Finite Group Databasebeta

← Group #13047465

Character table — Group #13047465

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size12336661818182727271233666181818272727246612121236363654545424661212123636365454542466121212363636545454
order13339993332662666181818666266412121236363612121241212412121236363612121241212412121236363612121241212
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111-1-1-11111111111-1-1-11111111111-1-1-11111111111-1-1-11111111111-1-1-1
χ32222222-1-1-10002222222-1-1-10002222222-1-1-10002222222-1-1-10002222222-1-1-1000
χ42222-1-1-12-1-10002222-1-1-12-1-10002222-1-1-12-1-10002222-1-1-12-1-10002222-1-1-12-1-1000
χ52222-1-1-1-12-10002222-1-1-1-12-10002222-1-1-1-12-10002222-1-1-1-12-10002222-1-1-1-12-1000
χ62222-1-1-1-1-120002222-1-1-1-1-120002222-1-1-1-1-120002222-1-1-1-1-120002222-1-1-1-1-12000
χ733−3+3i32−3−3i320000001−1+i32−1−i3233−3+3i32−3−3i320000001−1+i32−1−i3233−3+3i32−3−3i320000001−1+i32−1−i3233−3+3i32−3−3i320000001−1+i32−1−i3233−3+3i32−3−3i320000001−1+i32−1−i32
χ833−3+3i32−3−3i32000000-11−i321+i3233−3+3i32−3−3i32000000-11−i321+i3233−3+3i32−3−3i32000000-11−i321+i3233−3+3i32−3−3i32000000-11−i321+i3233−3+3i32−3−3i32000000-11−i321+i32
χ933−3−3i32−3+3i320000001−1−i32−1+i3233−3−3i32−3+3i320000001−1−i32−1+i3233−3−3i32−3+3i320000001−1−i32−1+i3233−3−3i32−3+3i320000001−1−i32−1+i3233−3−3i32−3+3i320000001−1−i32−1+i32
χ1033−3−3i32−3+3i32000000-11+i321−i3233−3−3i32−3+3i32000000-11+i321−i3233−3−3i32−3+3i32000000-11+i321−i3233−3−3i32−3+3i32000000-11+i321−i3233−3−3i32−3+3i32000000-11+i321−i32
χ116-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ50000006-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ50000006-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ50000006-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ50000006-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5000000
χ126-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ50000006-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ50000006-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ50000006-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ50000006-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5000000
χ136-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ50000006-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ50000006-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ50000006-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ50000006-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5000000
χ14111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ151111111111-1-1-11111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111
χ162222222-1-1-10002222222-1-1-10002222222-1-1-1000-2-2-2-2-2-2-2111000-2-2-2-2-2-2-2111000
χ172222-1-1-12-1-10002222-1-1-12-1-10002222-1-1-12-1-1000-2-2-2-2111-211000-2-2-2-2111-211000
χ182222-1-1-1-12-10002222-1-1-1-12-10002222-1-1-1-12-1000-2-2-2-21111-21000-2-2-2-21111-21000
χ192222-1-1-1-1-120002222-1-1-1-1-120002222-1-1-1-1-12000-2-2-2-211111-2000-2-2-2-211111-2000
χ2033−3+3i32−3−3i320000001−1+i32−1−i3233−3+3i32−3−3i320000001−1+i32−1−i3233−3+3i32−3−3i320000001−1+i32−1−i32-3-33−3i323+3i32000000-11−i321+i32-3-33−3i323+3i32000000-11−i321+i32
χ2133−3+3i32−3−3i32000000-11−i321+i3233−3+3i32−3−3i32000000-11−i321+i3233−3+3i32−3−3i32000000-11−i321+i32-3-33−3i323+3i320000001−1+i32−1−i32-3-33−3i323+3i320000001−1+i32−1−i32
χ2233−3−3i32−3+3i320000001−1−i32−1+i3233−3−3i32−3+3i320000001−1−i32−1+i3233−3−3i32−3+3i320000001−1−i32−1+i32-3-33+3i323−3i32000000-11+i321−i32-3-33+3i323−3i32000000-11+i321−i32
χ2333−3−3i32−3+3i32000000-11+i321−i3233−3−3i32−3+3i32000000-11+i321−i3233−3−3i32−3+3i32000000-11+i321−i32-3-33+3i323−3i320000001−1−i32−1+i32-3-33+3i323−3i320000001−1−i32−1+i32
χ246-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ50000006-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ50000006-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5000000-6300−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ5000000-6300−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ5000000
χ256-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ50000006-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ50000006-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5000000-6300−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ5000000-6300−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ5000000
χ266-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ50000006-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ50000006-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5000000-63002ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ5000000-63002ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ5000000
χ2711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ281111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ292222222-1-1-10002222222-1-1-1000-2-2-2-2-2-2-21110002222222-1-1-1000-2-2-2-2-2-2-2111000
χ302222-1-1-12-1-10002222-1-1-12-1-1000-2-2-2-2111-2110002222-1-1-12-1-1000-2-2-2-2111-211000
χ312222-1-1-1-12-10002222-1-1-1-12-1000-2-2-2-21111-210002222-1-1-1-12-1000-2-2-2-21111-21000
χ322222-1-1-1-1-120002222-1-1-1-1-12000-2-2-2-211111-20002222-1-1-1-1-12000-2-2-2-211111-2000
χ3333−3+3i32−3−3i320000001−1+i32−1−i3233−3+3i32−3−3i320000001−1+i32−1−i32-3-33−3i323+3i32000000-11−i321+i3233−3+3i32−3−3i320000001−1+i32−1−i32-3-33−3i323+3i32000000-11−i321+i32
χ3433−3+3i32−3−3i32000000-11−i321+i3233−3+3i32−3−3i32000000-11−i321+i32-3-33−3i323+3i320000001−1+i32−1−i3233−3+3i32−3−3i32000000-11−i321+i32-3-33−3i323+3i320000001−1+i32−1−i32
χ3533−3−3i32−3+3i320000001−1−i32−1+i3233−3−3i32−3+3i320000001−1−i32−1+i32-3-33+3i323−3i32000000-11+i321−i3233−3−3i32−3+3i320000001−1−i32−1+i32-3-33+3i323−3i32000000-11+i321−i32
χ3633−3−3i32−3+3i32000000-11+i321−i3233−3−3i32−3+3i32000000-11+i321−i32-3-33+3i323−3i320000001−1−i32−1+i3233−3−3i32−3+3i32000000-11+i321−i32-3-33+3i323−3i320000001−1−i32−1+i32
χ376-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ50000006-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5000000-6300−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ50000006-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5000000-6300−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ5000000
χ386-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ50000006-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5000000-6300−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ50000006-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5000000-6300−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ5000000
χ396-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ50000006-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5000000-63002ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ50000006-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5000000-63002ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ5000000
χ4011111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111
χ411111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1
χ422222222-1-1-10002222222-1-1-1000-2-2-2-2-2-2-2111000-2-2-2-2-2-2-21110002222222-1-1-1000
χ432222-1-1-12-1-10002222-1-1-12-1-1000-2-2-2-2111-211000-2-2-2-2111-2110002222-1-1-12-1-1000
χ442222-1-1-1-12-10002222-1-1-1-12-1000-2-2-2-21111-21000-2-2-2-21111-210002222-1-1-1-12-1000
χ452222-1-1-1-1-120002222-1-1-1-1-12000-2-2-2-211111-2000-2-2-2-211111-20002222-1-1-1-1-12000
χ4633−3+3i32−3−3i320000001−1+i32−1−i3233−3+3i32−3−3i320000001−1+i32−1−i32-3-33−3i323+3i32000000-11−i321+i32-3-33−3i323+3i32000000-11−i321+i3233−3+3i32−3−3i320000001−1+i32−1−i32
χ4733−3+3i32−3−3i32000000-11−i321+i3233−3+3i32−3−3i32000000-11−i321+i32-3-33−3i323+3i320000001−1+i32−1−i32-3-33−3i323+3i320000001−1+i32−1−i3233−3+3i32−3−3i32000000-11−i321+i32
χ4833−3−3i32−3+3i320000001−1−i32−1+i3233−3−3i32−3+3i320000001−1−i32−1+i32-3-33+3i323−3i32000000-11+i321−i32-3-33+3i323−3i32000000-11+i321−i3233−3−3i32−3+3i320000001−1−i32−1+i32
χ4933−3−3i32−3+3i32000000-11+i321−i3233−3−3i32−3+3i32000000-11+i321−i32-3-33+3i323−3i320000001−1−i32−1+i32-3-33+3i323−3i320000001−1−i32−1+i3233−3−3i32−3+3i32000000-11+i321−i32
χ506-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ50000006-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5000000-6300−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ5000000-6300−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ50000006-300ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5000000
χ516-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ50000006-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5000000-6300−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ5000000-6300−ζ+ζ2+ζ4+2ζ52ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ50000006-300ζ−ζ2−ζ4−2ζ5−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5000000
χ526-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ50000006-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5000000-63002ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ5000000-63002ζ−2ζ2+ζ4−ζ5−ζ+ζ2−2ζ4−ζ5−ζ+ζ2+ζ4+2ζ50000006-300−2ζ+2ζ2−ζ4+ζ5ζ−ζ2+2ζ4+ζ5ζ−ζ2−ζ4−2ζ5000000
χ532222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000
χ542222222222-2-2-2-2-2-2-2-2-2-2-2-2-2222000000000000000000000000000000000000000
χ554444444-2-2-2000-4-4-4-4-4-4-4222000000000000000000000000000000000000000000
χ564444-2-2-24-2-2000-4-4-4-4222-422000000000000000000000000000000000000000000
χ574444-2-2-2-24-2000-4-4-4-42222-42000000000000000000000000000000000000000000
χ584444-2-2-2-2-24000-4-4-4-422222-4000000000000000000000000000000000000000000
χ5966−3+3i3−3−3i30000002−1+i3−1−i3-6-63−3i33+3i3000000-21−i31+i3000000000000000000000000000000000000000
χ6066−3+3i3−3−3i3000000-21−i31+i3-6-63−3i33+3i30000002−1+i3−1−i3000000000000000000000000000000000000000
χ6166−3−3i3−3+3i30000002−1−i3−1+i3-6-63+3i33−3i3000000-21+i31−i3000000000000000000000000000000000000000
χ6266−3−3i3−3+3i3000000-21+i31−i3-6-63+3i33−3i30000002−1−i3−1+i3000000000000000000000000000000000000000
χ6312-6002ζ−2ζ2+4ζ4+2ζ52ζ−2ζ2−2ζ4−4ζ5−4ζ+4ζ2−2ζ4+2ζ5000000-12600−2ζ+2ζ2−4ζ4−2ζ5−2ζ+2ζ2+2ζ4+4ζ54ζ−4ζ2+2ζ4−2ζ5000000000000000000000000000000000000000000000
χ6412-6002ζ−2ζ2−2ζ4−4ζ5−4ζ+4ζ2−2ζ4+2ζ52ζ−2ζ2+4ζ4+2ζ5000000-12600−2ζ+2ζ2+2ζ4+4ζ54ζ−4ζ2+2ζ4−2ζ5−2ζ+2ζ2−4ζ4−2ζ5000000000000000000000000000000000000000000000
χ6512-600−4ζ+4ζ2−2ζ4+2ζ52ζ−2ζ2+4ζ4+2ζ52ζ−2ζ2−2ζ4−4ζ5000000-126004ζ−4ζ2+2ζ4−2ζ5−2ζ+2ζ2−4ζ4−2ζ5−2ζ+2ζ2+2ζ4+4ζ5000000000000000000000000000000000000000000000

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