-11-11−iii−i−iii−i00
χ362-2-22-2222-2-2-222-22002-2-22-22-21+i321−i3201+i321−i32−1−i32−1−i32−1+i32−1+i3200000000000000002i−2i−2i2i1+i321−i321+i32−1−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ700
χ372-2-22-2222-2-2-222-22002-2-22-22-21+i321−i3201+i321−i32−1−i32−1−i32−1+i32−1+i320000000000000000−2i2i2i−2i1+i321−i321+i32−1−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ700
χ382-2-22-2222-2-2-222-22002-2-22-22-21−i321+i3201−i321+i32−1+i32−1+i32−1−i32−1−i3200000000000000002i−2i−2i2i1−i321+i321−i32−1+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ1100
χ392-2-22-2222-2-2-222-22002-2-22-22-21−i321+i3201−i321+i32−1+i32−1+i32−1−i32−1−i320000000000000000−2i2i2i−2i1−i321+i321−i32−1+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ1100
χ40333333333333333-1-1333333300-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133330000000000000000000000000000-1-1
χ41333333333333333-1-1333333300-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-3000000000000000000000000000011
χ423333-3-3333-3-3-3-333-1-133-3-3-3-33001000000-1-111-1-1-1-1-1-111111133-3-300000000000000000000000000001-1
χ433333-3-3333-3-3-3-333-1-133-3-3-3-33001000000-1-111-1-1-1-1-1-1111111-3-3330000000000000000000000000000-11
χ4444-4-4004-440000-4400-440000-4-2-20222-22-200000000000000000000-2-200002-2200002-2200000000000000
χ4544-4-4004-440000-4400-440000-41+i31−i30−1−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000001+i31−i30000−1−i31+i3−1−i30000−1+i31−i3−1+i300000000000000
χ4644-4-4004-440000-4400-440000-41−i31+i30−1+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000001−i31+i30000−1+i31−i3−1+i30000−1−i31+i3−1−i300000000000000
χ4744-4-4004-440000-4-2002-2−2i32i32i3−2i32-2-20222-22-200000000000000000000110000-11-1−i3i3i3−i3-11-1−i3i3i3−i30000000000
χ4844-4-4004-440000-4-2002-2−2i32i32i3−2i321+i31−i30−1−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000−1−i32−1+i3200001+i32−1−i321+i32−3+i323−i323−i32−3+i321−i32−1+i321−i323+i32−3−i32−3−i323+i320000000000
χ4944-4-4004-440000-4-2002-2−2i32i32i3−2i321−i31+i30−1+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000−1+i32−1−i3200001−i32−1+i321−i323+i32−3−i32−3−i323+i321+i32−1−i321+i32−3+i323−i323−i32−3+i320000000000
χ5044-4-4004-440000-4-2002-22i3−2i3−2i32i32-2-20222-22-200000000000000000000110000-11-1i3−i3−i3i3-11-1i3−i3−i3i30000000000
χ5144-4-4004-440000-4-2002-22i3−2i3−2i32i321+i31−i30−1−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000−1−i32−1+i3200001+i32−1−i321+i323−i32−3+i32−3+i323−i321−i32−1+i321−i32−3−i323+i323+i32−3−i320000000000
χ5244-4-4004-440000-4-2002-22i3−2i3−2i32i321−i31+i30−1+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000−1+i32−1−i3200001−i32−1+i321−i32−3−i323+i323+i32−3−i321+i32−1−i321+i323−i32−3+i32−3+i323−i320000000000
χ534-4-444-444-444-4-4-4-200-22-22-222-2-20-2-2222200000000000000000000112-22-2-1-11-11-11-1-11-11-110000000000
χ544-4-444-444-444-4-4-4-200-22-22-2221+i31−i301+i31−i3−1−i3−1−i3−1+i3−1+i300000000000000000000−1−i32−1+i32−1−i31+i3−1+i31−i31+i321+i32−1−i321+i32−1−i321+i32−1−i321−i321−i32−1+i321−i32−1+i321−i32−1+i320000000000
χ554-4-444-444-444-4-4-4-200-22-22-2221−i31+i301−i31+i3−1+i3−1+i3−1−i3−1−i300000000000000000000−1+i32−1−i32−1+i31−i3−1−i31+i31−i321−i32−1+i321−i32−1+i321−i32−1+i321+i321+i32−1−i321+i32−1−i321+i32−1−i320000000000
χ564-4-44-4444-4-4-444-4-200-222-22-22-2-20-2-222220000000000000000000011-22-22-1-111-11-1-1-111-11-10000000000
χ574-4-44-4444-4-4-444-4-200-222-22-221+i31−i301+i31−i3−1−i3−1−i3−1+i3−1+i300000000000000000000−1−i32−1+i321+i3−1−i31−i3−1+i31+i321+i32−1−i32−1−i321+i32−1−i321+i321−i321−i32−1+i32−1+i321−i32−1+i321−i320000000000
χ584-4-44-4444-4-4-444-4-200-222-22-221−i31+i301−i31+i3−1+i3−1+i3−1−i3−1−i300000000000000000000−1+i32−1−i321−i3−1+i31+i3−1−i31−i321−i32−1+i32−1+i321−i32−1+i321−i321+i321+i32−1−i32−1−i321+i32−1−i321+i320000000000
χ5966666666666666-3-2-2-3-3-3-3-3-3-300-2000000-2-2-2-21111111111110000000000000000000000000000000000
χ60666666-3-3-3-3-3-3-3-30660000000006000000-3-3-3-30000000000000000000000000000000000000000000000
χ61666666-3-3-3-3-3-3-3-30-2-2000000000-200000011114-2-24-2-24-2-24-2-20000000000000000000000000000000000
χ62666666-3-3-3-3-3-3-3-30-2-2000000000-20000001111-24-2-24-2-24-2-24-20000000000000000000000000000000000
χ63666666-3-3-3-3-3-3-3-30-2-2000000000-20000001111-2-24-2-24-2-24-2-240000000000000000000000000000000000
χ646666-6-6666-6-6-6-66-3-2-2-3-33333-3002000000-2-222111111-1-1-1-1-1-10000000000000000000000000000000000
χ656666-6-6-3-3-33333-3066000000000-6000000-3-3330000000000000000000000000000000000000000000000
χ666666-6-6-3-3-33333-30-2-2000000000200000011-1-14-2-24-2-2-422-4220000000000000000000000000000000000
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χ726-66-600-333−3i33i3−3i33i3-306-60000000000000000-33−3i33i30000000000000000000000000000000000000000000000
χ736-66-600-333−3i33i3−3i33i3-30-2200000000000000001-1i3−i34-2-2-4220−2i32i302i3−2i30000000000000000000000000000000000
χ746-66-600-333−3i33i3−3i33i3-30-2200000000000000001-1i3−i3-24-22-422i30−2i3−2i302i30000000000000000000000000000000000
χ756-66-600-333−3i33i3−3i33i3-30-2200000000000000001-1i3−i3-2-2422-4−2i32i302i3−2i300000000000000000000000000000000000
χ766-66-600-3333i3−3i33i3−3i3-306-60000000000000000-333i3−3i30000000000000000000000000000000000000000000000
χ776-66-600-3333i3−3i33i3−3i3-30-2200000000000000001-1−i3i34-2-2-42202i3−2i30−2i32i30000000000000000000000000000000000
χ786-66-600-3333i3−3i33i3−3i3-30-2200000000000000001-1−i3i3-24-22-42−2i302i32i30−2i30000000000000000000000000000000000
χ796-66-600-3333i3−3i33i3−3i3-30-2200000000000000001-1−i3i3-2-2422-42i3−2i30−2i32i300000000000000000000000000000000000
χ801212-12-1200-66-6−6i36i36i3−6i36000000000000000000000000000000000000000000000000000000000000000000000
χ811212-12-1200-66-66i3−6i3−6i36i36000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-121212-12-6-66-6-6666000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-1212-6-6666-6-66000000000000000000000000000000000000000000000000000000000000000000000

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