Finite Group Databasebeta

← Group #13181423

Character table — Group #13181423

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112266612121212121232323232323236367272721122666121212121212323232323232363672727211226661212121212123232323232323636727272
order123622246661212333666444443636666126661212333666121212121236366661266612123336661212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111-1-1-1-1-11111111111111111111-1-1-1-1-11111111111111111111-1-1-1-1-1
χ32222222222222-1-1-1-1-1-1000002222222222222-1-1-1-1-1-1000002222222222222-1-1-1-1-1-100000
χ422-1-12222-1-1-1-1-12-1-12-1-10000022-1-12222-1-1-1-1-12-1-12-1-10000022-1-12222-1-1-1-1-12-1-12-1-100000
χ522-1-12222-1-1-1-1-1-12-1-12-10000022-1-12222-1-1-1-1-1-12-1-12-10000022-1-12222-1-1-1-1-1-12-1-12-100000
χ622-1-12222-1-1-1-1-1-1-12-1-120000022-1-12222-1-1-1-1-1-1-12-1-120000022-1-12222-1-1-1-1-1-1-12-1-1200000
χ733333-1-1-13-1-1-1-1000000111-1-133333-1-1-13-1-1-1-1000000111-1-133333-1-1-13-1-1-1-1000000111-1-1
χ833333-1-1-13-1-1-1-1000000-1-1-11133333-1-1-13-1-1-1-1000000-1-1-11133333-1-1-13-1-1-1-1000000-1-1-111
χ93333-13-1-1-13-1-1-100000011-11-13333-13-1-1-13-1-1-100000011-11-13333-13-1-1-13-1-1-100000011-11-1
χ103333-13-1-1-13-1-1-1000000-1-11-113333-13-1-1-13-1-1-1000000-1-11-113333-13-1-1-13-1-1-1000000-1-11-11
χ113333-1-13-1-1-13-1-100000011-1-113333-1-13-1-1-13-1-100000011-1-113333-1-13-1-1-13-1-100000011-1-11
χ123333-1-13-1-1-13-1-1000000-1-111-13333-1-13-1-1-13-1-1000000-1-111-13333-1-13-1-1-13-1-1000000-1-111-1
χ134-44-4000000000111-1-1-12i−2i0004-44-4000000000111-1-1-12i−2i0004-44-4000000000111-1-1-12i−2i000
χ144-44-4000000000111-1-1-1−2i2i0004-44-4000000000111-1-1-1−2i2i0004-44-4000000000111-1-1-1−2i2i000
χ156666-2-2-22-2-2-222000000000006666-2-2-22-2-2-222000000000006666-2-2-22-2-2-22200000000000
χ1666-3-36-2-2-2-311110000000000066-3-36-2-2-2-311110000000000066-3-36-2-2-2-3111100000000000
χ1766-3-3-26-2-21-31110000000000066-3-3-26-2-21-31110000000000066-3-3-26-2-21-311100000000000
χ1866-3-3-2-26-211-3110000000000066-3-3-2-26-211-3110000000000066-3-3-2-26-211-31100000000000
χ1966-3-3-2-2-22111−1−2i3−1+2i30000000000066-3-3-2-2-22111−1−2i3−1+2i30000000000066-3-3-2-2-22111−1−2i3−1+2i300000000000
χ2066-3-3-2-2-22111−1+2i3−1−2i30000000000066-3-3-2-2-22111−1+2i3−1−2i30000000000066-3-3-2-2-22111−1+2i3−1−2i300000000000
χ218-88-8000000000-1-1-1111000008-88-8000000000-1-1-1111000008-88-8000000000-1-1-111100000
χ228-8-440000000002-1-1-211000008-8-440000000002-1-1-211000008-8-440000000002-1-1-21100000
χ238-8-44000000000-12-11-21000008-8-44000000000-12-11-21000008-8-44000000000-12-11-2100000
χ248-8-44000000000-1-1211-2000008-8-44000000000-1-1211-2000008-8-44000000000-1-1211-200000
χ25111111111111111111111111−1+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−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
χ261111111111111111111-1-1-1-1-1−1+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+i321−i321−i321−i321−i321−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+i32
χ272222222222222-1-1-1-1-1-100000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i3200000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i3200000
χ2822-1-12222-1-1-1-1-12-1-12-1-100000−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i32−1+i31−i321−i3200000−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i32−1−i31+i321+i3200000
χ2922-1-12222-1-1-1-1-1-12-1-12-100000−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i32−1+i31−i321−i32−1+i31−i3200000−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i32−1−i31+i321+i32−1−i31+i3200000
χ3022-1-12222-1-1-1-1-1-1-12-1-1200000−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i31−i321−i32−1+i300000−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i31+i321+i32−1−i300000
χ3133333-1-1-13-1-1-1-1000000111-1-1−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i321−i32000000−1+i32−1+i32−1+i321−i321−i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i321+i32000000−1−i32−1−i32−1−i321+i321+i32
χ3233333-1-1-13-1-1-1-1000000-1-1-111−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i321−i320000001−i321−i321−i32−1+i32−1+i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i321+i320000001+i321+i321+i32−1−i32−1−i32
χ333333-13-1-1-13-1-1-100000011-11-1−3+3i32−3+3i32−3+3i32−3+3i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i32000000−1+i32−1+i321−i32−1+i321−i32−3−3i32−3−3i32−3−3i32−3−3i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i32000000−1−i32−1−i321+i32−1−i321+i32
χ343333-13-1-1-13-1-1-1000000-1-11-11−3+3i32−3+3i32−3+3i32−3+3i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i320000001−i321−i32−1+i321−i32−1+i32−3−3i32−3−3i32−3−3i32−3−3i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i320000001+i321+i32−1−i321+i32−1−i32
χ353333-1-13-1-1-13-1-100000011-1-11−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i32000000−1+i32−1+i321−i321−i32−1+i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i32000000−1−i32−1−i321+i321+i32−1−i32
χ363333-1-13-1-1-13-1-1000000-1-111-1−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i320000001−i321−i32−1+i32−1+i321−i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i320000001+i321+i32−1−i32−1−i321+i32
χ374-44-4000000000111-1-1-12i−2i000−2+2i32−2i3−2+2i32−2i3000000000−1+i32−1+i32−1+i321−i321−i321−i322ζ7−2ζ7000−2−2i32+2i3−2−2i32+2i3000000000−1−i32−1−i32−1−i321+i321+i321+i322ζ11−2ζ11000
χ384-44-4000000000111-1-1-1−2i2i000−2+2i32−2i3−2+2i32−2i3000000000−1+i32−1+i32−1+i321−i321−i321−i32−2ζ72ζ7000−2−2i32+2i3−2−2i32+2i3000000000−1−i32−1−i32−1−i321+i321+i321+i32−2ζ112ζ11000
χ396666-2-2-22-2-2-22200000000000−3+3i3−3+3i3−3+3i3−3+3i31−i31−i31−i3−1+i31−i31−i31−i3−1+i3−1+i300000000000−3−3i3−3−3i3−3−3i3−3−3i31+i31+i31+i3−1−i31+i31+i31+i3−1−i3−1−i300000000000
χ4066-3-36-2-2-2-3111100000000000−3+3i3−3+3i33−3i323−3i32−3+3i31−i31−i31−i33−3i32−1+i32−1+i32−1+i32−1+i3200000000000−3−3i3−3−3i33+3i323+3i32−3−3i31+i31+i31+i33+3i32−1−i32−1−i32−1−i32−1−i3200000000000
χ4166-3-3-26-2-21-311100000000000−3+3i3−3+3i33−3i323−3i321−i3−3+3i31−i31−i3−1+i323−3i32−1+i32−1+i32−1+i3200000000000−3−3i3−3−3i33+3i323+3i321+i3−3−3i31+i31+i3−1−i323+3i32−1−i32−1−i32−1−i3200000000000
χ4266-3-3-2-26-211-31100000000000−3+3i3−3+3i33−3i323−3i321−i31−i3−3+3i31−i3−1+i32−1+i323−3i32−1+i32−1+i3200000000000−3−3i3−3−3i33+3i323+3i321+i31+i3−3−3i31+i3−1−i32−1−i323+3i32−1−i32−1−i3200000000000
χ4366-3-3-2-2-22111−1−2i3−1+2i300000000000−3+3i3−3+3i33−3i323−3i321−i31−i31−i3−1+i3−1+i32−1+i32−1+i327+i32−5−3i3200000000000−3−3i3−3−3i33+3i323+3i321+i31+i31+i3−1−i3−1−i32−1−i32−1−i32−5+3i327−i3200000000000
χ4466-3-3-2-2-22111−1+2i3−1−2i300000000000−3+3i3−3+3i33−3i323−3i321−i31−i31−i3−1+i3−1+i32−1+i32−1+i32−5−3i327+i3200000000000−3−3i3−3−3i33+3i323+3i321+i31+i31+i3−1−i3−1−i32−1−i32−1−i327−i32−5+3i3200000000000
χ458-88-8000000000-1-1-111100000−4+4i34−4i3−4+4i34−4i30000000001−i321−i321−i32−1+i32−1+i32−1+i3200000−4−4i34+4i3−4−4i34+4i30000000001+i321+i321+i32−1−i32−1−i32−1−i3200000
χ468-8-440000000002-1-1-21100000−4+4i34−4i32−2i3−2+2i3000000000−1+i31−i321−i321−i3−1+i32−1+i3200000−4−4i34+4i32+2i3−2−2i3000000000−1−i31+i321+i321+i3−1−i32−1−i3200000
χ478-8-44000000000-12-11-2100000−4+4i34−4i32−2i3−2+2i30000000001−i32−1+i31−i32−1+i321−i3−1+i3200000−4−4i34+4i32+2i3−2−2i30000000001+i32−1−i31+i32−1−i321+i3−1−i3200000
χ488-8-44000000000-1-1211-200000−4+4i34−4i32−2i3−2+2i30000000001−i321−i32−1+i3−1+i32−1+i321−i300000−4−4i34+4i32+2i3−2−2i30000000001+i321+i32−1−i3−1−i32−1−i321+i300000
χ49111111111111111111111111−1−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+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
χ501111111111111111111-1-1-1-1-1−1−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−i321+i321+i321+i321+i321+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−i32
χ512222222222222-1-1-1-1-1-100000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i3200000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i3200000
χ5222-1-12222-1-1-1-1-12-1-12-1-100000−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i32−1−i31+i321+i32−1−i31+i321+i3200000−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i32−1+i31−i321−i32−1+i31−i321−i3200000
χ5322-1-12222-1-1-1-1-1-12-1-12-100000−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i32−1−i31+i321+i32−1−i31+i3200000−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i32−1+i31−i321−i32−1+i31−i3200000
χ5422-1-12222-1-1-1-1-1-1-12-1-1200000−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i31+i321+i32−1−i300000−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i31−i321−i32−1+i300000
χ5533333-1-1-13-1-1-1-1000000111-1-1−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i321+i32000000−1−i32−1−i32−1−i321+i321+i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i321−i32000000−1+i32−1+i32−1+i321−i321−i32
χ5633333-1-1-13-1-1-1-1000000-1-1-111−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i321+i320000001+i321+i321+i32−1−i32−1−i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i321−i320000001−i321−i321−i32−1+i32−1+i32
χ573333-13-1-1-13-1-1-100000011-11-1−3−3i32−3−3i32−3−3i32−3−3i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i32000000−1−i32−1−i321+i32−1−i321+i32−3+3i32−3+3i32−3+3i32−3+3i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i32000000−1+i32−1+i321−i32−1+i321−i32
χ583333-13-1-1-13-1-1-1000000-1-11-11−3−3i32−3−3i32−3−3i32−3−3i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i321+i320000001+i321+i32−1−i321+i32−1−i32−3+3i32−3+3i32−3+3i32−3+3i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i321−i320000001−i321−i32−1+i321−i32−1+i32
χ593333-1-13-1-1-13-1-100000011-1-11−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i32000000−1−i32−1−i321+i321+i32−1−i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i32000000−1+i32−1+i321−i321−i32−1+i32
χ603333-1-13-1-1-13-1-1000000-1-111-1−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i32−3−3i321+i321+i320000001+i321+i32−1−i32−1−i321+i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i32−3+3i321−i321−i320000001−i321−i32−1+i32−1+i321−i32
χ614-44-4000000000111-1-1-12i−2i000−2−2i32+2i3−2−2i32+2i3000000000−1−i32−1−i32−1−i321+i321+i321+i322ζ11−2ζ11000−2+2i32−2i3−2+2i32−2i3000000000−1+i32−1+i32−1+i321−i321−i321−i322ζ7−2ζ7000
χ624-44-4000000000111-1-1-1−2i2i000−2−2i32+2i3−2−2i32+2i3000000000−1−i32−1−i32−1−i321+i321+i321+i32−2ζ112ζ11000−2+2i32−2i3−2+2i32−2i3000000000−1+i32−1+i32−1+i321−i321−i321−i32−2ζ72ζ7000
χ636666-2-2-22-2-2-22200000000000−3−3i3−3−3i3−3−3i3−3−3i31+i31+i31+i3−1−i31+i31+i31+i3−1−i3−1−i300000000000−3+3i3−3+3i3−3+3i3−3+3i31−i31−i31−i3−1+i31−i31−i31−i3−1+i3−1+i300000000000
χ6466-3-36-2-2-2-3111100000000000−3−3i3−3−3i33+3i323+3i32−3−3i31+i31+i31+i33+3i32−1−i32−1−i32−1−i32−1−i3200000000000−3+3i3−3+3i33−3i323−3i32−3+3i31−i31−i31−i33−3i32−1+i32−1+i32−1+i32−1+i3200000000000
χ6566-3-3-26-2-21-311100000000000−3−3i3−3−3i33+3i323+3i321+i3−3−3i31+i31+i3−1−i323+3i32−1−i32−1−i32−1−i3200000000000−3+3i3−3+3i33−3i323−3i321−i3−3+3i31−i31−i3−1+i323−3i32−1+i32−1+i32−1+i3200000000000
χ6666-3-3-2-26-211-31100000000000−3−3i3−3−3i33+3i323+3i321+i31+i3−3−3i31+i3−1−i32−1−i323+3i32−1−i32−1−i3200000000000−3+3i3−3+3i33−3i323−3i321−i31−i3−3+3i31−i3−1+i32−1+i323−3i32−1+i32−1+i3200000000000
χ6766-3-3-2-2-22111−1−2i3−1+2i300000000000−3−3i3−3−3i33+3i323+3i321+i31+i31+i3−1−i3−1−i32−1−i32−1−i32−5+3i327−i3200000000000−3+3i3−3+3i33−3i323−3i321−i31−i31−i3−1+i3−1+i32−1+i32−1+i327+i32−5−3i3200000000000
χ6866-3-3-2-2-22111−1+2i3−1−2i300000000000−3−3i3−3−3i33+3i323+3i321+i31+i31+i3−1−i3−1−i32−1−i32−1−i327−i32−5+3i3200000000000−3+3i3−3+3i33−3i323−3i321−i31−i31−i3−1+i3−1+i32−1+i32−1+i32−5−3i327+i3200000000000
χ698-88-8000000000-1-1-111100000−4−4i34+4i3−4−4i34+4i30000000001+i321+i321+i32−1−i32−1−i32−1−i3200000−4+4i34−4i3−4+4i34−4i30000000001−i321−i321−i32−1+i32−1+i32−1+i3200000
χ708-8-440000000002-1-1-21100000−4−4i34+4i32+2i3−2−2i3000000000−1−i31+i321+i321+i3−1−i32−1−i3200000−4+4i34−4i32−2i3−2+2i3000000000−1+i31−i321−i321−i3−1+i32−1+i3200000
χ718-8-44000000000-12-11-2100000−4−4i34+4i32+2i3−2−2i30000000001+i32−1−i31+i32−1−i321+i3−1−i3200000−4+4i34−4i32−2i3−2+2i30000000001−i32−1+i31−i32−1+i321−i3−1+i3200000
χ728-8-44000000000-1-1211-200000−4−4i34+4i32+2i3−2−2i30000000001+i321+i32−1−i3−1−i32−1−i321+i300000−4+4i34−4i32−2i3−2+2i30000000001−i321−i32−1+i3−1+i32−1+i321−i300000

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