Finite Group Databasebeta

← Group #11724281

Character table — Group #11724281

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112444444812121212121212121818242436361124444448121212121212121218182424363611244444481212121212121212181824243636
order12433661212122444661212241212883612336612121261212126612126121212242436123366121212612121266121261212122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111-1-1111111-1-1-1-1111111111111-1-1111111-1-1-1-1111111111111-1-1111111-1-1-1-1
χ31111111111-1-111-1-1-1-11111-1-11111111111-1-111-1-1-1-11111-1-11111111111-1-111-1-1-1-11111-1-1
χ41111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111-1-111
χ511-11111-1-1-11-11-111-1-1-111-11-111-11111-1-1-11-11-111-1-1-111-11-111-11111-1-1-11-11-111-1-1-111-11-1
χ611-11111-1-1-11-1-1111-1-1-11-11-1111-11111-1-1-11-1-1111-1-1-11-11-1111-11111-1-1-11-1-1111-1-1-11-11-11
χ711-11111-1-1-1-111-1-1-111-111-1-1111-11111-1-1-1-111-1-1-111-111-1-1111-11111-1-1-1-111-1-1-111-111-1-11
χ811-11111-1-1-1-11-11-1-111-11-111-111-11111-1-1-1-11-11-1-111-11-111-111-11111-1-1-1-11-11-1-111-11-111-1
χ9222222222200000000-2-20000222222222200000000-2-20000222222222200000000-2-20000
χ1022-22222-2-2-2000000002-2000022-22222-2-2-2000000002-2000022-22222-2-2-2000000002-20000
χ114441-2-21-2-210022000000-1-1004441-2-21-2-210022000000-1-1004441-2-21-2-210022000000-1-100
χ124441-2-21-2-2100-2-200000011004441-2-21-2-2100-2-200000011004441-2-21-2-2100-2-20000001100
χ13444-211-211-22200-1-1-1-1000000444-211-211-22200-1-1-1-1000000444-211-211-22200-1-1-1-1000000
χ14444-211-211-2-2-2001111000000444-211-211-2-2-2001111000000444-211-211-2-2-2001111000000
χ1544-41-2-2122-1002-2000000-110044-41-2-2122-1002-2000000-110044-41-2-2122-1002-2000000-1100
χ1644-41-2-2122-100-220000001-10044-41-2-2122-100-220000001-10044-41-2-2122-100-220000001-100
χ1744-4-211-2-1-122-200-1-11100000044-4-211-2-1-122-200-1-11100000044-4-211-2-1-122-200-1-111000000
χ1844-4-211-2-1-12-220011-1-100000044-4-211-2-1-12-220011-1-100000044-4-211-2-1-12-220011-1-1000000
χ194-4044-4-4000000000000000004-4044-4-4000000000000000004-4044-4-400000000000000000
χ204-40-21-123i−3i00000−i3i33−30000004-40-21-123i−3i00000−i3i33−30000004-40-21-123i−3i00000−i3i33−3000000
χ214-40-21-123i−3i00000i3−i3−330000004-40-21-123i−3i00000i3−i3−330000004-40-21-123i−3i00000i3−i3−33000000
χ224-40-21-12−3i3i00000−i3i3−330000004-40-21-12−3i3i00000−i3i3−330000004-40-21-12−3i3i00000−i3i3−33000000
χ234-40-21-12−3i3i00000i3−i33−30000004-40-21-12−3i3i00000i3−i33−30000004-40-21-12−3i3i00000i3−i33−3000000
χ248-802-44-2000000000000000008-802-44-2000000000000000008-802-44-200000000000000000
χ25111111111111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ26111111111111-1-1111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ271111111111-1-111-1-1-1-11111-1-1−1+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−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−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+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ281111111111-1-1-1-1-1-1-1-111-1-111−1+i32−1+i32−1+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+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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ2911-11111-1-1-11-11-111-1-1-111-11-1−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32
χ3011-11111-1-1-11-1-1111-1-1-11-11-11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32
χ3111-11111-1-1-1-111-1-1-111-111-1-11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32
χ3211-11111-1-1-1-11-11-1-111-11-111-1−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32
χ33222222222200000000-2-20000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3000000001−i31−i30000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3000000001+i31+i30000
χ3422-22222-2-2-2000000002-20000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i300000000−1+i31−i30000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i300000000−1−i31+i30000
χ354441-2-21-2-210022000000-1-100−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i321−i31−i3−1+i3200−1+i3−1+i30000001−i321−i3200−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i321+i31+i3−1−i3200−1−i3−1−i30000001+i321+i3200
χ364441-2-21-2-2100-2-20000001100−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i321−i31−i3−1+i32001−i31−i3000000−1+i32−1+i3200−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i321+i31+i3−1−i32001+i31+i3000000−1−i32−1−i3200
χ37444-211-211-22200-1-1-1-1000000−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i3−1+i32−1+i321−i3−1+i3−1+i3001−i321−i321−i321−i32000000−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i3−1−i32−1−i321+i3−1−i3−1−i3001+i321+i321+i321+i32000000
χ38444-211-211-2-2-2001111000000−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i3−1+i32−1+i321−i31−i31−i300−1+i32−1+i32−1+i32−1+i32000000−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i3−1−i32−1−i321+i31+i31+i300−1−i32−1−i32−1−i32−1−i32000000
χ3944-41-2-2122-1002-2000000-1100−2+2i3−2+2i32−2i3−1+i321−i31−i3−1+i32−1+i3−1+i31−i3200−1+i31−i30000001−i32−1+i3200−2−2i3−2−2i32+2i3−1−i321+i31+i3−1−i32−1−i3−1−i31+i3200−1−i31+i30000001+i32−1−i3200
χ4044-41-2-2122-100-220000001-100−2+2i3−2+2i32−2i3−1+i321−i31−i3−1+i32−1+i3−1+i31−i32001−i3−1+i3000000−1+i321−i3200−2−2i3−2−2i32+2i3−1−i321+i31+i3−1−i32−1−i3−1−i31+i32001+i3−1−i3000000−1−i321+i3200
χ4144-4-211-2-1-122-200-1-111000000−2+2i3−2+2i32−2i31−i3−1+i32−1+i321−i31−i321−i32−1+i3−1+i31−i3001−i321−i32−1+i32−1+i32000000−2−2i3−2−2i32+2i31+i3−1−i32−1−i321+i31+i321+i32−1−i3−1−i31+i3001+i321+i32−1−i32−1−i32000000
χ4244-4-211-2-1-12-220011-1-1000000−2+2i3−2+2i32−2i31−i3−1+i32−1+i321−i31−i321−i32−1+i31−i3−1+i300−1+i32−1+i321−i321−i32000000−2−2i3−2−2i32+2i31+i3−1−i32−1−i321+i31+i321+i32−1−i31+i3−1−i300−1−i32−1−i321+i321+i32000000
χ434-4044-4-400000000000000000−2+2i32−2i30−2+2i3−2+2i32−2i32−2i300000000000000000−2−2i32+2i30−2−2i3−2−2i32+2i32+2i300000000000000000
χ444-40-21-123i−3i00000−i3i33−3000000−2+2i32−2i301−i3−1+i321−i32−1+i33ζ7−3ζ7000003+i32−3−i32−ζ7−2ζ11ζ7+2ζ11000000−2−2i32+2i301+i3−1−i321+i32−1−i33ζ11−3ζ1100000−3+i323−i322ζ7+ζ11−2ζ7−ζ11000000
χ454-40-21-123i−3i00000i3−i3−33000000−2+2i32−2i301−i3−1+i321−i32−1+i33ζ7−3ζ700000−3−i323+i32ζ7+2ζ11−ζ7−2ζ11000000−2−2i32+2i301+i3−1−i321+i32−1−i33ζ11−3ζ11000003−i32−3+i32−2ζ7−ζ112ζ7+ζ11000000
χ464-40-21-12−3i3i00000−i3i3−33000000−2+2i32−2i301−i3−1+i321−i32−1+i3−3ζ73ζ7000003+i32−3−i32ζ7+2ζ11−ζ7−2ζ11000000−2−2i32+2i301+i3−1−i321+i32−1−i3−3ζ113ζ1100000−3+i323−i32−2ζ7−ζ112ζ7+ζ11000000
χ474-40-21-12−3i3i00000i3−i33−3000000−2+2i32−2i301−i3−1+i321−i32−1+i3−3ζ73ζ700000−3−i323+i32−ζ7−2ζ11ζ7+2ζ11000000−2−2i32+2i301+i3−1−i321+i32−1−i3−3ζ113ζ11000003−i32−3+i322ζ7+ζ11−2ζ7−ζ11000000
χ488-802-44-200000000000000000−4+4i34−4i30−1+i32−2i3−2+2i31−i300000000000000000−4−4i34+4i30−1−i32+2i3−2−2i31+i300000000000000000
χ49111111111111111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ50111111111111-1-1111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ511111111111-1-111-1-1-1-11111-1-1−1−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+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+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−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ521111111111-1-1-1-1-1-1-1-111-1-111−1−i32−1−i32−1−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−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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ5311-11111-1-1-11-11-111-1-1-111-11-1−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32
χ5411-11111-1-1-11-1-1111-1-1-11-11-11−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32
χ5511-11111-1-1-1-111-1-1-111-111-1-11−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32
χ5611-11111-1-1-1-11-11-1-111-11-111-1−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32
χ57222222222200000000-2-20000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3000000001+i31+i30000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3000000001−i31−i30000
χ5822-22222-2-2-2000000002-20000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i300000000−1−i31+i30000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i300000000−1+i31−i30000
χ594441-2-21-2-210022000000-1-100−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i321+i31+i3−1−i3200−1−i3−1−i30000001+i321+i3200−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i321−i31−i3−1+i3200−1+i3−1+i30000001−i321−i3200
χ604441-2-21-2-2100-2-20000001100−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i321+i31+i3−1−i32001+i31+i3000000−1−i32−1−i3200−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i321−i31−i3−1+i32001−i31−i3000000−1+i32−1+i3200
χ61444-211-211-22200-1-1-1-1000000−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i3−1−i32−1−i321+i3−1−i3−1−i3001+i321+i321+i321+i32000000−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i3−1+i32−1+i321−i3−1+i3−1+i3001−i321−i321−i321−i32000000
χ62444-211-211-2-2-2001111000000−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i3−1−i32−1−i321+i31+i31+i300−1−i32−1−i32−1−i32−1−i32000000−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i3−1+i32−1+i321−i31−i31−i300−1+i32−1+i32−1+i32−1+i32000000
χ6344-41-2-2122-1002-2000000-1100−2−2i3−2−2i32+2i3−1−i321+i31+i3−1−i32−1−i3−1−i31+i3200−1−i31+i30000001+i32−1−i3200−2+2i3−2+2i32−2i3−1+i321−i31−i3−1+i32−1+i3−1+i31−i3200−1+i31−i30000001−i32−1+i3200
χ6444-41-2-2122-100-220000001-100−2−2i3−2−2i32+2i3−1−i321+i31+i3−1−i32−1−i3−1−i31+i32001+i3−1−i3000000−1−i321+i3200−2+2i3−2+2i32−2i3−1+i321−i31−i3−1+i32−1+i3−1+i31−i32001−i3−1+i3000000−1+i321−i3200
χ6544-4-211-2-1-122-200-1-111000000−2−2i3−2−2i32+2i31+i3−1−i32−1−i321+i31+i321+i32−1−i3−1−i31+i3001+i321+i32−1−i32−1−i32000000−2+2i3−2+2i32−2i31−i3−1+i32−1+i321−i31−i321−i32−1+i3−1+i31−i3001−i321−i32−1+i32−1+i32000000
χ6644-4-211-2-1-12-220011-1-1000000−2−2i3−2−2i32+2i31+i3−1−i32−1−i321+i31+i321+i32−1−i31+i3−1−i300−1−i32−1−i321+i321+i32000000−2+2i3−2+2i32−2i31−i3−1+i32−1+i321−i31−i321−i32−1+i31−i3−1+i300−1+i32−1+i321−i321−i32000000
χ674-4044-4-400000000000000000−2−2i32+2i30−2−2i3−2−2i32+2i32+2i300000000000000000−2+2i32−2i30−2+2i3−2+2i32−2i32−2i300000000000000000
χ684-40-21-123i−3i00000−i3i33−3000000−2−2i32+2i301+i3−1−i321+i32−1−i33ζ11−3ζ1100000−3+i323−i322ζ7+ζ11−2ζ7−ζ11000000−2+2i32−2i301−i3−1+i321−i32−1+i33ζ7−3ζ7000003+i32−3−i32−ζ7−2ζ11ζ7+2ζ11000000
χ694-40-21-123i−3i00000i3−i3−33000000−2−2i32+2i301+i3−1−i321+i32−1−i33ζ11−3ζ11000003−i32−3+i32−2ζ7−ζ112ζ7+ζ11000000−2+2i32−2i301−i3−1+i321−i32−1+i33ζ7−3ζ700000−3−i323+i32ζ7+2ζ11−ζ7−2ζ11000000
χ704-40-21-12−3i3i00000−i3i3−33000000−2−2i32+2i301+i3−1−i321+i32−1−i3−3ζ113ζ1100000−3+i323−i32−2ζ7−ζ112ζ7+ζ11000000−2+2i32−2i301−i3−1+i321−i32−1+i3−3ζ73ζ7000003+i32−3−i32ζ7+2ζ11−ζ7−2ζ11000000
χ714-40-21-12−3i3i00000i3−i33−3000000−2−2i32+2i301+i3−1−i321+i32−1−i3−3ζ113ζ11000003−i32−3+i322ζ7+ζ11−2ζ7−ζ11000000−2+2i32−2i301−i3−1+i321−i32−1+i3−3ζ73ζ700000−3−i323+i32−ζ7−2ζ11ζ7+2ζ11000000
χ728-802-44-200000000000000000−4−4i34+4i30−1−i32+2i3−2−2i31+i300000000000000000−4+4i34−4i30−1+i32−2i3−2+2i31−i300000000000000000

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