Finite Group Databasebeta

← Group #11724056

Character table — Group #11724056

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size12366666912122424273636123666669121224242736361236666691212242427363612366666912122424273636
order1326918181823399266262618181818266181826626261818181826618182662626181818182661818266
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ3111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ411111111-11111-1-1-111111111-11111-1-1-111111111-11111-1-1-111111111-11111-1-1-1
χ511111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32
χ611111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ72222-1-1-1-1022-1-10002222-1-1-1-1022-1-10002222-1-1-1-1022-1-10002222-1-1-1-1022-1-1000
χ82222-1-1-1-10−1+i3−1−i31−i321+i320002222-1-1-1-10−1+i3−1−i31−i321+i320002222-1-1-1-10−1+i3−1−i31−i321+i320002222-1-1-1-10−1+i3−1−i31−i321+i32000
χ92222-1-1-1-10−1−i3−1+i31+i321−i320002222-1-1-1-10−1−i3−1+i31+i321−i320002222-1-1-1-10−1−i3−1+i31+i321−i320002222-1-1-1-10−1−i3−1+i31+i321−i32000
χ1033-1-13-1-1-130000-10033-1-13-1-1-130000-10033-1-13-1-1-130000-10033-1-13-1-1-130000-100
χ1133-1-13-1-1-1-3000010033-1-13-1-1-1-3000010033-1-13-1-1-1-3000010033-1-13-1-1-1-30000100
χ1266-2-2-31110000000066-2-2-31110000000066-2-2-31110000000066-2-2-311100000000
χ136-36-30000000000006-36-30000000000006-36-30000000000006-36-3000000000000
χ146-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000
χ156-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000
χ166-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000
χ171111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ18111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32
χ19111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32
χ2011111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111
χ2111111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i32
χ2211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i32
χ232222-1-1-1-1022-1-1000-2-2-2-211110-2-2110002222-1-1-1-1022-1-1000-2-2-2-211110-2-211000
χ242222-1-1-1-10−1+i3−1−i31−i321+i32000-2-2-2-2111101−i31+i3−1+i32−1−i320002222-1-1-1-10−1+i3−1−i31−i321+i32000-2-2-2-2111101−i31+i3−1+i32−1−i32000
χ252222-1-1-1-10−1−i3−1+i31+i321−i32000-2-2-2-2111101+i31−i3−1−i32−1+i320002222-1-1-1-10−1−i3−1+i31+i321−i32000-2-2-2-2111101+i31−i3−1−i32−1+i32000
χ2633-1-13-1-1-130000-100-3-311-3111-3000010033-1-13-1-1-130000-100-3-311-3111-30000100
χ2733-1-13-1-1-1-30000100-3-311-311130000-10033-1-13-1-1-1-30000100-3-311-311130000-100
χ2866-2-2-311100000000-6-6223-1-1-10000000066-2-2-311100000000-6-6223-1-1-100000000
χ296-36-3000000000000-63-630000000000006-36-3000000000000-63-63000000000000
χ306-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ500000000
χ316-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ800000000
χ326-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ700000000
χ3311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ34111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32
χ35111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32
χ3611111111-11111-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1111
χ3711111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i32
χ3811111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i32
χ392222-1-1-1-1022-1-10002222-1-1-1-1022-1-1000-2-2-2-211110-2-211000-2-2-2-211110-2-211000
χ402222-1-1-1-10−1+i3−1−i31−i321+i320002222-1-1-1-10−1+i3−1−i31−i321+i32000-2-2-2-2111101−i31+i3−1+i32−1−i32000-2-2-2-2111101−i31+i3−1+i32−1−i32000
χ412222-1-1-1-10−1−i3−1+i31+i321−i320002222-1-1-1-10−1−i3−1+i31+i321−i32000-2-2-2-2111101+i31−i3−1−i32−1+i32000-2-2-2-2111101+i31−i3−1−i32−1+i32000
χ4233-1-13-1-1-130000-10033-1-13-1-1-130000-100-3-311-3111-30000100-3-311-3111-30000100
χ4333-1-13-1-1-1-3000010033-1-13-1-1-1-30000100-3-311-311130000-100-3-311-311130000-100
χ4466-2-2-31110000000066-2-2-311100000000-6-6223-1-1-100000000-6-6223-1-1-100000000
χ456-36-30000000000006-36-3000000000000-63-63000000000000-63-63000000000000
χ466-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ500000000
χ476-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ800000000
χ486-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ700000000
χ491111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ50111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ51111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ5211111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111111-11111-1-1-1
χ5311111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32
χ5411111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ552222-1-1-1-1022-1-1000-2-2-2-211110-2-211000-2-2-2-211110-2-2110002222-1-1-1-1022-1-1000
χ562222-1-1-1-10−1+i3−1−i31−i321+i32000-2-2-2-2111101−i31+i3−1+i32−1−i32000-2-2-2-2111101−i31+i3−1+i32−1−i320002222-1-1-1-10−1+i3−1−i31−i321+i32000
χ572222-1-1-1-10−1−i3−1+i31+i321−i32000-2-2-2-2111101+i31−i3−1−i32−1+i32000-2-2-2-2111101+i31−i3−1−i32−1+i320002222-1-1-1-10−1−i3−1+i31+i321−i32000
χ5833-1-13-1-1-130000-100-3-311-3111-30000100-3-311-3111-3000010033-1-13-1-1-130000-100
χ5933-1-13-1-1-1-30000100-3-311-311130000-100-3-311-311130000-10033-1-13-1-1-1-30000100
χ6066-2-2-311100000000-6-6223-1-1-100000000-6-6223-1-1-10000000066-2-2-311100000000
χ616-36-3000000000000-63-63000000000000-63-630000000000006-36-3000000000000
χ626-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000
χ636-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000
χ646-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000

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