Finite Group Databasebeta

← Group #13164570

Character table — Group #13164570

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1236666691212242427363612366666912122424273636246121212121218242448485472722461212121212182424484854727224612121212121824244848547272
order13269181818233992662626181818182661818266262618181818266181826626261818181826618182664124123636363641212363641212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
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−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+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ411111111-11111-1-1-111111111-11111-1-1-111111111-11111-1-1-111111111-11111-1-1-111111111-11111-1-1-1
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+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−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ72222-1-1-1-1022-1-10002222-1-1-1-1022-1-10002222-1-1-1-1022-1-10002222-1-1-1-1022-1-10002222-1-1-1-1022-1-1000
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+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−i320002222-1-1-1-10−1−i3−1+i31+i321−i32000
χ1033-1-13-1-1-130000-10033-1-13-1-1-130000-10033-1-13-1-1-130000-10033-1-13-1-1-130000-10033-1-13-1-1-130000-100
χ1133-1-13-1-1-1-3000010033-1-13-1-1-1-3000010033-1-13-1-1-1-3000010033-1-13-1-1-1-3000010033-1-13-1-1-1-30000100
χ1266-2-2-31110000000066-2-2-31110000000066-2-2-31110000000066-2-2-31110000000066-2-2-311100000000
χ136-36-30000000000006-36-30000000000006-36-30000000000006-36-30000000000006-36-3000000000000
χ146-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+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+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+2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000
χ17111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ18111111111−1+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−i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32
χ19111111111−1−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+i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32
χ2011111111-11111-1-1-111111111-11111-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1111
χ2111111111-1−1+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+i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i32
χ2211111111-1−1−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−i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i32
χ232222-1-1-1-1022-1-10002222-1-1-1-1022-1-10002222-1-1-1-1022-1-1000-2-2-2-211110-2-211000-2-2-2-211110-2-211000
χ242222-1-1-1-10−1+i3−1−i31−i321+i320002222-1-1-1-10−1+i3−1−i31−i321+i320002222-1-1-1-10−1+i3−1−i31−i321+i32000-2-2-2-2111101−i31+i3−1+i32−1−i32000-2-2-2-2111101−i31+i3−1+i32−1−i32000
χ252222-1-1-1-10−1−i3−1+i31+i321−i320002222-1-1-1-10−1−i3−1+i31+i321−i320002222-1-1-1-10−1−i3−1+i31+i321−i32000-2-2-2-2111101+i31−i3−1−i32−1+i32000-2-2-2-2111101+i31−i3−1−i32−1+i32000
χ2633-1-13-1-1-130000-10033-1-13-1-1-130000-10033-1-13-1-1-130000-100-3-311-3111-30000100-3-311-3111-30000100
χ2733-1-13-1-1-1-3000010033-1-13-1-1-1-3000010033-1-13-1-1-1-30000100-3-311-311130000-100-3-311-311130000-100
χ2866-2-2-31110000000066-2-2-31110000000066-2-2-311100000000-6-6223-1-1-100000000-6-6223-1-1-100000000
χ296-36-30000000000006-36-30000000000006-36-3000000000000-63-63000000000000-63-63000000000000
χ306-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ500000000
χ316-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ800000000
χ326-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ700000000
χ3311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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+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
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−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
χ3611111111-11111-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111
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−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
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+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
χ392222-1-1-1-1022-1-10002222-1-1-1-1022-1-1000-2-2-2-211110-2-2110002222-1-1-1-1022-1-1000-2-2-2-211110-2-211000
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−i320002222-1-1-1-10−1+i3−1−i31−i321+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+i320002222-1-1-1-10−1−i3−1+i31+i321−i32000-2-2-2-2111101+i31−i3−1−i32−1+i32000
χ4233-1-13-1-1-130000-10033-1-13-1-1-130000-100-3-311-3111-3000010033-1-13-1-1-130000-100-3-311-3111-30000100
χ4333-1-13-1-1-1-3000010033-1-13-1-1-1-30000100-3-311-311130000-10033-1-13-1-1-1-30000100-3-311-311130000-100
χ4466-2-2-31110000000066-2-2-311100000000-6-6223-1-1-10000000066-2-2-311100000000-6-6223-1-1-100000000
χ456-36-30000000000006-36-3000000000000-63-630000000000006-36-3000000000000-63-63000000000000
χ466-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ500000000
χ476-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ800000000
χ486-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ700000000
χ4911111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ50111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−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+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+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−i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ5211111111-11111-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111111-11111-1-1-1
χ5311111111-1−1+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−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−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+i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ552222-1-1-1-1022-1-10002222-1-1-1-1022-1-1000-2-2-2-211110-2-211000-2-2-2-211110-2-2110002222-1-1-1-1022-1-1000
χ562222-1-1-1-10−1+i3−1−i31−i321+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−i320002222-1-1-1-10−1+i3−1−i31−i321+i32000
χ572222-1-1-1-10−1−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+i320002222-1-1-1-10−1−i3−1+i31+i321−i32000
χ5833-1-13-1-1-130000-10033-1-13-1-1-130000-100-3-311-3111-30000100-3-311-3111-3000010033-1-13-1-1-130000-100
χ5933-1-13-1-1-1-3000010033-1-13-1-1-1-30000100-3-311-311130000-100-3-311-311130000-10033-1-13-1-1-1-30000100
χ6066-2-2-31110000000066-2-2-311100000000-6-6223-1-1-100000000-6-6223-1-1-10000000066-2-2-311100000000
χ616-36-30000000000006-36-3000000000000-63-63000000000000-63-630000000000006-36-3000000000000
χ626-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000
χ636-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000
χ646-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000
χ652222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ66222222222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3-2-2-2-2-2-2-2-2-21−i31+i31−i31+i3-21−i31+i3000000000000000000000000000000000000000000000000
χ67222222222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3-2-2-2-2-2-2-2-2-21+i31−i31+i31−i3-21+i31−i3000000000000000000000000000000000000000000000000
χ6822222222-22222-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2222000000000000000000000000000000000000000000000000
χ6922222222-2−1+i3−1−i3−1+i3−1−i3-21−i31+i3-2-2-2-2-2-2-2-221−i31+i31−i31+i32−1+i3−1−i3000000000000000000000000000000000000000000000000
χ7022222222-2−1−i3−1+i3−1−i3−1+i3-21+i31−i3-2-2-2-2-2-2-2-221+i31−i31+i31−i32−1−i3−1+i3000000000000000000000000000000000000000000000000
χ714444-2-2-2-2044-2-2000-4-4-4-422220-4-422000000000000000000000000000000000000000000000000000
χ724444-2-2-2-20−2+2i3−2−2i31−i31+i3000-4-4-4-4222202−2i32+2i3−1+i3−1−i3000000000000000000000000000000000000000000000000000
χ734444-2-2-2-20−2−2i3−2+2i31+i31−i3000-4-4-4-4222202+2i32−2i3−1−i3−1+i3000000000000000000000000000000000000000000000000000
χ7466-2-26-2-2-260000-200-6-622-6222-60000200000000000000000000000000000000000000000000000000
χ7566-2-26-2-2-2-60000200-6-622-622260000-200000000000000000000000000000000000000000000000000
χ761212-4-4-622200000000-12-12446-2-2-200000000000000000000000000000000000000000000000000000000
χ7712-612-6000000000000-126-126000000000000000000000000000000000000000000000000000000000000
χ7812-6-4204ζ+4ζ84ζ2+4ζ74ζ4+4ζ500000000-1264-20−4ζ−4ζ8−4ζ2−4ζ7−4ζ4−4ζ500000000000000000000000000000000000000000000000000000000
χ7912-6-4204ζ2+4ζ74ζ4+4ζ54ζ+4ζ800000000-1264-20−4ζ2−4ζ7−4ζ4−4ζ5−4ζ−4ζ800000000000000000000000000000000000000000000000000000000
χ8012-6-4204ζ4+4ζ54ζ+4ζ84ζ2+4ζ700000000-1264-20−4ζ4−4ζ5−4ζ−4ζ8−4ζ2−4ζ700000000000000000000000000000000000000000000000000000000

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