Finite Group Databasebeta

← Group #72913

Character table — Group #72913

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size112444444444888881616161124444444448888816161611244444444488888161616
order12222444444422444448366661212121212121266121212121224366661212121212121266121212121224
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-111-1-1-11111111111111-1-111-1-1-11111111111111-1-111-1-1-1
χ31111111-1-1-1-11-1111-11-1-11111111-1-1-1-11-1111-11-1-11111111-1-1-1-11-1111-11-1-1
χ41111111-1-1-1-11-1-1-11-1-1111111111-1-1-1-11-1-1-11-1-1111111111-1-1-1-11-1-1-11-1-111
χ511111-1-111-1-11-111-11-11-111111-1-111-1-11-111-11-11-111111-1-111-1-11-111-11-11-1
χ611111-1-111-1-11-1-1-1-111-1111111-1-111-1-11-1-1-1-111-1111111-1-111-1-11-1-1-1-111-11
χ711111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111111-1-1-1-11
χ811111-1-1-1-11111-1-1-1-111-111111-1-1-1-11111-1-1-1-111-111111-1-1-1-11111-1-1-1-111-1
χ92222-2002200-20000-20002222-2002200-20000-20002222-2002200-20000-2000
χ102222-200-2-200-2000020002222-200-2-200-2000020002222-200-2-200-200002000
χ11222-22220000-2000-20000222-22220000-2000-20000222-22220000-2000-20000
χ12222-22-2-20000-200020000222-22-2-20000-200020000222-22-2-20000-200020000
χ13222-2-20000222-20000000222-2-20000222-20000000222-2-20000222-20000000
χ14222-2-20000-2-2220000000222-2-20000-2-2220000000222-2-20000-2-2220000000
χ1544-400000000002-20000044-400000000002-20000044-400000000002-200000
χ1644-40000000000-220000044-40000000000-220000044-40000000000-2200000
χ174-40002i−2i2i−2i2-20000000004-40002i−2i2i−2i2-20000000004-40002i−2i2i−2i2-2000000000
χ184-40002i−2i−2i2i-220000000004-40002i−2i−2i2i-220000000004-40002i−2i−2i2i-22000000000
χ194-4000−2i2i2i−2i-220000000004-4000−2i2i2i−2i-220000000004-4000−2i2i2i−2i-22000000000
χ204-4000−2i2i−2i2i2-20000000004-4000−2i2i−2i2i2-20000000004-4000−2i2i−2i2i2-2000000000
χ2111111111111111111111−1+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
χ221111111111111-1-111-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+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−i321+i321+i32−1−i32−1−i321+i321+i321+i32
χ231111111-1-1-1-11-1111-11-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32
χ241111111-1-1-1-11-1-1-11-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32
χ2511111-1-111-1-11-111-11-11-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32
χ2611111-1-111-1-11-1-1-1-111-11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ2711111-1-1-1-1111111-1-1-1-11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32
χ2811111-1-1-1-11111-1-1-1-111-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32
χ292222-2002200-20000-2000−1+i3−1+i3−1+i3−1+i31−i300−1+i3−1+i3001−i300001−i3000−1−i3−1−i3−1−i3−1−i31+i300−1−i3−1−i3001+i300001+i3000
χ302222-200-2-200-200002000−1+i3−1+i3−1+i3−1+i31−i3001−i31−i3001−i30000−1+i3000−1−i3−1−i3−1−i3−1−i31+i3001+i31+i3001+i30000−1−i3000
χ31222-22220000-2000-20000−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i300001−i30001−i30000−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i300001+i30001+i30000
χ32222-22-2-20000-200020000−1+i3−1+i3−1+i31−i3−1+i31−i31−i300001−i3000−1+i30000−1−i3−1−i3−1−i31+i3−1−i31+i31+i300001+i3000−1−i30000
χ33222-2-20000222-20000000−1+i3−1+i3−1+i31−i31−i30000−1+i3−1+i3−1+i31−i30000000−1−i3−1−i3−1−i31+i31+i30000−1−i3−1−i3−1−i31+i30000000
χ34222-2-20000-2-2220000000−1+i3−1+i3−1+i31−i31−i300001−i31−i3−1+i3−1+i30000000−1−i3−1−i3−1−i31+i31+i300001+i31+i3−1−i3−1−i30000000
χ3544-400000000002-200000−2+2i3−2+2i32−2i30000000000−1+i31−i300000−2−2i3−2−2i32+2i30000000000−1−i31+i300000
χ3644-40000000000-2200000−2+2i3−2+2i32−2i300000000001−i3−1+i300000−2−2i3−2−2i32+2i300000000001+i3−1−i300000
χ374-40002i−2i2i−2i2-2000000000−2+2i32−2i30002ζ7−2ζ72ζ7−2ζ7−1+i31−i3000000000−2−2i32+2i30002ζ11−2ζ112ζ11−2ζ11−1−i31+i3000000000
χ384-40002i−2i−2i2i-22000000000−2+2i32−2i30002ζ7−2ζ7−2ζ72ζ71−i3−1+i3000000000−2−2i32+2i30002ζ11−2ζ11−2ζ112ζ111+i3−1−i3000000000
χ394-4000−2i2i2i−2i-22000000000−2+2i32−2i3000−2ζ72ζ72ζ7−2ζ71−i3−1+i3000000000−2−2i32+2i3000−2ζ112ζ112ζ11−2ζ111+i3−1−i3000000000
χ404-4000−2i2i−2i2i2-2000000000−2+2i32−2i3000−2ζ72ζ7−2ζ72ζ7−1+i31−i3000000000−2−2i32+2i3000−2ζ112ζ11−2ζ112ζ11−1−i31+i3000000000
χ4111111111111111111111−1−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
χ421111111111111-1-111-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−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+i321−i321−i32−1+i32−1+i321−i321−i321−i32
χ431111111-1-1-1-11-1111-11-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32
χ441111111-1-1-1-11-1-1-11-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32
χ4511111-1-111-1-11-111-11-11-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32
χ4611111-1-111-1-11-1-1-1-111-11−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ4711111-1-1-1-1111111-1-1-1-11−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32
χ4811111-1-1-1-11111-1-1-1-111-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32
χ492222-2002200-20000-2000−1−i3−1−i3−1−i3−1−i31+i300−1−i3−1−i3001+i300001+i3000−1+i3−1+i3−1+i3−1+i31−i300−1+i3−1+i3001−i300001−i3000
χ502222-200-2-200-200002000−1−i3−1−i3−1−i3−1−i31+i3001+i31+i3001+i30000−1−i3000−1+i3−1+i3−1+i3−1+i31−i3001−i31−i3001−i30000−1+i3000
χ51222-22220000-2000-20000−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i300001+i30001+i30000−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i300001−i30001−i30000
χ52222-22-2-20000-200020000−1−i3−1−i3−1−i31+i3−1−i31+i31+i300001+i3000−1−i30000−1+i3−1+i3−1+i31−i3−1+i31−i31−i300001−i3000−1+i30000
χ53222-2-20000222-20000000−1−i3−1−i3−1−i31+i31+i30000−1−i3−1−i3−1−i31+i30000000−1+i3−1+i3−1+i31−i31−i30000−1+i3−1+i3−1+i31−i30000000
χ54222-2-20000-2-2220000000−1−i3−1−i3−1−i31+i31+i300001+i31+i3−1−i3−1−i30000000−1+i3−1+i3−1+i31−i31−i300001−i31−i3−1+i3−1+i30000000
χ5544-400000000002-200000−2−2i3−2−2i32+2i30000000000−1−i31+i300000−2+2i3−2+2i32−2i30000000000−1+i31−i300000
χ5644-40000000000-2200000−2−2i3−2−2i32+2i300000000001+i3−1−i300000−2+2i3−2+2i32−2i300000000001−i3−1+i300000
χ574-40002i−2i2i−2i2-2000000000−2−2i32+2i30002ζ11−2ζ112ζ11−2ζ11−1−i31+i3000000000−2+2i32−2i30002ζ7−2ζ72ζ7−2ζ7−1+i31−i3000000000
χ584-40002i−2i−2i2i-22000000000−2−2i32+2i30002ζ11−2ζ11−2ζ112ζ111+i3−1−i3000000000−2+2i32−2i30002ζ7−2ζ7−2ζ72ζ71−i3−1+i3000000000
χ594-4000−2i2i2i−2i-22000000000−2−2i32+2i3000−2ζ112ζ112ζ11−2ζ111+i3−1−i3000000000−2+2i32−2i3000−2ζ72ζ72ζ7−2ζ71−i3−1+i3000000000
χ604-4000−2i2i−2i2i2-2000000000−2−2i32+2i3000−2ζ112ζ11−2ζ112ζ11−1−i31+i3000000000−2+2i32−2i3000−2ζ72ζ7−2ζ72ζ7−1+i31−i3000000000

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