Finite Group Databasebeta

← Group #72243896

Character table — Group #72243896

Order 2916.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size126666669991212121212181818181818183636363636363636363636363636545454548181818181818181162162162162162162162162
order13333999233333333333699339999999999996181818226666666666661818
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111
χ3111111111−1+i32−1−i3211111−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32
χ4111111111−1+i32−1−i3211111−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111-1-1−1+i32−1−i321−i321−i321+i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i32
χ5111111111−1−i32−1+i3211111−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32
χ6111111111−1−i32−1+i3211111−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111-1-1−1−i32−1+i321+i321+i321−i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i32
χ711111111-111111111111-11111111111111111-1-1-1-11-1-1-11-11-11-11-11-1-1-1
χ811111111-111111111111-11111111111111111-1-1-1-1-11-1-1-11-11-11-11-11-1-1
χ911111111-1−1+i32−1−i3211111−1+i32−1+i32−1−i32−1−i32-1−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11-11−i321+i32−1+i321−i32−1−i321+i321-1−1+i321−i32−1−i321+i321−i321+i32
χ1011111111-1−1+i32−1−i3211111−1+i32−1+i32−1−i32−1−i32-1−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-111−i321+i321−i32−1+i321+i32−1−i32-111−i32−1+i321+i32−1−i321−i321+i32
χ1111111111-1−1−i32−1+i3211111−1−i32−1−i32−1+i32−1+i32-1−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11-11+i321−i32−1−i321+i32−1+i321−i321-1−1−i321+i32−1+i321−i321+i321−i32
χ1211111111-1−1−i32−1+i3211111−1−i32−1−i32−1+i32−1+i32-1−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-111+i321−i321+i32−1−i321−i32−1+i32-111+i32−1−i321−i32−1+i321+i321−i32
χ1322222-1-1-12222222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-12-1-1-100220000000000-1-1
χ1422222-1-1-12−1+i3−1−i322222−1+i3−1+i3−1−i3−1−i321−i321+i32−1+i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i322-1-1-100−1+i3−1−i300000000001−i321+i32
χ1522222-1-1-12−1−i3−1+i322222−1−i3−1−i3−1+i3−1+i321+i321−i32−1−i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i322-1-1-100−1−i3−1+i300000000001+i321−i32
χ1622222-1-1-1-222222222222-2-1-122-1-1-1-1-1-1-1-1-1-1-1-1-211100-2-2000000000011
χ1722222-1-1-1-2−1+i3−1−i322222−1+i3−1+i3−1−i3−1−i3-21−i321+i32−1+i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-2111001−i31+i30000000000−1+i32−1−i32
χ1822222-1-1-1-2−1−i3−1+i322222−1−i3−1−i3−1+i3−1+i3-21+i321−i32−1−i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-2111001+i31−i30000000000−1−i32−1+i32
χ192222-12220222-1-1-1-12-12-1022-1-12-1-1-12-1-1-12-1-1-10000020002020-10-10-100
χ202222-12220222-1-1-1-12-12-1022-1-12-1-1-12-1-1-12-1-1-100000-2000-20-201010100
χ212222-12220−1+i3−1−i32-1-1-1-1−1+i31−i32−1−i31+i320−1+i3−1−i31−i321+i322-1-1-1−1+i31−i321−i321−i32−1−i31+i321+i321+i32000002000−1+i30−1−i30-101−i3201+i3200
χ222222-12220−1+i3−1−i32-1-1-1-1−1+i31−i32−1−i31+i320−1+i3−1−i31−i321+i322-1-1-1−1+i31−i321−i321−i32−1−i31+i321+i321+i3200000-20001−i301+i3010−1+i320−1−i3200
χ232222-12220−1−i3−1+i32-1-1-1-1−1−i31+i32−1+i31−i320−1−i3−1+i31+i321−i322-1-1-1−1−i31+i321+i321+i32−1+i31−i321−i321−i32000002000−1−i30−1+i30-101+i3201−i3200
χ242222-12220−1−i3−1+i32-1-1-1-1−1−i31+i32−1+i31−i320−1−i3−1+i31+i321−i322-1-1-1−1−i31+i321+i321+i32−1+i31−i321−i321−i3200000-20001+i301−i3010−1−i320−1+i3200
χ25222-12222022-12-1-1-1-12-12022-1-1-12-1-1-12-1-1-12-1-1000020002020-10-10-1000
χ26222-12222022-12-1-1-1-12-12022-1-1-12-1-1-12-1-1-12-1-10000-2000-20-2010101000
χ27222-122220−1+i3−1−i3-12-1-1-11−i32−1+i31+i32−1−i30−1+i3−1−i31−i321+i32-12-1-11−i32−1+i31−i321−i321+i32−1−i31+i321+i3200002000−1+i30−1−i30-101−i3201+i32000
χ28222-122220−1+i3−1−i3-12-1-1-11−i32−1+i31+i32−1−i30−1+i3−1−i31−i321+i32-12-1-11−i32−1+i31−i321−i321+i32−1−i31+i321+i320000-20001−i301+i3010−1+i320−1−i32000
χ29222-122220−1−i3−1+i3-12-1-1-11+i32−1−i31−i32−1+i30−1−i3−1+i31+i321−i32-12-1-11+i32−1−i31+i321+i321−i32−1+i31−i321−i3200002000−1−i30−1+i30-101+i3201−i32000
χ30222-122220−1−i3−1+i3-12-1-1-11+i32−1−i31−i32−1+i30−1−i3−1+i31+i321−i32-12-1-11+i32−1−i31+i321+i321−i32−1+i31−i321−i320000-20001+i301−i3010−1−i320−1+i32000
χ314444-2-2-2-20444-2-2-2-24-24-20-2-2-2-2-2111-2111-211100000000000000000000
χ324444-2-2-2-20−2+2i3−2−2i34-2-2-2-2−2+2i31−i3−2−2i31+i301−i31+i31−i31+i3-21111−i3−1+i32−1+i32−1+i321+i3−1−i32−1−i32−1−i3200000000000000000000
χ334444-2-2-2-20−2−2i3−2+2i34-2-2-2-2−2−2i31+i3−2+2i31−i301+i31−i31+i31−i3-21111+i3−1−i32−1−i32−1−i321−i3−1+i32−1+i32−1+i3200000000000000000000
χ34444-24-2-2-2044-24-2-2-2-24-240-2-2-2-21-2111-2111-21100000000000000000000
χ35444-24-2-2-20−2+2i3−2−2i3-24-2-2-21−i3−2+2i31+i3−2−2i301−i31+i31−i31+i31-211−1+i321−i3−1+i32−1+i32−1−i321+i3−1−i32−1−i3200000000000000000000
χ36444-24-2-2-20−2−2i3−2+2i3-24-2-2-21+i3−2−2i31−i3−2+2i301+i31−i31+i31−i31-211−1−i321+i3−1−i32−1−i32−1+i321−i3−1+i32−1+i3200000000000000000000
χ37444-2-2444044-2-2111-2-2-2-204411-2-211-2-211-2-21100000000000000000000
χ38444-2-24440−2+2i3−2−2i3-2-21111−i31−i31+i31+i30−2+2i3−2−2i3−1+i32−1−i32-2-2111−i31−i3−1+i32−1+i321+i31+i3−1−i32−1−i3200000000000000000000
χ39444-2-24440−2−2i3−2+2i3-2-21111+i31+i31−i31−i30−2−2i3−2+2i3−1−i32−1+i32-2-2111+i31+i3−1−i32−1−i321−i31−i3−1+i32−1+i3200000000000000000000
χ40444-2-2-2-2-2044-2-2111-2-2-2-20-2-21111−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i3200000000000000000000
χ41444-2-2-2-2-2044-2-2111-2-2-2-20-2-21111−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i3200000000000000000000
χ42444-2-2-2-2-20−2+2i3−2−2i3-2-21111−i31−i31+i31+i301−i31+i3−1+i32−1−i3211−1+3i32−1−3i32−1+i32−1+i32−2−i35+i32−1−i32−1−i325−i32−2+i300000000000000000000
χ43444-2-2-2-2-20−2+2i3−2−2i3-2-21111−i31−i31+i31+i301−i31+i3−1+i32−1−i3211−1−3i32−1+3i32−1+i32−1+i325+i32−2−i3−1−i32−1−i32−2+i35−i3200000000000000000000
χ44444-2-2-2-2-20−2−2i3−2+2i3-2-21111+i31+i31−i31−i301+i31−i3−1−i32−1+i3211−1+3i32−1−3i32−1−i32−1−i325−i32−2+i3−1+i32−1+i32−2−i35+i3200000000000000000000
χ45444-2-2-2-2-20−2−2i3−2+2i3-2-21111+i31+i31−i31−i301+i31−i3−1−i32−1+i3211−1−3i32−1+3i32−1−i32−1−i32−2+i35−i32−1+i32−1+i325+i32−2−i300000000000000000000
χ4666-366000600-3-36-3-3000060000000000000000-30000000000000000000
χ4766-366000-600-3-36-3-30000-6000000000000000030000000000000000000
χ481212-612-6000000-63-63300000000000000000000000000000000000000000
χ491212-6-6120000003-6-63300000000000000000000000000000000000000000
χ501212-6-6-6000000333−3+9i32−3−9i3200000000000000000000000000000000000000000
χ511212-6-6-6000000333−3−9i32−3+9i3200000000000000000000000000000000000000000
χ5218-90006ζ−6ζ2+3ζ4−3ζ5−3ζ+3ζ2+3ζ4+6ζ5−3ζ+3ζ2−6ζ4−3ζ5600000000000-3000000000000000002ζ−2ζ2+ζ4−ζ5−ζ+ζ2+ζ4+2ζ5−ζ+ζ2−2ζ4−ζ50000000000000000
χ5318-90006ζ−6ζ2+3ζ4−3ζ5−3ζ+3ζ2+3ζ4+6ζ5−3ζ+3ζ2−6ζ4−3ζ5-600000000000300000000000000000−2ζ+2ζ2−ζ4+ζ5ζ−ζ2−ζ4−2ζ5ζ−ζ2+2ζ4+ζ50000000000000000
χ5418-9000−3ζ+3ζ2+3ζ4+6ζ5−3ζ+3ζ2−6ζ4−3ζ56ζ−6ζ2+3ζ4−3ζ5600000000000-300000000000000000−ζ+ζ2+ζ4+2ζ5−ζ+ζ2−2ζ4−ζ52ζ−2ζ2+ζ4−ζ50000000000000000
χ5518-9000−3ζ+3ζ2+3ζ4+6ζ5−3ζ+3ζ2−6ζ4−3ζ56ζ−6ζ2+3ζ4−3ζ5-600000000000300000000000000000ζ−ζ2−ζ4−2ζ5ζ−ζ2+2ζ4+ζ5−2ζ+2ζ2−ζ4+ζ50000000000000000
χ5618-9000−3ζ+3ζ2−6ζ4−3ζ56ζ−6ζ2+3ζ4−3ζ5−3ζ+3ζ2+3ζ4+6ζ5600000000000-300000000000000000−ζ+ζ2−2ζ4−ζ52ζ−2ζ2+ζ4−ζ5−ζ+ζ2+ζ4+2ζ50000000000000000
χ5718-9000−3ζ+3ζ2−6ζ4−3ζ56ζ−6ζ2+3ζ4−3ζ5−3ζ+3ζ2+3ζ4+6ζ5-600000000000300000000000000000ζ−ζ2+2ζ4+ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2−ζ4−2ζ50000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.