Finite Group Databasebeta

← Group #72222818

Character table — Group #72222818

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111133334888888121616161616161616161616242424242424242424243232323232323232323232324848486464646464646464
order122222222222222233444666666444444444466666666666624466121212121212
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111−1+i32−1−i32111−1+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−i32111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ31111111111111111−1−i32−1+i32111−1−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+i32111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ411111111111-1-1-1-11111-1-1111111-1-111-1-1111111-1-1-1-111-1-1-1-1-11-1111-1-11-1-1
χ511111111111-1-1-1-11−1+i32−1−i321-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-111-1-11111−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32-11-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ611111111111-1-1-1-11−1−i32−1+i321-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-111-1-11111−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32-11-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ7111111111-1-111-1-1111-11-1111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1111-11-1-11-1
χ8111111111-1-111-1-11−1+i32−1−i32-11-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-11111111−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32-1-11−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ9111111111-1-111-1-11−1−i32−1+i32-11-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-11111111+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32-1-11−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ10111111111-1-1-1-111111-1-1111111111-1-1-1-11111-1-1-1-111-1-1-1-1111-1-111-1-11-1-11
χ11111111111-1-1-1-1111−1+i32−1−i32-1-11−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-1-1-111111−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321-1-1−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ12111111111-1-1-1-1111−1−i32−1+i32-1-11−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-1-1-111111+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321-1-1−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ1311111111-1111111-111-1-1-111111111-1-1-1-111-1-1111111111111-111-1-1-1-1-1-1-1-1
χ1411111111-1111111-1−1+i32−1−i32-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-1-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1111−i321+i321−i321−i321−i321+i321+i321+i32
χ1511111111-1111111-1−1−i32−1+i32-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-1-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1111+i321−i321+i321+i321+i321−i321−i321−i32
χ1611111111-111-1-1-1-1-111-111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-111
χ1711111111-111-1-1-1-1-1−1+i32−1−i32-111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-11111-1-1−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i3211-11−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ1811111111-111-1-1-1-1-1−1−i32−1+i32-111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-11111-1-1−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i3211-11+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ1911111111-1-1-111-1-1-1111-11111111-1-111-1-111-1-1-1-111-1-1-1-111-1-11-11-1-11-111-11
χ2011111111-1-1-111-1-1-1−1+i32−1−i321-11−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-111-1-111-1-11−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i321-111−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ2111111111-1-1-111-1-1-1−1−i32−1+i321-11−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-111-1-111-1-11+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i321-111+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ2211111111-1-1-1-1-111-11111-111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-111-111-1
χ2311111111-1-1-1-1-111-1−1+i32−1−i3211-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111-1-11−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32-1-1-11−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ2411111111-1-1-1-1-111-1−1−i32−1+i3211-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111-1-11+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32-1-1-11+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ252-2-222-2-22000002-20220002-2-22-2-22-200002-20000002-200002-200000000000
χ262-2-222-2-22000002-20−1+i3−1−i3000−1+i31−i31−i3−1−i31+i31+i32-200002-2000000−1+i31−i30000−1−i31+i300000000000
χ272-2-222-2-22000002-20−1−i3−1+i3000−1−i31+i31+i3−1+i31−i31−i32-200002-2000000−1−i31+i30000−1+i31−i300000000000
χ282-2-222-2-2200000-220220002-2-22-2-2-2200002-2000000-220000-2200000000000
χ292-2-222-2-2200000-220−1+i3−1−i3000−1+i31−i31−i3−1−i31+i31+i3-2200002-20000001−i3−1+i300001+i3−1−i300000000000
χ302-2-222-2-2200000-220−1−i3−1+i3000−1−i31+i31+i3−1+i31−i31−i3-2200002-20000001+i3−1−i300001−i3−1+i300000000000
χ31333333333333333300333000000-1-1-1-1-1-1-1-1-1-1000000000000-1-1-100000000
χ3233333333333-3-3-3-33003-3-300000011-1-111-1-1-1-10000000000001-1100000000
χ33333333333-3-333-3-3300-33-30000001111-1-1-1-1-1-100000000000011-100000000
χ34333333333-3-3-3-333300-3-33000000-1-11111-1-1-1-1000000000000-11100000000
χ3533333333-3333333-300-3-3-3000000-1-11111-1-1110000000000001-1-100000000
χ3633333333-333-3-3-3-3-300-3330000001111-1-1-1-111000000000000-1-1100000000
χ3733333333-3-3-333-3-3-3003-3300000011-1-111-1-111000000000000-11-100000000
χ3833333333-3-3-3-3-333-30033-3000000-1-1-1-1-1-1-1-11100000000000011100000000
χ3944-4-444-4-40004-4000-2-200022-222-20000000000002-200002-20000000000000
χ4044-4-444-4-40004-40001−i31+i3000−1+i3−1+i31−i3−1−i3−1−i31+i3000000000000−1+i31−i30000−1−i31+i30000000000000
χ4144-4-444-4-40004-40001+i31−i3000−1−i3−1−i31+i3−1+i3−1+i31−i3000000000000−1−i31+i30000−1+i31−i30000000000000
χ4244-4-444-4-4000-44000-2-200022-222-2000000000000-220000-220000000000000
χ4344-4-444-4-4000-440001−i31+i3000−1+i3−1+i31−i3−1−i3−1−i31+i30000000000001−i3−1+i300001+i3−1−i30000000000000
χ4444-4-444-4-4000-440001+i31−i3000−1−i3−1−i31+i3−1+i3−1+i31−i30000000000001+i3−1−i300001−i3−1+i30000000000000
χ454-44-44-44-404-400000-2-20002-222-2200000000002-200002-2000000000000000
χ464-44-44-44-404-4000001−i31+i3000−1+i31−i3−1+i3−1−i31+i3−1−i30000000000−1+i31−i30000−1−i31+i3000000000000000
χ474-44-44-44-404-4000001+i31−i3000−1−i31+i3−1−i3−1+i31−i3−1+i30000000000−1−i31+i30000−1+i31−i3000000000000000
χ484-44-44-44-40-4400000-2-20002-222-220000000000-220000-22000000000000000
χ494-44-44-44-40-44000001−i31+i3000−1+i31−i3−1+i3−1−i31+i3−1−i300000000001−i3−1+i300001+i3−1−i3000000000000000
χ504-44-44-44-40-44000001+i31−i3000−1−i31+i3−1−i3−1+i31−i3−1+i300000000001+i3−1−i300001−i3−1+i3000000000000000
χ516-6-666-6-66000006-6000000000000-220000-220000000000000000000000000
χ526-6-666-6-6600000-660000000000002-20000-220000000000000000000000000
χ5312121212-4-4-4-412000000-400000000000000000000000000000000000000000000
χ5412121212-4-4-4-4-12000000400000000000000000000000000000000000000000000
χ551212-12-12-4-444000000000000000000000004-4000000000000000000000000000
χ561212-12-12-4-44400000000000000000000000-44000000000000000000000000000
χ5712-1212-12-44-440000000000000000000004-400000000000000000000000000000
χ5812-1212-12-44-44000000000000000000000-4400000000000000000000000000000
χ5912-12-1212-444-40000000000000000000000000004-400000000000000000000000
χ6012-12-1212-444-4000000000000000000000000000-4400000000000000000000000

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