Finite Group Databasebeta

← Group #13180907

Character table — Group #13180907

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222444444444466666688888888889912121212121212121616161616161616161616161818181818242424242424242424243636363636363636484848484848484854547272
order12334663336661212121222222433336666121222666666121233661212121212121212444446666666661266661212121266666666241212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-111111111111-1-11111-1-11111111111111111-1-1-111111-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-11111111111111-1-111-1-11111111111111111-1-111-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111-1-1-1-1111111111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111−1−i32−1+i321−1−i32−1+i321111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+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+i321−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32
χ611111111−1−i32−1+i321−1−i32−1+i321111111-1-11−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11111-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-11−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211+i321+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-11+i321−i32
χ711111111−1−i32−1+i321−1−i32−1+i3211111-1-1111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i3211+i321+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i32
χ811111111−1−i32−1+i321−1−i32−1+i3211111-1-1-1-11−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1111+i321+i321−i321−i321+i321+i321−i321−i321−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i3211−1−i32−1+i32
χ911111111−1+i32−1−i321−1+i32−1−i321111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−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−i321−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32
χ1011111111−1+i32−1−i321−1+i32−1−i321111111-1-11−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-11111-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-11−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211−i321−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-11−i321+i32
χ1111111111−1+i32−1−i321−1+i32−1−i3211111-1-1111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i3211−i321−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i32
χ1211111111−1+i32−1−i321−1+i32−1−i3211111-1-1-1-11−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1111−i321−i321+i321+i321−i321−i321+i321+i321−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1−i32
χ131111-111111111-1-1-1-1-11-11-1111111111-1-111-1-11-11-1111111-1-1-1-1-1-1-1-11-11-1-1-11-11-11-11-1111111-11-11-11-11-11-1-11-1-1
χ141111-111111111-1-1-1-1-11-1-11111111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-11-1-111-11-11-1-11-111-1-1-1-11-1-111-11-1-11-111-111
χ151111-111111111-1-1-1-1-1-111-1111111111-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-111-11-1-11-111-11-11-1-1-1-1-111-1-11-111-11-11-111
χ161111-111111111-1-1-1-1-1-11-11111111111-1-111-1-1-11-11111111-1-1-1-1-1-1-1-1-11-11-1-1-11-11-11-1111111-11-11-11-11-11-11-11-1-1
χ171111-1111−1−i32−1+i321−1−i32−1+i32-1-1-1-1-11-11-11−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i3211-1-11-11-111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321-11-1-1-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i321−1−i32−1−i32−1+i32−1+i321-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32-111+i321−i32
χ181111-1111−1−i32−1+i321−1−i32−1+i32-1-1-1-1-11-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32-1-1-1-11-1-1111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321-1-111-1−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i3211+i321+i321−i321−i321-1-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i321-1−1−i32−1+i32
χ191111-1111−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-111-11−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32-1-1-1-1-111-111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-111-11-11+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i3211+i321+i321−i321−i32-111-11+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i321-1−1−i32−1+i32
χ201111-1111−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-11-111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i3211-1-1-11-1111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-11-11-1-11+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i321−1−i32−1−i32−1+i32−1+i32-11-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32-111+i321−i32
χ211111-1111−1+i32−1−i321−1+i32−1−i32-1-1-1-1-11-11-11−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i3211-1-11-11-111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321-11-1-1-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i321−1+i32−1+i32−1−i32−1−i321-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32-111−i321+i32
χ221111-1111−1+i32−1−i321−1+i32−1−i32-1-1-1-1-11-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32-1-1-1-11-1-1111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321-1-111-1−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i3211−i321−i321+i321+i321-1-11−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i321-1−1+i32−1−i32
χ231111-1111−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-111-11−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32-1-1-1-1-111-111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-111-11-11−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i3211−i321−i321+i321+i32-111-11−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i321-1−1+i32−1−i32
χ241111-1111−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-11-111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i3211-1-1-11-1111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-11-11-1-11−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i321−1+i32−1+i32−1−i32−1−i32-11-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32-111−i321+i32
χ25222-122-1-122-1222-1-1-12002222-12-12-12-122002-100-1-12-1-1-1-1-12-12-1-1-1-1-100220-100002222-1000000-1-10000-1-1-1-10000
χ26222-122-1-122-1222-1-1-1200-2-222-12-12-12-122002-100112-1-1-1-1-12-12-1-1-1-1-100-2-20-10000-2-2-2-2-100000011000011110000
χ27222-122-1-1−1−i3−1+i3-1−1−i3−1+i32-1-1-1200222−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i32−1−i3−1+i3002-100-1-12-11+i321−i321+i321−i32−1−i31+i32−1+i31−i321+i321+i321−i321−i3200220-10000−1−i3−1−i3−1+i3−1+i3-1000000-1-100001+i321+i321−i321−i320000
χ28222-122-1-1−1−i3−1+i3-1−1−i3−1+i32-1-1-1200-2-22−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i32−1−i3−1+i3002-100112-11+i321−i321+i321−i32−1−i31+i32−1+i31−i321+i321+i321−i321−i3200-2-20-100001+i31+i31−i31−i3-1000000110000−1−i32−1−i32−1+i32−1+i320000
χ29222-122-1-1−1+i3−1−i3-1−1+i3−1−i32-1-1-1200222−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i32−1+i3−1−i3002-100-1-12-11−i321+i321−i321+i32−1+i31−i32−1−i31+i321−i321−i321+i321+i3200220-10000−1+i3−1+i3−1−i3−1−i3-1000000-1-100001−i321−i321+i321+i320000
χ30222-122-1-1−1+i3−1−i3-1−1+i3−1−i32-1-1-1200-2-22−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i32−1+i3−1−i3002-100112-11−i321+i321−i321+i32−1+i31−i32−1−i31+i321−i321−i321+i321+i3200-2-20-100001−i31−i31+i31+i3-1000000110000−1+i32−1+i32−1−i32−1−i320000
χ31222-1-22-1-122-122-2111-2002-222-12-12-12-1-2-200-2100-112-1-1-1-1-1-21-211111002-20100002-22-2-1000000-110000-11-110000
χ32222-1-22-1-122-122-2111-200-2222-12-12-12-1-2-200-21001-12-1-1-1-1-1-21-21111100-22010000-22-22-10000001-100001-11-10000
χ33222-1-22-1-1−1−i3−1+i3-1−1−i3−1+i3-2111-2002-22−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i321+i31−i300-2100-112-11+i321−i321+i321−i321+i3−1−i321−i3−1+i32−1−i32−1−i32−1+i32−1+i32002-2010000−1−i31+i3−1+i31−i3-1000000-1100001+i32−1−i321−i32−1+i320000
χ34222-1-22-1-1−1−i3−1+i3-1−1−i3−1+i3-2111-200-222−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i321+i31−i300-21001-12-11+i321−i321+i321−i321+i3−1−i321−i3−1+i32−1−i32−1−i32−1+i32−1+i3200-220100001+i3−1−i31−i3−1+i3-10000001-10000−1−i321+i32−1+i321−i320000
χ35222-1-22-1-1−1+i3−1−i3-1−1+i3−1−i3-2111-2002-22−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i321−i31+i300-2100-112-11−i321+i321−i321+i321−i3−1+i321+i3−1−i32−1+i32−1+i32−1−i32−1−i32002-2010000−1+i31−i3−1−i31+i3-1000000-1100001−i32−1+i321+i32−1−i320000
χ36222-1-22-1-1−1+i3−1−i3-1−1+i3−1−i3-2111-200-222−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i321−i31+i300-21001-12-11−i321+i321−i321+i321−i3−1+i321+i3−1−i32−1+i32−1+i32−1−i32−1−i3200-220100001−i3−1+i31+i3−1−i3-10000001-10000−1+i321−i32−1−i321+i320000
χ3722-122-12-122-122-12-1-1222002-12-12-12-122200-12-1-100-12-1-1-1-1-12-12-1-1-1-122000-122220000-10000-1-100-1-1-1-100000000
χ3822-122-12-122-122-12-1-12-2-2002-12-12-12-122200-121100-12-1-1-1-1-12-12-1-1-1-1-2-2000-1-2-2-2-20000-100001100111100000000
χ3922-122-12-1−1−i3−1+i3-1−1−i3−1+i3-12-1-12220021+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i3−1−i3−1+i300-12-1-100-121+i321−i321+i321−i321+i32−1−i31−i32−1+i31+i321+i321−i321−i3222000-1−1−i3−1−i3−1+i3−1+i30000-10000-1-1001+i321+i321−i321−i3200000000
χ4022-122-12-1−1−i3−1+i3-1−1−i3−1+i3-12-1-12-2-20021+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i3−1−i3−1+i300-121100-121+i321−i321+i321−i321+i32−1−i31−i32−1+i31+i321+i321−i321−i32-2-2000-11+i31+i31−i31−i30000-100001100−1−i32−1−i32−1+i32−1+i3200000000
χ4122-122-12-1−1+i3−1−i3-1−1+i3−1−i3-12-1-12220021−i32−1+i31+i32−1−i31−i32−1+i31+i32−1−i3−1+i3−1−i300-12-1-100-121−i321+i321−i321+i321−i32−1+i31+i32−1−i31−i321−i321+i321+i3222000-1−1+i3−1+i3−1−i3−1−i30000-10000-1-1001−i321−i321+i321+i3200000000
χ4222-122-12-1−1+i3−1−i3-1−1+i3−1−i3-12-1-12-2-20021−i32−1+i31+i32−1−i31−i32−1+i31+i32−1−i3−1+i3−1−i300-121100-121−i321+i321−i321+i321−i32−1+i31+i32−1−i31−i321−i321+i321+i32-2-2000-11−i31−i31+i31+i30000-100001100−1+i32−1+i32−1−i32−1−i3200000000
χ4322-12-2-12-122-1221-211-22-2002-12-12-12-12-2-2001-2-1100-12-1-1-1-11-21-211112-200012-22-20000-10000-1100-11-1100000000
χ4422-12-2-12-122-1221-211-2-22002-12-12-12-12-2-2001-21-100-12-1-1-1-11-21-21111-220001-22-220000-100001-1001-11-100000000
χ4522-12-2-12-1−1−i3−1+i3-1−1−i3−1+i31-211-22-20021+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i31+i31−i3001-2-1100-121+i321−i321+i321−i32−1−i321+i3−1+i321−i3−1−i32−1−i32−1+i32−1+i322-20001−1−i31+i3−1+i31−i30000-10000-11001+i32−1−i321−i32−1+i3200000000
χ4622-12-2-12-1−1−i3−1+i3-1−1−i3−1+i31-211-2-220021+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i31+i31−i3001-21-100-121+i321−i321+i321−i32−1−i321+i3−1+i321−i3−1−i32−1−i32−1+i32−1+i32-2200011+i3−1−i31−i3−1+i30000-100001-100−1−i321+i32−1+i321−i3200000000
χ4722-12-2-12-1−1+i3−1−i3-1−1+i3−1−i31-211-22-20021−i32−1+i31+i32−1−i31−i32−1+i31+i32−1−i31−i31+i3001-2-1100-121−i321+i321−i321+i32−1+i321−i3−1−i321+i3−1+i32−1+i32−1−i32−1−i322-20001−1+i31−i3−1−i31+i30000-10000-11001−i32−1+i321+i32−1−i3200000000
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χ654-4440-4-441+i31−i3-4−1−i3−1+i300000000001+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i3004-4000000001+i31−i3−1−i3−1+i300000000000000000000000−1−i31+i3−1+i31−i30000000000000000
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χ828-8-4804-8-42−2i32+2i34−2+2i3−2−2i30000000000−1+i32−2i3−1−i32+2i31−i3−2+2i31+i3−2−2i3000000000000−1+i3−1−i31−i31+i30000000000000000000000000000000000000000000
χ838-8-4-40442-4-4-244006i−6i0000002222-2-2-2-2000000000000-1-11100003i−3i3i−3i00000000000000000000000000000000000
χ848-8-4-40442-4-4-24400−6i6i0000002222-2-2-2-2000000000000-1-1110000−3i3i−3i3i00000000000000000000000000000000000
χ858-8-4-404422+2i32−2i3-2−2−2i3−2+2i3006i−6i000000−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i30000000000001+i321−i32−1−i32−1+i3200003ζ11−3ζ113ζ7−3ζ700000000000000000000000000000000000
χ868-8-4-404422+2i32−2i3-2−2−2i3−2+2i300−6i6i000000−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i30000000000001+i321−i32−1−i32−1+i320000−3ζ113ζ11−3ζ73ζ700000000000000000000000000000000000
χ878-8-4-404422−2i32+2i3-2−2+2i3−2−2i3006i−6i000000−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i30000000000001−i321+i32−1+i32−1−i3200003ζ7−3ζ73ζ11−3ζ1100000000000000000000000000000000000
χ888-8-4-404422−2i32+2i3-2−2+2i3−2−2i300−6i6i000000−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i30000000000001−i321+i32−1+i32−1−i320000−3ζ73ζ7−3ζ113ζ1100000000000000000000000000000000000
χ891212-6-612-6-6300300-6-633-40000-40000000000002200002200000000000000000-100000000-100000000000000000000
χ901212-6-6-12-6-630030066-3-340000-4000000000000-2-200002200000000000000000100000000-100000000000000000000

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