Finite Group Databasebeta

← Group #72268879

Character table — Group #72268879

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112446688888161616161616161632323232323232323232323248484848112446688888161616161616161632323232323232323232323248484848
order12422242222433666666666666661212121288882242224222246666666666666666121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111−1+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−i321111111111111111−1+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−i321111
χ3111111111111−1−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+i321111111111111111−1−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+i321111
χ41111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1
χ51111111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i3211-1-11111111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i3211-1-1
χ61111111-1-1-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i3211-1-11111111-1-1-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i3211-1-1
χ7111-1-11111-1-1-111-1-1-1-11111-1-111-1-11-11-1-111-1111-1-11111-1-1-111-1-1-1-11111-1-111-1-11-11-1-111-1
χ8111-1-11111-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1−i321+i32-111-1111-1-11111-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1−i321+i32-111-1
χ9111-1-11111-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1+i321−i32-111-1111-1-11111-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1+i321−i32-111-1
χ10111-1-111-1-111-111-1-1-1-111-1-111-1-1111-11-1-11-11111-1-111-1-111-111-1-1-1-111-1-111-1-1111-11-1-11-11
χ11111-1-111-1-111-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i32-11-11111-1-111-1-111-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i32-11-11
χ12111-1-111-1-111-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i32-11-11111-1-111-1-111-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i32-11-11
χ1322-2222-22-22-2-2-1-1-1-1-1-1-1-11-11-11-11-11111000022-2222-22-22-2-2-1-1-1-1-1-1-1-11-11-11-11-111110000
χ1422-2222-22-22-2-21−i321+i321−i321−i321+i321+i321−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1−i32−1−i32000022-2222-22-22-2-21−i321+i321−i321−i321+i321+i321−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1−i32−1−i320000
χ1522-2222-22-22-2-21+i321−i321+i321+i321−i321−i321+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1+i32−1+i32000022-2222-22-22-2-21+i321−i321+i321+i321−i321−i321+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1+i32−1+i320000
χ1622-2222-2-22-22-2-1-1-1-1-1-1-1-1-11-11-11-111111000022-2222-2-22-22-2-1-1-1-1-1-1-1-1-11-11-11-1111110000
χ1722-2222-2-22-22-21−i321+i321−i321−i321+i321+i321−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i32−1+i32−1−i32−1−i32000022-2222-2-22-22-21−i321+i321−i321−i321+i321+i321−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i32−1+i32−1−i32−1−i320000
χ1822-2222-2-22-22-21+i321−i321+i321+i321−i321−i321+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i32−1−i32−1+i32−1+i32000022-2222-2-22-22-21+i321−i321+i321+i321−i321−i321+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i32−1−i32−1+i32−1+i320000
χ1922-2-2-22-22-2-222-1-11111-1-11-1-111-1-111-11-1000022-2-2-22-22-2-222-1-11111-1-11-1-111-1-111-11-10000
χ2022-2-2-22-22-2-2221−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i32−1−i321+i32000022-2-2-22-22-2-2221−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i32−1−i321+i320000
χ2122-2-2-22-22-2-2221+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i32−1+i321−i32000022-2-2-22-22-2-2221+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i32−1+i321−i320000
χ2222-2-2-22-2-222-22-1-11111-1-1-111-1-111-11-11-1000022-2-2-22-2-222-22-1-11111-1-1-111-1-111-11-11-10000
χ2322-2-2-22-2-222-221−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32−1+i321−i32−1−i321+i32000022-2-2-22-2-222-221−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32−1+i321−i32−1−i321+i320000
χ2422-2-2-22-2-222-221+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32−1−i321+i32−1+i321−i32000022-2-2-22-2-222-221+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32−1−i321+i32−1+i321−i320000
χ2533333333333300000000000000000000-1-1-1-133333333333300000000000000000000-1-1-1-1
χ263333333-3-3-3-3300000000000000000000-1-1113333333-3-3-3-3300000000000000000000-1-111
χ27333-3-33333-3-3-3000000000000000000001-1-11333-3-33333-3-3-3000000000000000000001-1-11
χ28333-3-333-3-333-3000000000000000000001-11-1333-3-333-3-333-3000000000000000000001-11-1
χ298-804-40000000222-22-2-2-200000000000000008-804-40000000222-22-2-2-20000000000000000
χ308-804-40000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i300000000000000008-804-40000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i30000000000000000
χ318-804-40000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i300000000000000008-804-40000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i30000000000000000
χ328-80-44000000022-22-22-2-200000000000000008-80-44000000022-22-22-2-20000000000000000
χ338-80-440000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i300000000000000008-80-440000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i30000000000000000
χ348-80-440000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i300000000000000008-80-440000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i30000000000000000
χ3512121200-4-40000000000000000000000000000012121200-4-400000000000000000000000000000
χ361212-1200-44000000000000000000000000000001212-1200-4400000000000000000000000000000
χ37111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ38111111111111−1+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−i321111-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321−i321+i321+i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32-1-1-1-1
χ39111111111111−1−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+i321111-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321+i321−i321−i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32-1-1-1-1
χ401111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ411111111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-1-1-1-1-1-11111-11−i321+i321−i321−i321+i321+i321−i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32-1-111
χ421111111-1-1-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-1-1-1-1-1-11111-11+i321−i321+i321+i321−i321−i321+i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32-1-111
χ43111-1-11111-1-1-111-1-1-1-11111-1-111-1-11-11-1-111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-111-11-111-1-11
χ44111-1-11111-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1−i321+i32-111-1-1-1-111-1-1-1-11111−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i32−1+i321+i32−1−i321-1-11
χ45111-1-11111-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1+i321−i32-111-1-1-1-111-1-1-1-11111+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i32−1−i321−i32−1+i321-1-11
χ46111-1-111-1-111-111-1-1-1-111-1-111-1-1111-11-1-11-11-1-1-111-1-111-1-11-1-11111-1-111-1-111-1-1-11-111-11-1
χ47111-1-111-1-111-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i32-11-11-1-1-111-1-111-1-111−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i32−1+i321+i32−1−i321-11-1
χ48111-1-111-1-111-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i32-11-11-1-1-111-1-111-1-111+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i32−1−i321−i32−1+i321-11-1
χ4922-2222-22-22-2-2-1-1-1-1-1-1-1-11-11-11-11-111110000-2-22-2-2-22-22-22211111111-11-11-11-11-1-1-1-10000
χ5022-2222-22-22-2-21−i321+i321−i321−i321+i321+i321−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1−i32−1−i320000-2-22-2-2-22-22-222−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321−i321−i321+i321+i320000
χ5122-2222-22-22-2-21+i321−i321+i321+i321−i321−i321+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1+i32−1+i320000-2-22-2-2-22-22-222−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321+i321+i321−i321−i320000
χ5222-2222-2-22-22-2-1-1-1-1-1-1-1-1-11-11-11-1111110000-2-22-2-2-222-22-22111111111-11-11-11-1-1-1-1-10000
χ5322-2222-2-22-22-21−i321+i321−i321−i321+i321+i321−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i32−1+i32−1−i32−1−i320000-2-22-2-2-222-22-22−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i321−i321+i321+i320000
χ5422-2222-2-22-22-21+i321−i321+i321+i321−i321−i321+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i32−1−i32−1+i32−1+i320000-2-22-2-2-222-22-22−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i321+i321−i321−i320000
χ5522-2-2-22-22-2-222-1-11111-1-11-1-111-1-111-11-10000-2-2222-22-222-2-211-1-1-1-111-111-1-111-1-11-110000
χ5622-2-2-22-22-2-2221−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i32−1−i321+i320000-2-2222-22-222-2-2−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321−i32−1+i321+i32−1−i320000
χ5722-2-2-22-22-2-2221+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i32−1+i321−i320000-2-2222-22-222-2-2−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321+i32−1−i321−i32−1+i320000
χ5822-2-2-22-2-222-22-1-11111-1-1-111-1-111-11-11-10000-2-2222-222-2-22-211-1-1-1-1111-1-111-1-11-11-110000
χ5922-2-2-22-2-222-221−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32−1+i321−i32−1−i321+i320000-2-2222-222-2-22-2−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i32−1+i321+i32−1−i320000
χ6022-2-2-22-2-222-221+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32−1−i321+i32−1+i321−i320000-2-2222-222-2-22-2−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i32−1−i321−i32−1+i320000
χ6133333333333300000000000000000000-1-1-1-1-3-3-3-3-3-3-3-3-3-3-3-3000000000000000000001111
χ623333333-3-3-3-3300000000000000000000-1-111-3-3-3-3-3-3-33333-30000000000000000000011-1-1
χ63333-3-33333-3-3-3000000000000000000001-1-11-3-3-333-3-3-3-333300000000000000000000-111-1
χ64333-3-333-3-333-3000000000000000000001-11-1-3-3-333-3-333-3-3300000000000000000000-11-11
χ658-804-40000000222-22-2-2-20000000000000000-880-440000000-2-2-22-22220000000000000000
χ668-804-40000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i30000000000000000-880-4400000001−i31+i31−i3−1+i31+i3−1−i3−1+i3−1−i30000000000000000
χ678-804-40000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i30000000000000000-880-4400000001+i31−i31+i3−1−i31−i3−1+i3−1−i3−1+i30000000000000000
χ688-80-44000000022-22-22-2-20000000000000000-8804-40000000-2-22-22-2220000000000000000
χ698-80-440000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i30000000000000000-8804-400000001−i31+i3−1+i31−i3−1−i31+i3−1+i3−1−i30000000000000000
χ708-80-440000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i30000000000000000-8804-400000001+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i30000000000000000
χ7112121200-4-400000000000000000000000000000-12-12-12004400000000000000000000000000000
χ721212-1200-4400000000000000000000000000000-12-1212004-400000000000000000000000000000

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