Finite Group Databasebeta

← Group #72243914

Character table — Group #72243914

Order 2916.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size126666669991212121212181818181818183636363636363636363636363636545454548181818181818181162162162162162162162162
order133339992333333333333363333333333999961818182266666666666666
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1
χ3111111111−1+i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321111111111−1+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−i32−1−i32−1−i321−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111111-1-1−1+i32−1−i321−i321−i321+i321+i32-1-1−1+i32−1−i321−i321−i321+i321+i32
χ5111111111−1−i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321111111111−1−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+i32−1+i32−1+i321−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111111-1-1−1−i32−1+i321+i321+i321−i321−i32-1-1−1−i32−1+i321+i321+i321−i321−i32
χ711111111-11111111111111-111111111111111-1-1-1-11-1-1-11-11-11-1-1-11-11-1
χ811111111-11111111111111-111111111111111-1-1-1-1-11-1-1-11-11-11-1-1-11-11
χ911111111-1−1+i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321111-1-1-1-11-11−i321+i32−1+i321−i32−1−i321+i321-11−i321+i32−1+i321−i32−1−i321+i32
χ1011111111-1−1+i32−1−i3211111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321111-1-1-1-1-111−i321+i321−i32−1+i321+i32−1−i32-111−i321+i321−i32−1+i321+i32−1−i32
χ1111111111-1−1−i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321111-1-1-1-11-11+i321−i32−1−i321+i32−1+i321−i321-11+i321−i32−1−i321+i32−1+i321−i32
χ1211111111-1−1−i32−1+i3211111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321111-1-1-1-1-111+i321−i321+i32−1−i321−i32−1+i32-111+i321−i321+i32−1−i321−i32−1+i32
χ1322222-1-1-12222222222-122-122-1-1-1-12-1-1-1-1-1-1-1-12-1-1-10022000000-1-10000
χ1422222-1-1-12−1+i3−1−i322222−1+i3−1+i31−i32−1−i3−1−i31+i322−1+i31−i321−i321−i321−i32−1−i31+i321+i321+i321+i32-1-1-1-12-1-1-100−1+i3−1−i30000001−i321+i320000
χ1522222-1-1-12−1−i3−1+i322222−1−i3−1−i31+i32−1+i3−1+i31−i322−1−i31+i321+i321+i321+i32−1+i31−i321−i321−i321−i32-1-1-1-12-1-1-100−1−i3−1+i30000001+i321−i320000
χ1622222-1-1-1-2222222222-122-1-22-1-1-1-12-1-1-1-1-1-1-1-1-211100-2-2000000110000
χ1722222-1-1-1-2−1+i3−1−i322222−1+i3−1+i31−i32−1−i3−1−i31+i32-2−1+i31−i321−i321−i321−i32−1−i31+i321+i321+i321+i32-1-1-1-1-2111001−i31+i3000000−1+i32−1−i320000
χ1822222-1-1-1-2−1−i3−1+i322222−1−i3−1−i31+i32−1+i3−1+i31−i32-2−1−i31+i321+i321+i321+i32−1+i31−i321−i321−i321−i32-1-1-1-1-2111001+i31−i3000000−1−i32−1+i320000
χ192222-12220222-1-1-1-12-122-120-12-1-1-1-12-1-1-12-1-1-10000020002020-1000-10-1
χ202222-12220222-1-1-1-12-122-120-12-1-1-1-12-1-1-12-1-1-100000-2000-20-201000101
χ212222-12220−1+i3−1−i32-1-1-1-1−1+i31−i32−1+i3−1−i31+i32−1−i301−i32−1+i31−i321−i321−i321+i32−1−i31+i321+i321+i322-1-1-1000002000−1+i30−1−i30-10001−i3201+i32
χ222222-12220−1+i3−1−i32-1-1-1-1−1+i31−i32−1+i3−1−i31+i32−1−i301−i32−1+i31−i321−i321−i321+i32−1−i31+i321+i321+i322-1-1-100000-20001−i301+i301000−1+i320−1−i32
χ232222-12220−1−i3−1+i32-1-1-1-1−1−i31+i32−1−i3−1+i31−i32−1+i301+i32−1−i31+i321+i321+i321−i32−1+i31−i321−i321−i322-1-1-1000002000−1−i30−1+i30-10001+i3201−i32
χ242222-12220−1−i3−1+i32-1-1-1-1−1−i31+i32−1−i3−1+i31−i32−1+i301+i32−1−i31+i321+i321+i321−i32−1+i31−i321−i321−i322-1-1-100000-20001+i301−i301000−1−i320−1+i32
χ25222-12222022-12-1-1-1-122-1220-1-12-1-1-1-12-1-1-12-1-1000020002020-1000-10-10
χ26222-12222022-12-1-1-1-122-1220-1-12-1-1-1-12-1-1-12-1-10000-2000-20-2010001010
χ27222-122220−1+i3−1−i3-12-1-1-11−i32−1+i3−1+i31+i32−1−i3−1−i301−i321−i32−1+i31−i321−i321+i321+i32−1−i31+i321+i32-12-1-100002000−1+i30−1−i30-10001−i3201+i320
χ28222-122220−1+i3−1−i3-12-1-1-11−i32−1+i3−1+i31+i32−1−i3−1−i301−i321−i32−1+i31−i321−i321+i321+i32−1−i31+i321+i32-12-1-10000-20001−i301+i301000−1+i320−1−i320
χ29222-122220−1−i3−1+i3-12-1-1-11+i32−1−i3−1−i31−i32−1+i3−1+i301+i321+i32−1−i31+i321+i321−i321−i32−1+i31−i321−i32-12-1-100002000−1−i30−1+i30-10001+i3201−i320
χ30222-122220−1−i3−1+i3-12-1-1-11+i32−1−i3−1−i31−i32−1+i3−1+i301+i321+i32−1−i31+i321+i321−i321−i32−1+i31−i321−i32-12-1-10000-20001+i301−i301000−1−i320−1+i320
χ314444-2-2-2-20444-2-2-2-24-2-24-2-20-2-2111-2-2111-211100000000000000000000
χ324444-2-2-2-20−2+2i3−2−2i34-2-2-2-2−2+2i31−i31−i3−2−2i31+i31+i301−i31−i3−1+i32−1+i32−1+i321+i31+i3−1−i32−1−i32−1−i32-211100000000000000000000
χ334444-2-2-2-20−2−2i3−2+2i34-2-2-2-2−2−2i31+i31+i3−2+2i31−i31−i301+i31+i3−1−i32−1−i32−1−i321−i31−i3−1+i32−1+i32−1+i32-211100000000000000000000
χ34444-24-2-2-2044-24-2-2-2-24-2-24-20-21-211-21-2111-21100000000000000000000
χ35444-24-2-2-20−2+2i3−2−2i3-24-2-2-21−i3−2+2i31−i31+i3−2−2i31+i301−i3−1+i321−i3−1+i32−1+i321+i3−1−i321+i3−1−i32−1−i321-21100000000000000000000
χ36444-24-2-2-20−2−2i3−2+2i3-24-2-2-21+i3−2−2i31+i31−i3−2+2i31−i301+i3−1−i321+i3−1−i32−1−i321−i3−1+i321−i3−1+i32−1+i321-21100000000000000000000
χ37444-2-2444044-2-2111-2-24-2-2401-2-2111-2-211-2-21100000000000000000000
χ38444-2-24440−2+2i3−2−2i3-2-21111−i31−i3−2+2i31+i31+i3−2−2i30−1+i321−i31−i3−1+i32−1+i32−1−i321+i31+i3−1−i32−1−i32-2-21100000000000000000000
χ39444-2-24440−2−2i3−2+2i3-2-21111+i31+i3−2−2i31−i31−i3−2+2i30−1−i321+i31+i3−1−i32−1−i32−1+i321−i31−i3−1+i32−1+i32-2-21100000000000000000000
χ40444-2-2-2-2-2044-2-2111-2-2-2-2-2-20111−1+3i32−1−3i32111−1+3i32−1−3i3211−1+3i32−1−3i3200000000000000000000
χ41444-2-2-2-2-2044-2-2111-2-2-2-2-2-20111−1−3i32−1+3i32111−1−3i32−1+3i3211−1−3i32−1+3i3200000000000000000000
χ42444-2-2-2-2-20−2+2i3−2−2i3-2-21111−i31−i31−i31+i31+i31+i30−1+i32−1+i32−1+i325+i32−2−i3−1−i32−1−i32−1−i32−2+i35−i3211−1−3i32−1+3i3200000000000000000000
χ43444-2-2-2-2-20−2+2i3−2−2i3-2-21111−i31−i31−i31+i31+i31+i30−1+i32−1+i32−1+i32−2−i35+i32−1−i32−1−i32−1−i325−i32−2+i311−1+3i32−1−3i3200000000000000000000
χ44444-2-2-2-2-20−2−2i3−2+2i3-2-21111+i31+i31+i31−i31−i31−i30−1−i32−1−i32−1−i325−i32−2+i3−1+i32−1+i32−1+i32−2−i35+i3211−1+3i32−1−3i3200000000000000000000
χ45444-2-2-2-2-20−2−2i3−2+2i3-2-21111+i31+i31+i31−i31−i31−i30−1−i32−1−i32−1−i32−2+i35−i32−1+i32−1+i32−1+i325+i32−2−i311−1−3i32−1+3i3200000000000000000000
χ4666-366000600-3-36-3-3000000600000000000000-30000000000000000000
χ4766-366000-600-3-36-3-3000000-60000000000000030000000000000000000
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
χ5218-90003ζ−3ζ2+6ζ4+3ζ53ζ−3ζ2−3ζ4−6ζ5−6ζ+6ζ2−3ζ4+3ζ560000000000000-3000000000000000ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ50000000000000000
χ5318-90003ζ−3ζ2+6ζ4+3ζ53ζ−3ζ2−3ζ4−6ζ5−6ζ+6ζ2−3ζ4+3ζ5-600000000000003000000000000000−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ50000000000000000
χ5418-90003ζ−3ζ2−3ζ4−6ζ5−6ζ+6ζ2−3ζ4+3ζ53ζ−3ζ2+6ζ4+3ζ560000000000000-3000000000000000ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ50000000000000000
χ5518-90003ζ−3ζ2−3ζ4−6ζ5−6ζ+6ζ2−3ζ4+3ζ53ζ−3ζ2+6ζ4+3ζ5-600000000000003000000000000000−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ50000000000000000
χ5618-9000−6ζ+6ζ2−3ζ4+3ζ53ζ−3ζ2+6ζ4+3ζ53ζ−3ζ2−3ζ4−6ζ560000000000000-3000000000000000−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ50000000000000000
χ5718-9000−6ζ+6ζ2−3ζ4+3ζ53ζ−3ζ2+6ζ4+3ζ53ζ−3ζ2−3ζ4−6ζ5-6000000000000030000000000000002ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ50000000000000000

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