Finite Group Databasebeta

← Group #13048385

Character table — Group #13048385

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size112222222233336666666121212121212121212121212242424242424242424242424242424242424545454545454108108108
order12369991818183366499121218181212123636363636363636363336669999991818181818188824242424266
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ31111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32
χ41111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-11+i321−i32
χ51111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32
χ61111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-11−i321+i32
χ7222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000
χ82222222222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000
χ92222222222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000
χ102222-1-1-1-1-1-122222-1-122-1-1222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000
χ112222-1-1-1-1-1-122222-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-12-12-12-12-12-1000000000
χ122222-1-1-1-1-1-122222-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-12-12-12-12-12000000000
χ132222-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i321+i321−i32−1−i3−1+i31+i321−i322−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i322−1−i3−1+i32−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000
χ142222-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i321+i321−i32−1−i3−1+i31+i321−i322−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32-11+i321−i32-11+i321−i322-1−1−i31+i32−1+i31−i322-1−1−i31+i32−1+i31−i32000000000
χ152222-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i321+i321−i32−1−i3−1+i31+i321−i322−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32-11+i321−i32-11+i321−i32-121+i32−1−i31−i32−1+i3-121+i32−1−i31−i32−1+i3000000000
χ162222-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i321−i321+i32−1+i3−1−i31−i321+i322−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i322−1+i3−1−i32−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000
χ172222-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i321−i321+i32−1+i3−1−i31−i321+i322−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32-11−i321+i32-11−i321+i322-1−1+i31−i32−1−i31+i322-1−1+i31−i32−1−i31+i32000000000
χ182222-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i321−i321+i32−1+i3−1−i31−i321+i322−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32-11−i321+i32-11−i321+i32-121−i32−1+i31+i32−1−i3-121−i32−1+i31+i32−1−i3000000000
χ192-22-2222-2-2-222-2-202200-2-2000000000000-1-1-1111-1-1-1-1-1-1111111−i2i2−i2i2−i2i2000
χ202-22-2222-2-2-222-2-202200-2-2000000000000-1-1-1111-1-1-1-1-1-1111111i2−i2i2−i2i2−i2000
χ212-22-2222-2-2-2−1−i3−1+i31+i31−i30−1−i3−1+i3001+i31−i3000000000000-11+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32−i2i2ζ21+ζ39−ζ21−ζ39ζ15+ζ69−ζ15−ζ69000
χ222-22-2222-2-2-2−1−i3−1+i31+i31−i30−1−i3−1+i3001+i31−i3000000000000-11+i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32i2−i2−ζ21−ζ39ζ21+ζ39−ζ15−ζ69ζ15+ζ69000
χ232-22-2222-2-2-2−1+i3−1−i31−i31+i30−1+i3−1−i3001−i31+i3000000000000-11−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32−i2i2ζ15+ζ69−ζ15−ζ69ζ21+ζ39−ζ21−ζ39000
χ242-22-2222-2-2-2−1+i3−1−i31−i31+i30−1+i3−1−i3001−i31+i3000000000000-11−i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32i2−i2−ζ15−ζ69ζ15+ζ69−ζ21−ζ39ζ21+ζ39000
χ2533333333333333-133-1-133-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000111111-1-1-1
χ2633333333333333-133-1-133-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-1-1-1-1-1-1111
χ273333333333−3−3i32−3+3i32−3−3i32−3+3i32-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i32-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i3200000000000000000011−1−i32−1−i32−1+i32−1+i32-11+i321−i32
χ283333333333−3−3i32−3+3i32−3−3i32−3+3i32-1−3−3i32−3+3i321+i321−i32−3−3i32−3+3i32-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i32000000000000000000-1-11+i321+i321−i321−i321−1−i32−1+i32
χ293333333333−3+3i32−3−3i32−3+3i32−3−3i32-1−3+3i32−3−3i321−i321+i32−3+3i32−3−3i32-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i3200000000000000000011−1+i32−1+i32−1−i32−1−i32-11−i321+i32
χ303333333333−3+3i32−3−3i32−3+3i32−3−3i32-1−3+3i32−3−3i321−i321+i32−3+3i32−3−3i32-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i32000000000000000000-1-11−i321−i321+i321+i321−1+i32−1−i32
χ314-44-4444-4-4-444-4-404400-4-4000000000000111-1-1-1111111-1-1-1-1-1-1000000000
χ324-44-4444-4-4-4−2−2i3−2+2i32+2i32−2i30−2−2i3−2+2i3002+2i32−2i30000000000001−1−i32−1+i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000
χ334-44-4444-4-4-4−2+2i3−2−2i32−2i32+2i30−2+2i3−2−2i3002−2i32+2i30000000000001−1+i32−1−i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000
χ344-44-4-2-2-222244-4-40-2-20022000000000000111-1-1-11-21-21-2-12-12-12000000000
χ354-44-4-2-2-222244-4-40-2-20022000000000000111-1-1-1-21-21-212-12-12-1000000000
χ364-44-4-2-2-222244-4-40-2-20022000000000000-2-2-2222111111-1-1-1-1-1-1000000000
χ374-44-4-2-2-2222−2−2i3−2+2i32+2i32−2i301+i31−i300−1−i3−1+i30000000000001−1−i32−1+i32-11+i321−i321-2−1−i321+i3−1+i321−i3-121+i32−1−i31−i32−1+i3000000000
χ384-44-4-2-2-2222−2−2i3−2+2i32+2i32−2i301+i31−i300−1−i3−1+i30000000000001−1−i32−1+i32-11+i321−i32-211+i3−1−i321−i3−1+i322-1−1−i31+i32−1+i31−i32000000000
χ394-44-4-2-2-2222−2−2i3−2+2i32+2i32−2i301+i31−i300−1−i3−1+i3000000000000-21+i31−i32−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000
χ404-44-4-2-2-2222−2+2i3−2−2i32−2i32+2i301−i31+i300−1+i3−1−i30000000000001−1+i32−1−i32-11−i321+i321-2−1+i321−i3−1−i321+i3-121−i32−1+i31+i32−1−i3000000000
χ414-44-4-2-2-2222−2+2i3−2−2i32−2i32+2i301−i31+i300−1+i3−1−i30000000000001−1+i32−1−i32-11−i321+i32-211−i3−1+i321+i3−1−i322-1−1+i31−i32−1−i31+i32000000000
χ424-44-4-2-2-2222−2+2i3−2−2i32−2i32+2i301−i31+i300−1+i3−1−i3000000000000-21−i31+i32−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000
χ436666-3-3-3-3-3-36666-2-3-3-2-2-3-3-2-2-2111111111000000000000000000000000000
χ446666-3-3-3-3-3-3−3−3i3−3+3i3−3−3i3−3+3i3-23+3i323−3i321+i31−i33+3i323−3i32-21+i31−i3111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000000000000000000000000
χ456666-3-3-3-3-3-3−3+3i3−3−3i3−3+3i3−3−3i3-23−3i323+3i321−i31+i33−3i323+3i32-21−i31+i3111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000000000000000000000
χ4666-3-33ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ6800006000000-3003ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ68000000000000000000000000000000000
χ4766-3-33ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ680000-20044001-2-2−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ68000000000000000000000000000
χ4866-3-33ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ680000-200−2−2i3−2+2i30011+i31−i3−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ682ζ4+2ζ52−2ζ68−2ζ4+2ζ44+2ζ68−2ζ44−2ζ52−2ζ4−2ζ44−2ζ52−2ζ682ζ4+2ζ44+2ζ52+2ζ68000000000000000000000000000
χ4966-3-33ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ680000-200−2+2i3−2−2i30011−i31+i3−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−2ζ4−2ζ44−2ζ52−2ζ682ζ4+2ζ44+2ζ52+2ζ682ζ4+2ζ52−2ζ68−2ζ4+2ζ44+2ζ68−2ζ44−2ζ52000000000000000000000000000
χ5066-3-33ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ6800006000000-3003ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ68000000000000000000000000000000000
χ5166-3-33ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ680000-20044001-2-2−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ68000000000000000000000000000
χ5266-3-33ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ680000-200−2−2i3−2+2i30011+i31−i3−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−2ζ4+2ζ44+2ζ68−2ζ44−2ζ522ζ4+2ζ52−2ζ68−2ζ52−2ζ682ζ4+2ζ44+2ζ52+2ζ68−2ζ4−2ζ44000000000000000000000000000
χ5366-3-33ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ680000-200−2+2i3−2−2i30011−i31+i3−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−2ζ52−2ζ682ζ4+2ζ44+2ζ52+2ζ68−2ζ4−2ζ44−2ζ4+2ζ44+2ζ68−2ζ44−2ζ522ζ4+2ζ52−2ζ68000000000000000000000000000
χ5466-3-3−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ5200006000000-300−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52000000000000000000000000000000000
χ5566-3-3−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ520000-20044001-2-2ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52000000000000000000000000000
χ5666-3-3−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ520000-200−2−2i3−2+2i30011+i31−i3ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−2ζ44−2ζ522ζ4+2ζ52−2ζ68−2ζ4+2ζ44+2ζ682ζ4+2ζ44+2ζ52+2ζ68−2ζ4−2ζ44−2ζ52−2ζ68000000000000000000000000000
χ5766-3-3−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ52−3ζ4−3ζ683ζ44−3ζ52+3ζ683ζ4−3ζ44+3ζ520000-200−2+2i3−2−2i30011−i31+i3ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ522ζ4+2ζ44+2ζ52+2ζ68−2ζ4−2ζ44−2ζ52−2ζ68−2ζ44−2ζ522ζ4+2ζ52−2ζ68−2ζ4+2ζ44+2ζ68000000000000000000000000000
χ5812-12-666ζ44−6ζ52+6ζ686ζ4−6ζ44+6ζ52−6ζ4−6ζ68−6ζ44+6ζ52−6ζ68−6ζ4+6ζ44−6ζ526ζ4+6ζ6800000000000000000000000000000000000000000000000000
χ5912-12-666ζ4−6ζ44+6ζ52−6ζ4−6ζ686ζ44−6ζ52+6ζ68−6ζ4+6ζ44−6ζ526ζ4+6ζ68−6ζ44+6ζ52−6ζ6800000000000000000000000000000000000000000000000000
χ6012-12-66−6ζ4−6ζ686ζ44−6ζ52+6ζ686ζ4−6ζ44+6ζ526ζ4+6ζ68−6ζ44+6ζ52−6ζ68−6ζ4+6ζ44−6ζ5200000000000000000000000000000000000000000000000000

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