Finite Group Databasebeta

← Group #11724360

Character table — Group #11724360

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size112888899181818181836363636112888899181818181836363636112888899181818181836363636
order1223666222444444443663666666121212121212121236636666661212121212121212
χ1111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-1
χ31111111111-1-1-1-11-11-11111111111-1-1-1-11-11-11111111111-1-1-1-11-11-1
χ41111111111-1-1-1-1-11-111111111111-1-1-1-1-11-111111111111-1-1-1-1-11-11
χ511-111-1-111-111-1-111-1-111-111-1-111-111-1-111-1-111-111-1-111-111-1-111-1-1
χ611-111-1-111-111-1-1-1-11111-111-1-111-111-1-1-1-11111-111-1-111-111-1-1-1-111
χ711-111-1-111-1-1-1111-1-1111-111-1-111-1-1-1111-1-1111-111-1-111-1-1-1111-1-11
χ811-111-1-111-1-1-111-111-111-111-1-111-1-1-111-111-111-111-1-111-1-1-111-111-1
χ92222222-2-2-2000000002222222-2-2-2000000002222222-2-2-200000000
χ1022-222-2-2-2-220000000022-222-2-2-2-220000000022-222-2-2-2-2200000000
χ112-202-2002-20002i−2i00002-202-2002-20002i−2i00002-202-2002-20002i−2i0000
χ122-202-2002-2000−2i2i00002-202-2002-2000−2i2i00002-202-2002-2000−2i2i0000
χ132-202-200-2202-20000002-202-200-2202-20000002-202-200-2202-2000000
χ142-202-200-220-220000002-202-200-220-220000002-202-200-220-22000000
χ15888-1-1-1-100000000000888-1-1-1-100000000000888-1-1-1-100000000000
χ1688-8-1-1110000000000088-8-1-1110000000000088-8-1-11100000000000
χ178-80-113-3000000000008-80-113-3000000000008-80-113-300000000000
χ188-80-11-33000000000008-80-11-33000000000008-80-11-3300000000000
χ19111111111111111111−1+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
χ2011111111111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i321+i321+i321+i321+i32
χ211111111111-1-1-1-11-11-1−1+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−i32−1+i321−i32−1−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+i32−1−i321+i32
χ221111111111-1-1-1-1-11-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−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+i32−1−i321+i32−1−i32
χ2311-111-1-111-111-1-111-1-1−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ2411-111-1-111-111-1-1-1-111−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ2511-111-1-111-1-1-1111-1-11−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ2611-111-1-111-1-1-111-111-1−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ272222222-2-2-200000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i300000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i300000000
χ2822-222-2-2-2-2200000000−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i31−i3−1+i300000000−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i31+i3−1−i300000000
χ292-202-2002-20002i−2i0000−1+i31−i30−1+i31−i300−1+i31−i30002ζ7−2ζ70000−1−i31+i30−1−i31+i300−1−i31+i30002ζ11−2ζ110000
χ302-202-2002-2000−2i2i0000−1+i31−i30−1+i31−i300−1+i31−i3000−2ζ72ζ70000−1−i31+i30−1−i31+i300−1−i31+i3000−2ζ112ζ110000
χ312-202-200-2202-2000000−1+i31−i30−1+i31−i3001−i3−1+i30−1+i31−i3000000−1−i31+i30−1−i31+i3001+i3−1−i30−1−i31+i3000000
χ322-202-200-220-22000000−1+i31−i30−1+i31−i3001−i3−1+i301−i3−1+i3000000−1−i31+i30−1−i31+i3001+i3−1−i301+i3−1−i3000000
χ33888-1-1-1-100000000000−4+4i3−4+4i3−4+4i31−i321−i321−i321−i3200000000000−4−4i3−4−4i3−4−4i31+i321+i321+i321+i3200000000000
χ3488-8-1-11100000000000−4+4i3−4+4i34−4i31−i321−i32−1+i32−1+i3200000000000−4−4i3−4−4i34+4i31+i321+i32−1−i32−1−i3200000000000
χ358-80-113-300000000000−4+4i34−4i301−i32−1+i32−3+3i323−3i3200000000000−4−4i34+4i301+i32−1−i32−3−3i323+3i3200000000000
χ368-80-11-3300000000000−4+4i34−4i301−i32−1+i323−3i32−3+3i3200000000000−4−4i34+4i301+i32−1−i323+3i32−3−3i3200000000000
χ37111111111111111111−1−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
χ3811111111111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i32−1+i32−1+i321−i321−i321−i321−i32
χ391111111111-1-1-1-11-11-1−1−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+i32−1−i321+i32−1+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−i32−1+i321−i32
χ401111111111-1-1-1-1-11-11−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+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−i32−1+i321−i32−1+i32
χ4111-111-1-111-111-1-111-1-1−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ4211-111-1-111-111-1-1-1-111−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ4311-111-1-111-1-1-1111-1-11−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32
χ4411-111-1-111-1-1-111-111-1−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32
χ452222222-2-2-200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i300000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i300000000
χ4622-222-2-2-2-2200000000−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i31+i3−1−i300000000−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i31−i3−1+i300000000
χ472-202-2002-20002i−2i0000−1−i31+i30−1−i31+i300−1−i31+i30002ζ11−2ζ110000−1+i31−i30−1+i31−i300−1+i31−i30002ζ7−2ζ70000
χ482-202-2002-2000−2i2i0000−1−i31+i30−1−i31+i300−1−i31+i3000−2ζ112ζ110000−1+i31−i30−1+i31−i300−1+i31−i3000−2ζ72ζ70000
χ492-202-200-2202-2000000−1−i31+i30−1−i31+i3001+i3−1−i30−1−i31+i3000000−1+i31−i30−1+i31−i3001−i3−1+i30−1+i31−i3000000
χ502-202-200-220-22000000−1−i31+i30−1−i31+i3001+i3−1−i301+i3−1−i3000000−1+i31−i30−1+i31−i3001−i3−1+i301−i3−1+i3000000
χ51888-1-1-1-100000000000−4−4i3−4−4i3−4−4i31+i321+i321+i321+i3200000000000−4+4i3−4+4i3−4+4i31−i321−i321−i321−i3200000000000
χ5288-8-1-11100000000000−4−4i3−4−4i34+4i31+i321+i32−1−i32−1−i3200000000000−4+4i3−4+4i34−4i31−i321−i32−1+i32−1+i3200000000000
χ538-80-113-300000000000−4−4i34+4i301+i32−1−i32−3−3i323+3i3200000000000−4+4i34−4i301−i32−1+i32−3+3i323−3i3200000000000
χ548-80-11-3300000000000−4−4i34+4i301+i32−1−i323+3i32−3−3i3200000000000−4+4i34−4i301−i32−1+i323−3i32−3+3i3200000000000

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