Finite Group Databasebeta

← Group #72253807

Character table — Group #72253807

Order 2916.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size1223346666666669121212121212121818181818181818181818181818272736363636363636363636365454545454545454545454818181818181162162162162162162
order1333333333339992333399933336666999999663399999999966181818181818181818226666666666
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111-111111111111-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-11-111-1-1111-1-1-1
χ4111111111111111-111111111111-1-1-1-1111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1111
χ5111−1+i32−1−i3211111−1+i32−1−i321−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ6111−1+i32−1−i3211111−1+i32−1−i321−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i32
χ7111−1+i32−1−i3211111−1+i32−1−i321−1+i32−1−i32-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i321-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32
χ8111−1+i32−1−i3211111−1+i32−1−i321−1+i32−1−i32-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-111−i321+i32−1+i32−1−i32-11−i321+i321−1+i32−1−i32
χ9111−1−i32−1+i3211111−1−i32−1+i321−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ10111−1−i32−1+i3211111−1−i32−1+i321−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i32
χ11111−1−i32−1+i3211111−1−i32−1+i321−1−i32−1+i32-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i321-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32
χ12111−1−i32−1+i3211111−1−i32−1+i321−1−i32−1+i32-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-111+i321−i32−1−i32−1+i32-11+i321−i321−1−i32−1+i32
χ13222222222222-1-1-122222-1-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1000000000000
χ14222222222222-1-1-1-22222-1-1-12222-2-2-2-2-1-1-1-1-1-1-2-222-1-1-1-1-1-1-1-1-1-2-2111111111000000000000
χ15222222222-1222220-1-1-1-122222-1-1000022222200-1-1-1-1-1-1-1-1-1-1-100000000000020022000-1-1-1
χ16222222222-1222220-1-1-1-122222-1-1000022222200-1-1-1-1-1-1-1-1-1-1-1000000000000-200-2-2000111
χ17222222-1-1-122222222-1-1-1222-1-1222-1-1-1-1-1-1-1-1-122-1-12-1-12-1-12-1-1-1-1222-1-1-1-1-1-1000000000000
χ18222222-1-1-1222222-22-1-1-1222-1-122-2111-1-1-1-1-1-1-2-2-1-12-1-12-1-12-1-111-2-2-2111111000000000000
χ19222222-1-1-1222-1-1-122-1-1-1-1-1-1-1-1222-1-1-12-12-12-122-1-1-12-1-12-1-12-1-1-1-1-1-12-12-12-1000000000000
χ20222222-1-1-1222-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-12-12-1222-1-1-1-12-1-12-1-12-1-1-1-1-1-12-12-12000000000000
χ21222222-1-1-1222-1-1-1-22-1-1-1-1-1-1-1-122-21112-12-12-1-2-2-1-1-12-1-12-1-12-111111-21-21-21000000000000
χ22222222-1-1-1222-1-1-1-22-1-1-1-1-1-1-1-122-2111-12-12-12-2-2-1-1-1-12-1-12-1-12111111-21-21-2000000000000
χ23222−1+i3−1−i322222−1+i3−1−i3-11−i321+i3222222-11−i321+i32−1+i3−1−i3−1+i3−1−i32222-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32−1+i3−1−i3-11−i321+i32-1-11−i321−i321+i321+i32000000000000
χ24222−1+i3−1−i322222−1+i3−1−i3-11−i321+i32-22222-11−i321+i32−1+i3−1−i3−1+i3−1−i3-2-2-2-2-1-11−i321−i321+i321+i321−i31+i3−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i321−i31+i31−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000
χ25222−1+i3−1−i32222-1−1+i3−1−i32−1+i3−1−i30-1-1-1-12−1+i3−1−i3−1+i3−1−i31−i321+i32000022−1+i3−1+i3−1−i3−1−i3001−i321+i32-1-1-11−i321−i321−i321+i321+i321+i32000000000000200−1+i3−1−i3000-11−i321+i32
χ26222−1+i3−1−i32222-1−1+i3−1−i32−1+i3−1−i30-1-1-1-12−1+i3−1−i3−1+i3−1−i31−i321+i32000022−1+i3−1+i3−1−i3−1−i3001−i321+i32-1-1-11−i321−i321−i321+i321+i321+i32000000000000-2001−i31+i30001−1+i32−1−i32
χ27222−1+i3−1−i32-1-1-12−1+i3−1−i32−1+i3−1−i322-1-1-12−1+i3−1−i31−i321+i32−1+i3−1−i32-1-1-1-1-11−i321−i321+i321+i32−1+i3−1−i31−i321+i322-1-1−1+i31−i321−i32−1−i31+i321+i321−i321+i322−1+i3−1−i3-1-11−i321−i321+i321+i32000000000000
χ28222−1+i3−1−i32-1-1-12−1+i3−1−i32−1+i3−1−i3-22-1-1-12−1+i3−1−i31−i321+i32−1+i3−1−i3-2111-1-11−i321−i321+i321+i321−i31+i31−i321+i322-1-1−1+i31−i321−i32−1−i31+i321+i32−1+i32−1−i32-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000000000
χ29222−1+i3−1−i32-1-1-12−1+i3−1−i3-11−i321+i3222-1-1-1-11−i321+i321−i321+i32−1+i3−1−i32-1-1-12-1−1+i31−i32−1−i31+i32−1+i3−1−i31−i321+i32-12-11−i32−1+i31−i321+i32−1−i31+i321−i321+i32-11−i321+i322-1−1+i31−i32−1−i31+i32000000000000
χ30222−1+i3−1−i32-1-1-12−1+i3−1−i3-11−i321+i3222-1-1-1-11−i321+i321−i321+i32−1+i3−1−i32-1-1-1-121−i32−1+i31+i32−1−i3−1+i3−1−i31−i321+i32-1-121−i321−i32−1+i31+i321+i32−1−i31−i321+i32-11−i321+i32-121−i32−1+i31+i32−1−i3000000000000
χ31222−1+i3−1−i32-1-1-12−1+i3−1−i3-11−i321+i32-22-1-1-1-11−i321+i321−i321+i32−1+i3−1−i3-21112-1−1+i31−i32−1−i31+i321−i31+i31−i321+i32-12-11−i32−1+i31−i321+i32−1−i31+i32−1+i32−1−i321−1+i32−1−i32-211−i3−1+i321+i3−1−i32000000000000
χ32222−1+i3−1−i32-1-1-12−1+i3−1−i3-11−i321+i32-22-1-1-1-11−i321+i321−i321+i32−1+i3−1−i3-2111-121−i32−1+i31+i32−1−i31−i31+i31−i321+i32-1-121−i321−i32−1+i31+i321+i32−1−i3−1+i32−1−i321−1+i32−1−i321-2−1+i321−i3−1−i321+i3000000000000
χ33222−1−i3−1+i322222−1−i3−1+i3-11+i321−i3222222-11+i321−i32−1−i3−1+i3−1−i3−1+i32222-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32−1−i3−1+i3-11+i321−i32-1-11+i321+i321−i321−i32000000000000
χ34222−1−i3−1+i322222−1−i3−1+i3-11+i321−i32-22222-11+i321−i32−1−i3−1+i3−1−i3−1+i3-2-2-2-2-1-11+i321+i321−i321−i321+i31−i3−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i321+i31−i31−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ35222−1−i3−1+i32222-1−1−i3−1+i32−1−i3−1+i30-1-1-1-12−1−i3−1+i3−1−i3−1+i31+i321−i32000022−1−i3−1−i3−1+i3−1+i3001+i321−i32-1-1-11+i321+i321+i321−i321−i321−i32000000000000200−1−i3−1+i3000-11+i321−i32
χ36222−1−i3−1+i32222-1−1−i3−1+i32−1−i3−1+i30-1-1-1-12−1−i3−1+i3−1−i3−1+i31+i321−i32000022−1−i3−1−i3−1+i3−1+i3001+i321−i32-1-1-11+i321+i321+i321−i321−i321−i32000000000000-2001+i31−i30001−1−i32−1+i32
χ37222−1−i3−1+i32-1-1-12−1−i3−1+i32−1−i3−1+i322-1-1-12−1−i3−1+i31+i321−i32−1−i3−1+i32-1-1-1-1-11+i321+i321−i321−i32−1−i3−1+i31+i321−i322-1-1−1−i31+i321+i32−1+i31−i321−i321+i321−i322−1−i3−1+i3-1-11+i321+i321−i321−i32000000000000
χ38222−1−i3−1+i32-1-1-12−1−i3−1+i32−1−i3−1+i3-22-1-1-12−1−i3−1+i31+i321−i32−1−i3−1+i3-2111-1-11+i321+i321−i321−i321+i31−i31+i321−i322-1-1−1−i31+i321+i32−1+i31−i321−i32−1−i32−1+i32-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000000000
χ39222−1−i3−1+i32-1-1-12−1−i3−1+i3-11+i321−i3222-1-1-1-11+i321−i321+i321−i32−1−i3−1+i32-1-1-12-1−1−i31+i32−1+i31−i32−1−i3−1+i31+i321−i32-12-11+i32−1−i31+i321−i32−1+i31−i321+i321−i32-11+i321−i322-1−1−i31+i32−1+i31−i32000000000000
χ40222−1−i3−1+i32-1-1-12−1−i3−1+i3-11+i321−i3222-1-1-1-11+i321−i321+i321−i32−1−i3−1+i32-1-1-1-121+i32−1−i31−i32−1+i3−1−i3−1+i31+i321−i32-1-121+i321+i32−1−i31−i321−i32−1+i31+i321−i32-11+i321−i32-121+i32−1−i31−i32−1+i3000000000000
χ41222−1−i3−1+i32-1-1-12−1−i3−1+i3-11+i321−i32-22-1-1-1-11+i321−i321+i321−i32−1−i3−1+i3-21112-1−1−i31+i32−1+i31−i321+i31−i31+i321−i32-12-11+i32−1−i31+i321−i32−1+i31−i32−1−i32−1+i321−1−i32−1+i32-211+i3−1−i321−i3−1+i32000000000000
χ42222−1−i3−1+i32-1-1-12−1−i3−1+i3-11+i321−i32-22-1-1-1-11+i321−i321+i321−i32−1−i3−1+i3-2111-121+i32−1−i31−i32−1+i31+i31−i31+i321−i32-1-121+i321+i32−1−i31−i321−i32−1+i3−1−i32−1+i321−1−i32−1+i321-2−1−i321+i3−1+i321−i3000000000000
χ43444444444-244-2-2-20-2-2-2-2-2-2-244-2-20000-2-2-2-2-2-200-2-211111111100000000000000000000000
χ44444444-2-2-2-2444440-2111444-2-2-2-20000-2-2-2-2-2-20011-211-211-21100000000000000000000000
χ45444444-2-2-2-244-2-2-20-2111-2-2-2-2-2-2-200004-24-24-200111-211-211-2100000000000000000000000
χ46444444-2-2-2-244-2-2-20-2111-2-2-2-2-2-2-20000-24-24-24001111-211-211-200000000000000000000000
χ47444−2+2i3−2−2i34444-2−2+2i3−2−2i3-21−i31+i30-2-2-2-2-21−i31+i3−2+2i3−2−2i31−i31+i30000-2-21−i31−i31+i31+i3001−i31+i3111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000000000000000000000
χ48444−2+2i3−2−2i34-2-2-2-2−2+2i3−2−2i34−2+2i3−2−2i30-21114−2+2i3−2−2i31−i31+i31−i31+i30000-2-21−i31−i31+i31+i300−1+i32−1−i32-2111−i3−1+i32−1+i321+i3−1−i32−1−i3200000000000000000000000
χ49444−2+2i3−2−2i34-2-2-2-2−2+2i3−2−2i3-21−i31+i30-2111-21−i31+i31−i31+i31−i31+i300004-2−2+2i31−i3−2−2i31+i300−1+i32−1−i321-21−1+i321−i3−1+i32−1−i321+i3−1−i3200000000000000000000000
χ50444−2+2i3−2−2i34-2-2-2-2−2+2i3−2−2i3-21−i31+i30-2111-21−i31+i31−i31+i31−i31+i30000-241−i3−2+2i31+i3−2−2i300−1+i32−1−i3211-2−1+i32−1+i321−i3−1−i32−1−i321+i300000000000000000000000
χ51444−2−2i3−2+2i34444-2−2−2i3−2+2i3-21+i31−i30-2-2-2-2-21+i31−i3−2−2i3−2+2i31+i31−i30000-2-21+i31+i31−i31−i3001+i31−i3111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000000000000000000000
χ52444−2−2i3−2+2i34-2-2-2-2−2−2i3−2+2i34−2−2i3−2+2i30-21114−2−2i3−2+2i31+i31−i31+i31−i30000-2-21+i31+i31−i31−i300−1−i32−1+i32-2111+i3−1−i32−1−i321−i3−1+i32−1+i3200000000000000000000000
χ53444−2−2i3−2+2i34-2-2-2-2−2−2i3−2+2i3-21+i31−i30-2111-21+i31−i31+i31−i31+i31−i300004-2−2−2i31+i3−2+2i31−i300−1−i32−1+i321-21−1−i321+i3−1−i32−1+i321−i3−1+i3200000000000000000000000
χ54444−2−2i3−2+2i34-2-2-2-2−2−2i3−2+2i3-21+i31−i30-2111-21+i31−i31+i31−i31+i31−i30000-241+i3−2−2i31−i3−2+2i300−1−i32−1+i3211-2−1−i32−1−i321+i3−1+i32−1+i321−i300000000000000000000000
χ5566-300-36-3-36000006-36-3-30000000-36-3-3000000000000000000000000000000000000000000
χ5666-300-36-3-3600000-6-36-3-300000003-633000000000000000000000000000000000000000000
χ5766-300-3-36-36000006-3-36-30000000-3-36-3000000000000000000000000000000000000000000
χ5866-300-3-36-3600000-6-3-36-3000000033-63000000000000000000000000000000000000000000
χ5966-300-3-3-366000006-3-3-360000000-3-3-36000000000000000000000000000000000000000000
χ6066-300-3-3-36600000-6-3-3-360000000333-6000000000000000000000000000000000000000000
χ616-3666-30000-3-366600000-3-3-300000000000000000000000000000000000000202200-1-1-1000
χ626-3666-30000-3-366600000-3-3-300000000000000000000000000000000000000-20-2-200111000
χ636-36−3+3i3−3−3i3-300003−3i323+3i326−3+3i3−3−3i300000-33−3i323+3i320000000000000000000000000000000000000020−1+i3−1−i300-11−i321+i32000
χ646-36−3+3i3−3−3i3-300003−3i323+3i326−3+3i3−3−3i300000-33−3i323+3i3200000000000000000000000000000000000000-201−i31+i3001−1+i32−1−i32000
χ656-36−3−3i3−3+3i3-300003+3i323−3i326−3−3i3−3+3i300000-33+3i323−3i320000000000000000000000000000000000000020−1−i3−1+i300-11+i321−i32000
χ666-36−3−3i3−3+3i3-300003+3i323−3i326−3−3i3−3+3i300000-33+3i323−3i3200000000000000000000000000000000000000-201+i31−i3001−1−i32−1+i32000
χ671212-600-612-6-6-60000003-63300000000000000000000000000000000000000000000000000000
χ681212-600-6-612-6-600000033-6300000000000000000000000000000000000000000000000000000
χ691212-600-6-6-612-6000000333-600000000000000000000000000000000000000000000000000000
χ7012-6121212-60000-6-6-6-6-60000033300000000000000000000000000000000000000000000000000
χ7112-612−6+6i3−6−6i3-600003−3i33+3i3-63−3i33+3i3000003−3+3i32−3−3i3200000000000000000000000000000000000000000000000000
χ7212-612−6−6i3−6+6i3-600003+3i33−3i3-63+3i33−3i3000003−3−3i32−3+3i3200000000000000000000000000000000000000000000000000
χ7336-18-180090000000000000000000000000000000000000000000000000000000000000000000

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