Finite Group Databasebeta

← Group #13146262

Character table — Group #13146262

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size122223666666666666661212121212122424242424242424242424242424242424323664646464108108108216288
order139992226661818181818181818182461818184612121218181836363636363636363632399924446
χ1111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-11111-1-1-1-1-1
χ311111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-11
χ411111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-111-1
χ52222222222222222222200222200000000000000000-12-1-1-1-10200-1
χ62222222222222222222200222200000000000000000-1-2-1-1-1-10-2001
χ722-1-1-1222222-1-1-1-1-1-1-1-1-1222-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1202-1-1-100000
χ822-1-1-1222222-1-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2-2-2-2111111111111202-1-1-100000
χ92-1ζ+ζ8ζ2+ζ7ζ4+ζ5222-1-1-1ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ522-1ζ+ζ8ζ2+ζ7ζ4+ζ52-1-1-1-1ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ520-1ζ+ζ8ζ2+ζ7ζ4+ζ500000
χ102-1ζ+ζ8ζ2+ζ7ζ4+ζ5222-1-1-1ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5-2-2-1ζ+ζ8ζ2+ζ7ζ4+ζ5-21111−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ520-1ζ+ζ8ζ2+ζ7ζ4+ζ500000
χ112-1ζ2+ζ7ζ4+ζ5ζ+ζ8222-1-1-1ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ822-1ζ2+ζ7ζ4+ζ5ζ+ζ82-1-1-1-1ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ820-1ζ2+ζ7ζ4+ζ5ζ+ζ800000
χ122-1ζ2+ζ7ζ4+ζ5ζ+ζ8222-1-1-1ζ2+ζ7ζ2+ζ7ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8-2-2-1ζ2+ζ7ζ4+ζ5ζ+ζ8-21111−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ820-1ζ2+ζ7ζ4+ζ5ζ+ζ800000
χ132-1ζ4+ζ5ζ+ζ8ζ2+ζ7222-1-1-1ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ722-1ζ4+ζ5ζ+ζ8ζ2+ζ72-1-1-1-1ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ720-1ζ4+ζ5ζ+ζ8ζ2+ζ700000
χ142-1ζ4+ζ5ζ+ζ8ζ2+ζ7222-1-1-1ζ4+ζ5ζ4+ζ5ζ4+ζ5ζ+ζ8ζ+ζ8ζ+ζ8ζ2+ζ7ζ2+ζ7ζ2+ζ7-2-2-1ζ4+ζ5ζ+ζ8ζ2+ζ7-21111−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ4−ζ5−ζ4−ζ5−ζ−ζ8−ζ−ζ8−ζ−ζ8−ζ2−ζ7−ζ2−ζ7−ζ2−ζ720-1ζ4+ζ5ζ+ζ8ζ2+ζ700000
χ15333333-1-13-1-13-1-13-1-13-1-111-1-1-1-1-111-1-11111-1-11-1-11-1-10300001-11-10
χ16333333-1-13-1-13-1-13-1-13-1-111-1-1-1-1-111-1-11111-1-11-1-11-1-10-30000-11-110
χ17333333-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-11-1-111-1-1-1-111-111-111030000-1-1-110
χ18333333-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-11-1-111-1-1-1-111-111-1110-30000111-10
χ1944-2-2-2444444-2-2-2-2-2-2-2-2-2004-2-2-200000000000000000-20-211100000
χ204-22ζ+2ζ82ζ2+2ζ72ζ4+2ζ5444-2-2-22ζ+2ζ82ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ4+2ζ500-22ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000000-201−ζ−ζ8−ζ2−ζ7−ζ4−ζ500000
χ214-22ζ2+2ζ72ζ4+2ζ52ζ+2ζ8444-2-2-22ζ2+2ζ72ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ+2ζ800-22ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000000-201−ζ2−ζ7−ζ4−ζ5−ζ−ζ800000
χ224-22ζ4+2ζ52ζ+2ζ82ζ2+2ζ7444-2-2-22ζ4+2ζ52ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ2+2ζ700-22ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000000-201−ζ4−ζ5−ζ−ζ8−ζ2−ζ700000
χ2366666-22-2-222-222-222-2222-2-2-2-2-202-200222-200-200-20000000000000
χ2466666-22-2-222-222-222-222-22-2-2-2-20-2200-2-2-220020020000000000000
χ2566666-2-22-2-2-2-2-2-2-2-2-2-2-2-20022220000000000000000000000020-200
χ2666666-2-22-2-2-2-2-2-2-2-2-2-2-2-200222200000000000000000000000-20200
χ2766-3-3-36-2-26-2-2-311-311-31122-2111-222-2-2-1-1-1-111-111-11100000000000
χ2866-3-3-36-2-26-2-2-311-311-311-2-2-21112-2-2221111-1-11-1-11-1-100000000000
χ2966-3-3-3-22-2-2221−1+2i3−1−2i31−1+2i3−1−2i31−1+2i3−1−2i32-2-211102-200-1-1-11i3−i31i3−i31i3−i300000000000
χ3066-3-3-3-22-2-2221−1+2i3−1−2i31−1+2i3−1−2i31−1+2i3−1−2i3-22-21110-2200111-1−i3i3-1−i3i3-1−i3i300000000000
χ3166-3-3-3-22-2-2221−1−2i3−1+2i31−1−2i3−1+2i31−1−2i3−1+2i32-2-211102-200-1-1-11−i3i31−i3i31−i3i300000000000
χ3266-3-3-3-22-2-2221−1−2i3−1+2i31−1−2i3−1+2i31−1−2i3−1+2i3-22-21110-2200111-1i3−i3-1i3−i3-1i3−i300000000000
χ336-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ56-2-2-3113ζ+3ζ8−ζ−ζ8−ζ−ζ83ζ2+3ζ7−ζ2−ζ7−ζ2−ζ73ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5221−ζ−ζ8−ζ2−ζ7−ζ4−ζ5-2-1-111ζ+ζ8ζ2+ζ7ζ4+ζ5ζ+ζ8−ζ−ζ8−ζ−ζ8ζ2+ζ7−ζ2−ζ7−ζ2−ζ7ζ4+ζ5−ζ4−ζ5−ζ4−ζ500000000000
χ346-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ56-2-2-3113ζ+3ζ8−ζ−ζ8−ζ−ζ83ζ2+3ζ7−ζ2−ζ7−ζ2−ζ73ζ4+3ζ5−ζ4−ζ5−ζ4−ζ5-2-21−ζ−ζ8−ζ2−ζ7−ζ4−ζ5211-1-1−ζ−ζ8−ζ2−ζ7−ζ4−ζ5−ζ−ζ8ζ+ζ8ζ+ζ8−ζ2−ζ7ζ2+ζ7ζ2+ζ7−ζ4−ζ5ζ4+ζ5ζ4+ζ500000000000
χ356-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ5-22-21−1+2i3−1−2i3−ζ−ζ83ζ−ζ8−ζ+3ζ8−ζ2−ζ7−ζ2+3ζ73ζ2−ζ7−ζ4−ζ53ζ4−ζ5−ζ4+3ζ52-21−ζ−ζ8−ζ2−ζ7−ζ4−ζ50-11i3−i3ζ+ζ8ζ2+ζ7ζ4+ζ5−ζ−ζ8ζ−ζ8−ζ+ζ8−ζ2−ζ7−ζ2+ζ7ζ2−ζ7−ζ4−ζ5ζ4−ζ5−ζ4+ζ500000000000
χ366-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ5-22-21−1+2i3−1−2i3−ζ−ζ83ζ−ζ8−ζ+3ζ8−ζ2−ζ7−ζ2+3ζ73ζ2−ζ7−ζ4−ζ53ζ4−ζ5−ζ4+3ζ5-221−ζ−ζ8−ζ2−ζ7−ζ4−ζ501-1−i3i3−ζ−ζ8−ζ2−ζ7−ζ4−ζ5ζ+ζ8−ζ+ζ8ζ−ζ8ζ2+ζ7ζ2−ζ7−ζ2+ζ7ζ4+ζ5−ζ4+ζ5ζ4−ζ500000000000
χ376-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ5-22-21−1−2i3−1+2i3−ζ−ζ8−ζ+3ζ83ζ−ζ8−ζ2−ζ73ζ2−ζ7−ζ2+3ζ7−ζ4−ζ5−ζ4+3ζ53ζ4−ζ52-21−ζ−ζ8−ζ2−ζ7−ζ4−ζ50-11−i3i3ζ+ζ8ζ2+ζ7ζ4+ζ5−ζ−ζ8−ζ+ζ8ζ−ζ8−ζ2−ζ7ζ2−ζ7−ζ2+ζ7−ζ4−ζ5−ζ4+ζ5ζ4−ζ500000000000
χ386-33ζ+3ζ83ζ2+3ζ73ζ4+3ζ5-22-21−1−2i3−1+2i3−ζ−ζ8−ζ+3ζ83ζ−ζ8−ζ2−ζ73ζ2−ζ7−ζ2+3ζ7−ζ4−ζ5−ζ4+3ζ53ζ4−ζ5-221−ζ−ζ8−ζ2−ζ7−ζ4−ζ501-1i3−i3−ζ−ζ8−ζ2−ζ7−ζ4−ζ5ζ+ζ8ζ−ζ8−ζ+ζ8ζ2+ζ7−ζ2+ζ7ζ2−ζ7ζ4+ζ5ζ4−ζ5−ζ4+ζ500000000000
χ396-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ86-2-2-3113ζ2+3ζ7−ζ2−ζ7−ζ2−ζ73ζ4+3ζ5−ζ4−ζ5−ζ4−ζ53ζ+3ζ8−ζ−ζ8−ζ−ζ8221−ζ2−ζ7−ζ4−ζ5−ζ−ζ8-2-1-111ζ2+ζ7ζ4+ζ5ζ+ζ8ζ2+ζ7−ζ2−ζ7−ζ2−ζ7ζ4+ζ5−ζ4−ζ5−ζ4−ζ5ζ+ζ8−ζ−ζ8−ζ−ζ800000000000
χ406-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ86-2-2-3113ζ2+3ζ7−ζ2−ζ7−ζ2−ζ73ζ4+3ζ5−ζ4−ζ5−ζ4−ζ53ζ+3ζ8−ζ−ζ8−ζ−ζ8-2-21−ζ2−ζ7−ζ4−ζ5−ζ−ζ8211-1-1−ζ2−ζ7−ζ4−ζ5−ζ−ζ8−ζ2−ζ7ζ2+ζ7ζ2+ζ7−ζ4−ζ5ζ4+ζ5ζ4+ζ5−ζ−ζ8ζ+ζ8ζ+ζ800000000000
χ416-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ8-22-21−1+2i3−1−2i3−ζ2−ζ7−ζ2+3ζ73ζ2−ζ7−ζ4−ζ53ζ4−ζ5−ζ4+3ζ5−ζ−ζ83ζ−ζ8−ζ+3ζ82-21−ζ2−ζ7−ζ4−ζ5−ζ−ζ80-11i3−i3ζ2+ζ7ζ4+ζ5ζ+ζ8−ζ2−ζ7−ζ2+ζ7ζ2−ζ7−ζ4−ζ5ζ4−ζ5−ζ4+ζ5−ζ−ζ8ζ−ζ8−ζ+ζ800000000000
χ426-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ8-22-21−1+2i3−1−2i3−ζ2−ζ7−ζ2+3ζ73ζ2−ζ7−ζ4−ζ53ζ4−ζ5−ζ4+3ζ5−ζ−ζ83ζ−ζ8−ζ+3ζ8-221−ζ2−ζ7−ζ4−ζ5−ζ−ζ801-1−i3i3−ζ2−ζ7−ζ4−ζ5−ζ−ζ8ζ2+ζ7ζ2−ζ7−ζ2+ζ7ζ4+ζ5−ζ4+ζ5ζ4−ζ5ζ+ζ8−ζ+ζ8ζ−ζ800000000000
χ436-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ8-22-21−1−2i3−1+2i3−ζ2−ζ73ζ2−ζ7−ζ2+3ζ7−ζ4−ζ5−ζ4+3ζ53ζ4−ζ5−ζ−ζ8−ζ+3ζ83ζ−ζ82-21−ζ2−ζ7−ζ4−ζ5−ζ−ζ80-11−i3i3ζ2+ζ7ζ4+ζ5ζ+ζ8−ζ2−ζ7ζ2−ζ7−ζ2+ζ7−ζ4−ζ5−ζ4+ζ5ζ4−ζ5−ζ−ζ8−ζ+ζ8ζ−ζ800000000000
χ446-33ζ2+3ζ73ζ4+3ζ53ζ+3ζ8-22-21−1−2i3−1+2i3−ζ2−ζ73ζ2−ζ7−ζ2+3ζ7−ζ4−ζ5−ζ4+3ζ53ζ4−ζ5−ζ−ζ8−ζ+3ζ83ζ−ζ8-221−ζ2−ζ7−ζ4−ζ5−ζ−ζ801-1i3−i3−ζ2−ζ7−ζ4−ζ5−ζ−ζ8ζ2+ζ7−ζ2+ζ7ζ2−ζ7ζ4+ζ5ζ4−ζ5−ζ4+ζ5ζ+ζ8ζ−ζ8−ζ+ζ800000000000
χ456-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ76-2-2-3113ζ4+3ζ5−ζ4−ζ5−ζ4−ζ53ζ+3ζ8−ζ−ζ8−ζ−ζ83ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7221−ζ4−ζ5−ζ−ζ8−ζ2−ζ7-2-1-111ζ4+ζ5ζ+ζ8ζ2+ζ7ζ4+ζ5−ζ4−ζ5−ζ4−ζ5ζ+ζ8−ζ−ζ8−ζ−ζ8ζ2+ζ7−ζ2−ζ7−ζ2−ζ700000000000
χ466-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ76-2-2-3113ζ4+3ζ5−ζ4−ζ5−ζ4−ζ53ζ+3ζ8−ζ−ζ8−ζ−ζ83ζ2+3ζ7−ζ2−ζ7−ζ2−ζ7-2-21−ζ4−ζ5−ζ−ζ8−ζ2−ζ7211-1-1−ζ4−ζ5−ζ−ζ8−ζ2−ζ7−ζ4−ζ5ζ4+ζ5ζ4+ζ5−ζ−ζ8ζ+ζ8ζ+ζ8−ζ2−ζ7ζ2+ζ7ζ2+ζ700000000000
χ476-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ7-22-21−1+2i3−1−2i3−ζ4−ζ53ζ4−ζ5−ζ4+3ζ5−ζ−ζ83ζ−ζ8−ζ+3ζ8−ζ2−ζ7−ζ2+3ζ73ζ2−ζ72-21−ζ4−ζ5−ζ−ζ8−ζ2−ζ70-11i3−i3ζ4+ζ5ζ+ζ8ζ2+ζ7−ζ4−ζ5ζ4−ζ5−ζ4+ζ5−ζ−ζ8ζ−ζ8−ζ+ζ8−ζ2−ζ7−ζ2+ζ7ζ2−ζ700000000000
χ486-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ7-22-21−1+2i3−1−2i3−ζ4−ζ53ζ4−ζ5−ζ4+3ζ5−ζ−ζ83ζ−ζ8−ζ+3ζ8−ζ2−ζ7−ζ2+3ζ73ζ2−ζ7-221−ζ4−ζ5−ζ−ζ8−ζ2−ζ701-1−i3i3−ζ4−ζ5−ζ−ζ8−ζ2−ζ7ζ4+ζ5−ζ4+ζ5ζ4−ζ5ζ+ζ8−ζ+ζ8ζ−ζ8ζ2+ζ7ζ2−ζ7−ζ2+ζ700000000000
χ496-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ7-22-21−1−2i3−1+2i3−ζ4−ζ5−ζ4+3ζ53ζ4−ζ5−ζ−ζ8−ζ+3ζ83ζ−ζ8−ζ2−ζ73ζ2−ζ7−ζ2+3ζ72-21−ζ4−ζ5−ζ−ζ8−ζ2−ζ70-11−i3i3ζ4+ζ5ζ+ζ8ζ2+ζ7−ζ4−ζ5−ζ4+ζ5ζ4−ζ5−ζ−ζ8−ζ+ζ8ζ−ζ8−ζ2−ζ7ζ2−ζ7−ζ2+ζ700000000000
χ506-33ζ4+3ζ53ζ+3ζ83ζ2+3ζ7-22-21−1−2i3−1+2i3−ζ4−ζ5−ζ4+3ζ53ζ4−ζ5−ζ−ζ8−ζ+3ζ83ζ−ζ8−ζ2−ζ73ζ2−ζ7−ζ2+3ζ7-221−ζ4−ζ5−ζ−ζ8−ζ2−ζ701-1i3−i3−ζ4−ζ5−ζ−ζ8−ζ2−ζ7ζ4+ζ5ζ4−ζ5−ζ4+ζ5ζ+ζ8ζ−ζ8−ζ+ζ8ζ2+ζ7−ζ2+ζ7ζ2−ζ700000000000
χ511212-6-6-6-4-44-4-4-4222222222004-2-2-20000000000000000000000000000
χ5212-66ζ+6ζ86ζ2+6ζ76ζ4+6ζ5-4-44222−2ζ−2ζ8−2ζ−2ζ8−2ζ−2ζ8−2ζ2−2ζ7−2ζ2−2ζ7−2ζ2−2ζ7−2ζ4−2ζ5−2ζ4−2ζ5−2ζ4−2ζ500-22ζ+2ζ82ζ2+2ζ72ζ4+2ζ50000000000000000000000000000
χ5312-66ζ2+6ζ76ζ4+6ζ56ζ+6ζ8-4-44222−2ζ2−2ζ7−2ζ2−2ζ7−2ζ2−2ζ7−2ζ4−2ζ5−2ζ4−2ζ5−2ζ4−2ζ5−2ζ−2ζ8−2ζ−2ζ8−2ζ−2ζ800-22ζ2+2ζ72ζ4+2ζ52ζ+2ζ80000000000000000000000000000
χ5412-66ζ4+6ζ56ζ+6ζ86ζ2+6ζ7-4-44222−2ζ4−2ζ5−2ζ4−2ζ5−2ζ4−2ζ5−2ζ−2ζ8−2ζ−2ζ8−2ζ−2ζ8−2ζ2−2ζ7−2ζ2−2ζ7−2ζ2−2ζ700-22ζ4+2ζ52ζ+2ζ82ζ2+2ζ70000000000000000000000000000

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