Finite Group Databasebeta

← Group #13046828

Character table — Group #13046828

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1122233334444666666661212121212121212121212181818181818363636363636363636545454545454108108108
order123463366412121299912121818181212363636363636363636369918181212123636363636368824242424266
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ3111111111-11-1-111111111-1-1111-1-1-1-1-1-11111111-1-111-1-1-1-1111111-1-1-1
χ4111111111-11-1-111111111-1-1111-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1111
χ522222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000
χ62222222222222-1-1-122-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1000000000
χ72222222222222-1-1-122-1-1-122-1-1-1-1-1-1-1-1-1-1-12-12-1-1-1-12-122-1-1000000000
χ82222222222222-1-1-122-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12-12-1-1-1-12-1-122000000000
χ9222222222-22-2-222222222-2-2222-2-2-2-2-2-2-1-1-1-1-1-1-111-1-11111000000000
χ10222222222-22-2-2-1-1-122-1-1-1-2-2-1-1-111111122-1-1-1-12-2-2-1-11111000000000
χ11222222222-22-2-2-1-1-122-1-1-1-2-2-1-1-1111111-1-12-12-1-1112-1-2-211000000000
χ12222222222-22-2-2-1-1-122-1-1-1-2-2-1-1-1111111-1-1-12-12-111-1211-2-2000000000
χ13222-2222220-200222-2-222200-2-2-2000000222222-200-2-20000000000000
χ14222-2222220-200222-2-222200-2-2-2000000-1-1-1-1-1-11−i3i311−i3i3−i3i3000000000
χ15222-2222220-200222-2-222200-2-2-2000000-1-1-1-1-1-11i3−i311i3−i3i3−i3000000000
χ16222-2222220-200-1-1-1-2-2-1-1-100111−i3−i3−i3i3i3i322-1-1-1-1-20011−i3i3i3−i3000000000
χ17222-2222220-200-1-1-1-2-2-1-1-100111−i3−i3−i3i3i3i3-1-12-12-11i3−i3-2100−i3i3000000000
χ18222-2222220-200-1-1-1-2-2-1-1-100111−i3−i3−i3i3i3i3-1-1-12-121−i3i31-2i3−i300000000000
χ19222-2222220-200-1-1-1-2-2-1-1-100111i3i3i3−i3−i3−i322-1-1-1-1-20011i3−i3−i3i3000000000
χ20222-2222220-200-1-1-1-2-2-1-1-100111i3i3i3−i3−i3−i3-1-12-12-11−i3i3-2100i3−i3000000000
χ21222-2222220-200-1-1-1-2-2-1-1-100111i3i3i3−i3−i3−i3-1-1-12-121i3−i31-2−i3i300000000000
χ222-220-222-2-2000022200-2-2-2000000000002-222-2-2000000000−i2i2−i2−i2i2i2000
χ232-220-222-2-2000022200-2-2-2000000000002-222-2-2000000000i2−i2i2i2−i2−i2000
χ2433333−3−3i32−3+3i32−3−3i32−3+3i323333000−3−3i32−3+3i32000−3−3i32−3+3i3200000000000000000000000011−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ2533333−3−3i32−3+3i32−3−3i32−3+3i323333000−3−3i32−3+3i32000−3−3i32−3+3i32000000000000000000000000-1-11+i321−i321+i321−i32-11+i321−i32
χ2633333−3−3i32−3+3i32−3−3i32−3+3i32-33-3-3000−3−3i32−3+3i320003+3i323−3i3200000000000000000000000011−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ2733333−3−3i32−3+3i32−3−3i32−3+3i32-33-3-3000−3−3i32−3+3i320003+3i323−3i32000000000000000000000000-1-11+i321−i321+i321−i321−1−i32−1+i32
χ2833333−3+3i32−3−3i32−3+3i32−3−3i323333000−3+3i32−3−3i32000−3+3i32−3−3i3200000000000000000000000011−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ2933333−3+3i32−3−3i32−3+3i32−3−3i323333000−3+3i32−3−3i32000−3+3i32−3−3i32000000000000000000000000-1-11−i321+i321−i321+i32-11−i321+i32
χ3033333−3+3i32−3−3i32−3+3i32−3−3i32-33-3-3000−3+3i32−3−3i320003−3i323+3i3200000000000000000000000011−1+i32−1−i32−1+i32−1−i32-11−i321+i32
χ3133333−3+3i32−3−3i32−3+3i32−3−3i32-33-3-3000−3+3i32−3−3i320003−3i323+3i32000000000000000000000000-1-11−i321+i321−i321+i321−1+i32−1−i32
χ324-440-444-4-4000044400-4-4-400000000000-22-2-222000000000000000000
χ334-440-444-4-40000-2-2-200222000000000004-4-2-222000000000000000000
χ344-440-444-4-40000-2-2-20022200000000000-224-2-42000000000000000000
χ354-440-444-4-40000-2-2-20022200000000000-22-242-4000000000000000000
χ36666-66−3−3i3−3+3i3−3−3i3−3+3i30-6000003+3i33−3i300000000000000000000000000000000000000
χ37666-66−3+3i3−3−3i3−3+3i3−3−3i30-6000003−3i33+3i300000000000000000000000000000000000000
χ3866-36-300006-3-3-3ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68000000000000000000000000
χ3966-36-300006-3-3-3ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68000000000000000000000000
χ4066-36-300006-3-3-3−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ6800−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ6800−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68000000000000000000000000
χ4166-36-30000-6-333ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68000000000000000000000000
χ4266-36-30000-6-333ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68000000000000000000000000
χ4366-36-30000-6-333−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ6800−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ6800−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ68000000000000000000000000
χ4466-3-6-3000003−3i33i3ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68ζ4−ζ44−ζ52−2ζ68ζ4+2ζ44+2ζ52+ζ68−2ζ4−ζ44−ζ52+ζ68−ζ4+ζ44+ζ52+2ζ68−ζ4−2ζ44−2ζ52−ζ682ζ4+ζ44+ζ52−ζ68000000000000000000000000
χ4566-3-6-3000003−3i33i3ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68ζ4+2ζ44+2ζ52+ζ68−2ζ4−ζ44−ζ52+ζ68ζ4−ζ44−ζ52−2ζ68−ζ4−2ζ44−2ζ52−ζ682ζ4+ζ44+ζ52−ζ68−ζ4+ζ44+ζ52+2ζ68000000000000000000000000
χ4666-3-6-3000003−3i33i3−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ6800−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68002ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ68−2ζ4−ζ44−ζ52+ζ68ζ4−ζ44−ζ52−2ζ68ζ4+2ζ44+2ζ52+ζ682ζ4+ζ44+ζ52−ζ68−ζ4+ζ44+ζ52+2ζ68−ζ4−2ζ44−2ζ52−ζ68000000000000000000000000
χ4766-3-6-30000033i3−3i3ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4+ζ44+ζ52+2ζ68−ζ4−2ζ44−2ζ52−ζ682ζ4+ζ44+ζ52−ζ68ζ4−ζ44−ζ52−2ζ68ζ4+2ζ44+2ζ52+ζ68−2ζ4−ζ44−ζ52+ζ68000000000000000000000000
χ4866-3-6-30000033i3−3i3ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4−2ζ44−2ζ52−ζ682ζ4+ζ44+ζ52−ζ68−ζ4+ζ44+ζ52+2ζ68ζ4+2ζ44+2ζ52+ζ68−2ζ4−ζ44−ζ52+ζ68ζ4−ζ44−ζ52−2ζ68000000000000000000000000
χ4966-3-6-30000033i3−3i3−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ6800−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68002ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4+ζ44+ζ52−ζ68−ζ4+ζ44+ζ52+2ζ68−ζ4−2ζ44−2ζ52−ζ68−2ζ4−ζ44−ζ52+ζ68ζ4−ζ44−ζ52−2ζ68ζ4+2ζ44+2ζ52+ζ68000000000000000000000000
χ506-660-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000000000000000−i2i2ζ21+ζ39ζ15+ζ69−ζ21−ζ39−ζ15−ζ69000
χ516-660-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000000000000000i2−i2−ζ21−ζ39−ζ15−ζ69ζ21+ζ39ζ15+ζ69000
χ526-660-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000000000000000−i2i2ζ15+ζ69ζ21+ζ39−ζ15−ζ69−ζ21−ζ39000
χ536-660-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000000000000000i2−i2−ζ15−ζ69−ζ21−ζ39ζ15+ζ69ζ21+ζ39000
χ5412-12-606000000002ζ4+2ζ44−2ζ52+4ζ682ζ4−4ζ44+4ζ52−2ζ68−4ζ4+2ζ44−2ζ52−2ζ6800−2ζ4−2ζ44+2ζ52−4ζ68−2ζ4+4ζ44−4ζ52+2ζ684ζ4−2ζ44+2ζ52+2ζ6800000000000000000000000000000000000
χ5512-12-606000000002ζ4−4ζ44+4ζ52−2ζ68−4ζ4+2ζ44−2ζ52−2ζ682ζ4+2ζ44−2ζ52+4ζ6800−2ζ4+4ζ44−4ζ52+2ζ684ζ4−2ζ44+2ζ52+2ζ68−2ζ4−2ζ44+2ζ52−4ζ6800000000000000000000000000000000000
χ5612-12-60600000000−4ζ4+2ζ44−2ζ52−2ζ682ζ4+2ζ44−2ζ52+4ζ682ζ4−4ζ44+4ζ52−2ζ68004ζ4−2ζ44+2ζ52+2ζ68−2ζ4−2ζ44+2ζ52−4ζ68−2ζ4+4ζ44−4ζ52+2ζ6800000000000000000000000000000000000

Here ζ is a primitive root of unity of order 72 (ζ72 = 1); i = ζ18.