Finite Group Databasebeta

← Group #13049301

Character table — Group #13049301

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size12222366666666666666661212242424242424242427811081081222236666666666666666121224242424242424242781108108
order133332666699918181818181818181833339999992266266662666618181818181818181818181866661818181818182266
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1
χ31111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1−i321111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1−i32
χ41111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11−i321+i321111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11−i321+i32
χ51111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1+i321111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1+i32
χ61111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11+i321−i321111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11+i321−i32
χ72222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-100002222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-10000
χ82222222222-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321−i321−i321+i321+i321+i3200002222222222-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321−i321−i321+i321+i321+i320000
χ92222222222-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321+i321+i321−i321−i321−i3200002222222222-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321+i321+i321−i321−i321−i320000
χ102-1-1-122-1-1-122-1-1222-1-1-1-1-1-122-1-12-1-12-1-100002-1-1-122-1-1-122-1-1222-1-1-1-1-1-122-1-12-1-12-1-10000
χ112-1-1-122-1-1-122-1-1222-1-1-1-1-1-1−1+i3−1−i31−i321+i32−1+i31−i321−i32−1−i31+i321+i3200002-1-1-122-1-1-122-1-1222-1-1-1-1-1-1−1+i3−1−i31−i321+i32−1+i31−i321−i32−1−i31+i321+i320000
χ122-1-1-122-1-1-122-1-1222-1-1-1-1-1-1−1−i3−1+i31+i321−i32−1−i31+i321+i32−1+i31−i321−i3200002-1-1-122-1-1-122-1-1222-1-1-1-1-1-1−1−i3−1+i31+i321−i32−1−i31+i321+i32−1+i31−i321−i320000
χ132-1-1-122-1-1-12-12-1-1-1-1222-1-1-122-1-1-12-1-12-100002-1-1-122-1-1-12-12-1-1-1-1222-1-1-122-1-1-12-1-12-10000
χ142-1-1-122-1-1-12-12-1-1-1-1222-1-1-1−1+i3−1−i31−i321+i321−i32−1+i31−i321+i32−1−i31+i3200002-1-1-122-1-1-12-12-1-1-1-1222-1-1-1−1+i3−1−i31−i321+i321−i32−1+i31−i321+i32−1−i31+i320000
χ152-1-1-122-1-1-12-12-1-1-1-1222-1-1-1−1−i3−1+i31+i321−i321+i32−1−i31+i321−i32−1+i31−i3200002-1-1-122-1-1-12-12-1-1-1-1222-1-1-1−1−i3−1+i31+i321−i321+i32−1−i31+i321−i32−1+i31−i320000
χ162-1-1-122-1-1-12-1-12-1-1-1-1-1-122222-1-1-1-12-1-1200002-1-1-122-1-1-12-1-12-1-1-1-1-1-122222-1-1-1-12-1-120000
χ172-1-1-122-1-1-12-1-12-1-1-1-1-1-1222−1+i3−1−i31−i321+i321−i321−i32−1+i31+i321+i32−1−i300002-1-1-122-1-1-12-1-12-1-1-1-1-1-1222−1+i3−1−i31−i321+i321−i321−i32−1+i31+i321+i32−1−i30000
χ182-1-1-122-1-1-12-1-12-1-1-1-1-1-1222−1−i3−1+i31+i321−i321+i321+i32−1−i31−i321−i32−1+i300002-1-1-122-1-1-12-1-12-1-1-1-1-1-1222−1−i3−1+i31+i321−i321+i321+i32−1−i31−i321−i32−1+i30000
χ1933333-1-1-1-1-1333-1-1-1-1-1-1-1-1-100000000003-10033333-1-1-1-1-1333-1-1-1-1-1-1-1-1-100000000003-100
χ2033333-1-1-1-1-1333-1-1-1-1-1-1-1-1-10000000000-310033333-1-1-1-1-1333-1-1-1-1-1-1-1-1-10000000000-3100
χ2166666-2-2-2-2-2-3-3-31111111110000000000000066666-2-2-2-2-2-3-3-311111111100000000000000
χ2266-3-3-366-3-3-30000000000000000000000000066-3-3-366-3-3-300000000000000000000000000
χ2366-3-3-3-2-21110002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ50000000000000066-3-3-3-2-21110002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000
χ2466-3-3-3-2-21110002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ80000000000000066-3-3-3-2-21110002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000
χ2566-3-3-3-2-21110002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ70000000000000066-3-3-3-2-21110002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000
χ266-36-3-36-36-3-3000000000000000000000000006-36-3-36-36-3-300000000000000000000000000
χ276-36-3-3-21-2110002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000000000006-36-3-3-21-2110002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000
χ286-36-3-3-21-2110002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000000000006-36-3-3-21-2110002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000
χ296-36-3-3-21-2110002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000000000006-36-3-3-21-2110002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000
χ306-3-36-36-3-36-3000000000000000000000000006-3-36-36-3-36-300000000000000000000000000
χ316-3-36-3-211-210002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000000000006-3-36-3-211-210002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000
χ326-3-36-3-211-210002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000000000006-3-36-3-211-210002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000
χ336-3-36-3-211-210002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000000000006-3-36-3-211-210002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000
χ346-3-3-36-2111-26-3-3-2-2-2111111000000000000006-3-3-36-2111-26-3-3-2-2-211111100000000000000
χ356-3-3-36-2111-2-36-3111-2-2-2111000000000000006-3-3-36-2111-2-36-3111-2-2-211100000000000000
χ366-3-3-36-2111-2-3-36111111-2-2-2000000000000006-3-3-36-2111-2-3-36111111-2-2-200000000000000
χ37111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ391111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321−i321+i321+i321+i32-1-11−i321+i32
χ401111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11−i321+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321−i321+i321+i321+i3211−1+i32−1−i32
χ411111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321+i321−i321−i321−i32-1-11+i321−i32
χ421111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11+i321−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321+i321−i321−i321−i3211−1−i32−1+i32
χ432222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-2-2111111111111-2-2-2-21111110000
χ442222222222-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321−i321−i321+i321+i321+i320000-2-2-2-2-2-2-2-2-2-21111111111111−i31+i31−i31+i3−1+i32−1+i32−1+i32−1−i32−1−i32−1−i320000
χ452222222222-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321+i321+i321−i321−i321−i320000-2-2-2-2-2-2-2-2-2-21111111111111+i31−i31+i31−i3−1−i32−1−i32−1−i32−1+i32−1+i32−1+i320000
χ462-1-1-122-1-1-122-1-1222-1-1-1-1-1-122-1-12-1-12-1-10000-2111-2-2111-2-211-2-2-2111111-2-211-211-2110000
χ472-1-1-122-1-1-122-1-1222-1-1-1-1-1-1−1+i3−1−i31−i321+i32−1+i31−i321−i32−1−i31+i321+i320000-2111-2-2111-2-211-2-2-21111111−i31+i3−1+i32−1−i321−i3−1+i32−1+i321+i3−1−i32−1−i320000
χ482-1-1-122-1-1-122-1-1222-1-1-1-1-1-1−1−i3−1+i31+i321−i32−1−i31+i321+i32−1+i31−i321−i320000-2111-2-2111-2-211-2-2-21111111+i31−i3−1−i32−1+i321+i3−1−i32−1−i321−i3−1+i32−1+i320000
χ492-1-1-122-1-1-12-12-1-1-1-1222-1-1-122-1-1-12-1-12-10000-2111-2-2111-21-21111-2-2-2111-2-2111-211-210000
χ502-1-1-122-1-1-12-12-1-1-1-1222-1-1-1−1+i3−1−i31−i321+i321−i32−1+i31−i321+i32−1−i31+i320000-2111-2-2111-21-21111-2-2-21111−i31+i3−1+i32−1−i32−1+i321−i3−1+i32−1−i321+i3−1−i320000
χ512-1-1-122-1-1-12-12-1-1-1-1222-1-1-1−1−i3−1+i31+i321−i321+i32−1−i31+i321−i32−1+i31−i320000-2111-2-2111-21-21111-2-2-21111+i31−i3−1−i32−1+i32−1−i321+i3−1−i32−1+i321−i3−1+i320000
χ522-1-1-122-1-1-12-1-12-1-1-1-1-1-122222-1-1-1-12-1-120000-2111-2-2111-211-2111111-2-2-2-2-21111-211-20000
χ532-1-1-122-1-1-12-1-12-1-1-1-1-1-1222−1+i3−1−i31−i321+i321−i321−i32−1+i31+i321+i32−1−i30000-2111-2-2111-211-2111111-2-2-21−i31+i3−1+i32−1−i32−1+i32−1+i321−i3−1−i32−1−i321+i30000
χ542-1-1-122-1-1-12-1-12-1-1-1-1-1-1222−1−i3−1+i31+i321−i321+i321+i32−1−i31−i321−i32−1+i30000-2111-2-2111-211-2111111-2-2-21+i31−i3−1−i32−1+i32−1−i32−1−i321+i3−1+i32−1+i321−i30000
χ5533333-1-1-1-1-1333-1-1-1-1-1-1-1-1-100000000003-100-3-3-3-3-311111-3-3-31111111110000000000-3100
χ5633333-1-1-1-1-1333-1-1-1-1-1-1-1-1-10000000000-3100-3-3-3-3-311111-3-3-311111111100000000003-100
χ5766666-2-2-2-2-2-3-3-311111111100000000000000-6-6-6-6-622222333-1-1-1-1-1-1-1-1-100000000000000
χ5866-3-3-366-3-3-300000000000000000000000000-6-6333-6-633300000000000000000000000000
χ5966-3-3-3-2-21110002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000-6-633322-1-1-1000−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ500000000000000
χ6066-3-3-3-2-21110002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000-6-633322-1-1-1000−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ800000000000000
χ6166-3-3-3-2-21110002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000-6-633322-1-1-1000−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ700000000000000
χ626-36-3-36-36-3-300000000000000000000000000-63-633-63-63300000000000000000000000000
χ636-36-3-3-21-2110002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000-63-6332-12-1-1000−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ700000000000000
χ646-36-3-3-21-2110002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000-63-6332-12-1-1000−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ500000000000000
χ656-36-3-3-21-2110002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000-63-6332-12-1-1000−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ800000000000000
χ666-3-36-36-3-36-300000000000000000000000000-633-63-633-6300000000000000000000000000
χ676-3-36-3-211-210002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000000000-633-632-1-12-1000−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ800000000000000
χ686-3-36-3-211-210002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000000000-633-632-1-12-1000−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ700000000000000
χ696-3-36-3-211-210002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000000000-633-632-1-12-1000−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ500000000000000
χ706-3-3-36-2111-26-3-3-2-2-211111100000000000000-6333-62-1-1-12-633222-1-1-1-1-1-100000000000000
χ716-3-3-36-2111-2-36-3111-2-2-211100000000000000-6333-62-1-1-123-63-1-1-1222-1-1-100000000000000
χ726-3-3-36-2111-2-3-36111111-2-2-200000000000000-6333-62-1-1-1233-6-1-1-1-1-1-122200000000000000

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