Finite Group Databasebeta

← Group #72276545

Character table — Group #72276545

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size123666669121224242736363691818181818273636727281108108481224242424243648489696108144144481224242424243648489696108144144
order1326918181823399266262618181818266181826633669181818633996663366918181863399666
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
χ1711111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ18111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i321−1+i32−1−i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i321−1+i32−1−i321−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i321−1−i32−1+i321−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i321−1−i32−1+i321
χ2011111111-11111-1-1-111111111-11111-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32
χ2111111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1−i321−1−i3211−i321+i32-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321−1+i321−1+i321+i32-11−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−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−1−i321−1−i321−i32-11+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1+i321−1+i3211+i321−i32-1
χ232222-1-1-1-1022-1-10002222-1-1-1-1022-1-1000−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i320−1+i3−1+i31−i321−i32000−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i320−1−i3−1−i31+i321+i32000
χ242222-1-1-1-10−1+i3−1−i31−i321+i320002222-1-1-1-10−1+i3−1−i31−i321+i32000−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i320−1−i321+i32-1000−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i3202−1+i3-11−i32000
χ252222-1-1-1-10−1−i3−1+i31+i321−i320002222-1-1-1-10−1−i3−1+i31+i321−i32000−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i3202−1−i3-11+i32000−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i320−1+i321−i32-1000
χ2633-1-13-1-1-130000-10033-1-13-1-1-130000-100−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i32−3+3i3200001−i3200−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i32−3−3i3200001+i3200
χ2733-1-13-1-1-1-3000010033-1-13-1-1-1-30000100−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i323−3i320000−1+i3200−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i323+3i320000−1−i3200
χ2866-2-2-31110000000066-2-2-311100000000−3+3i3−3+3i31−i31−i33−3i32−1+i32−1+i32−1+i3200000000−3−3i3−3−3i31+i31+i33+3i32−1−i32−1−i32−1−i3200000000
χ296-36-30000000000006-36-3000000000000−3+3i33−3i32−3+3i33−3i32000000000000−3−3i33+3i32−3−3i33+3i32000000000000
χ306-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000−3+3i33−3i321−i3−1+i3202ζ2+2ζ42ζ+2ζ52ζ7+2ζ800000000−3−3i33+3i321+i3−1−i3202ζ5+2ζ72ζ4+2ζ82ζ+2ζ200000000
χ316-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000−3+3i33−3i321−i3−1+i3202ζ+2ζ52ζ7+2ζ82ζ2+2ζ400000000−3−3i33+3i321+i3−1−i3202ζ4+2ζ82ζ+2ζ22ζ5+2ζ700000000
χ326-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000−3+3i33−3i321−i3−1+i3202ζ7+2ζ82ζ2+2ζ42ζ+2ζ500000000−3−3i33+3i321+i3−1−i3202ζ+2ζ22ζ5+2ζ72ζ4+2ζ800000000
χ3311111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i321−1+i32−1−i321−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i321−1+i32−1−i321
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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i321−1−i32−1+i321−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i321−1−i32−1+i321−1−i32
χ3611111111-11111-1-1-111111111-11111-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32
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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321−1+i321−1+i321+i32-11−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1−i321−1−i3211−i321+i32-1
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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1+i321−1+i3211+i321−i32-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−1−i321−1−i321−i32-11+i32
χ392222-1-1-1-1022-1-10002222-1-1-1-1022-1-1000−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i320−1−i3−1−i31+i321+i32000−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i320−1+i3−1+i31−i321−i32000
χ402222-1-1-1-10−1+i3−1−i31−i321+i320002222-1-1-1-10−1+i3−1−i31−i321+i32000−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i3202−1+i3-11−i32000−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i320−1−i321+i32-1000
χ412222-1-1-1-10−1−i3−1+i31+i321−i320002222-1-1-1-10−1−i3−1+i31+i321−i32000−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i320−1+i321−i32-1000−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i3202−1−i3-11+i32000
χ4233-1-13-1-1-130000-10033-1-13-1-1-130000-100−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i32−3−3i3200001+i3200−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i32−3+3i3200001−i3200
χ4333-1-13-1-1-1-3000010033-1-13-1-1-1-30000100−3−3i32−3−3i321+i321+i32−3−3i321+i321+i321+i323+3i320000−1−i3200−3+3i32−3+3i321−i321−i32−3+3i321−i321−i321−i323−3i320000−1+i3200
χ4466-2-2-31110000000066-2-2-311100000000−3−3i3−3−3i31+i31+i33+3i32−1−i32−1−i32−1−i3200000000−3+3i3−3+3i31−i31−i33−3i32−1+i32−1+i32−1+i3200000000
χ456-36-30000000000006-36-3000000000000−3−3i33+3i32−3−3i33+3i32000000000000−3+3i33−3i32−3+3i33−3i32000000000000
χ466-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000006-3-2102ζ+2ζ82ζ2+2ζ72ζ4+2ζ500000000−3−3i33+3i321+i3−1−i3202ζ5+2ζ72ζ4+2ζ82ζ+2ζ200000000−3+3i33−3i321−i3−1+i3202ζ2+2ζ42ζ+2ζ52ζ7+2ζ800000000
χ476-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000006-3-2102ζ2+2ζ72ζ4+2ζ52ζ+2ζ800000000−3−3i33+3i321+i3−1−i3202ζ4+2ζ82ζ+2ζ22ζ5+2ζ700000000−3+3i33−3i321−i3−1+i3202ζ+2ζ52ζ7+2ζ82ζ2+2ζ400000000
χ486-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000006-3-2102ζ4+2ζ52ζ+2ζ82ζ2+2ζ700000000−3−3i33+3i321+i3−1−i3202ζ+2ζ22ζ5+2ζ72ζ4+2ζ800000000−3+3i33−3i321−i3−1+i3202ζ7+2ζ82ζ2+2ζ42ζ+2ζ500000000
χ493333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
χ50333333333−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i3200000000000000000000000000000000
χ51333333333−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i3200000000000000000000000000000000
χ5233333333-33333-3-3-3-1-1-1-1-1-1-1-11-1-1-1-111100000000000000000000000000000000
χ5333333333-3−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i3200000000000000000000000000000000
χ5433333333-3−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i3200000000000000000000000000000000
χ556666-3-3-3-3066-3-3000-2-2-2-211110-2-21100000000000000000000000000000000000
χ566666-3-3-3-30−3+3i3−3−3i33−3i323+3i32000-2-2-2-2111101−i31+i3−1+i32−1−i3200000000000000000000000000000000000
χ576666-3-3-3-30−3−3i3−3+3i33+3i323−3i32000-2-2-2-2111101+i31−i3−1−i32−1+i3200000000000000000000000000000000000
χ5899-3-39-3-3-390000-300-3-311-3111-3000010000000000000000000000000000000000
χ5999-3-39-3-3-3-90000300-3-311-311130000-10000000000000000000000000000000000
χ601818-6-6-933300000000-6-6223-1-1-10000000000000000000000000000000000000000
χ6118-918-9000000000000-63-6300000000000000000000000000000000000000000000
χ6218-9-6306ζ+6ζ86ζ2+6ζ76ζ4+6ζ500000000-632-10−2ζ−2ζ8−2ζ2−2ζ7−2ζ4−2ζ50000000000000000000000000000000000000000
χ6318-9-6306ζ2+6ζ76ζ4+6ζ56ζ+6ζ800000000-632-10−2ζ2−2ζ7−2ζ4−2ζ5−2ζ−2ζ80000000000000000000000000000000000000000
χ6418-9-6306ζ4+6ζ56ζ+6ζ86ζ2+6ζ700000000-632-10−2ζ4−2ζ5−2ζ−2ζ8−2ζ2−2ζ70000000000000000000000000000000000000000

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