Finite Group Databasebeta

← Group #10588317

Character table — Group #10588317

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size111111333333444444121212121212121212121212161616161616161616161616161616161616161616161616
order123366226666441212121244441212121212121212999999181818181818363636363636363636363636
χ1111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111−1−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
χ3111111111111111111111111111111−1+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
χ4111111111111-1-1-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ5111111111111-1-1-1-1-1-111-1-11111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32
χ6111111111111-1-1-1-1-1-111-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32
χ711−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34ζ14+ζ26ζ14+ζ26−ζ26−ζ26−ζ14−ζ14−ζ22−ζ22ζ22+ζ34ζ22+ζ34−ζ34−ζ34
χ811−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34−ζ26−ζ26−ζ14−ζ14ζ14+ζ26ζ14+ζ26−ζ34−ζ34−ζ22−ζ22ζ22+ζ34ζ22+ζ34
χ911−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22−ζ14−ζ14ζ14+ζ26ζ14+ζ26−ζ26−ζ26ζ22+ζ34ζ22+ζ34−ζ34−ζ34−ζ22−ζ22
χ1011−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34−ζ14−ζ26−ζ14−ζ26ζ26ζ26ζ14ζ14ζ22ζ22−ζ22−ζ34−ζ22−ζ34ζ34ζ34
χ1111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34ζ26ζ26ζ14ζ14−ζ14−ζ26−ζ14−ζ26ζ34ζ34ζ22ζ22−ζ22−ζ34−ζ22−ζ34
χ1211−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22ζ14ζ14−ζ14−ζ26−ζ14−ζ26ζ26ζ26−ζ22−ζ34−ζ22−ζ34ζ34ζ34ζ22ζ22
χ1311−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14−ζ22−ζ22−ζ34−ζ34ζ22+ζ34ζ22+ζ34−ζ26−ζ26ζ14+ζ26ζ14+ζ26−ζ14−ζ14
χ1411−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26ζ22+ζ34ζ22+ζ34−ζ22−ζ22−ζ34−ζ34ζ14+ζ26ζ14+ζ26−ζ14−ζ14−ζ26−ζ26
χ1511−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26−ζ34−ζ34ζ22+ζ34ζ22+ζ34−ζ22−ζ22−ζ14−ζ14−ζ26−ζ26ζ14+ζ26ζ14+ζ26
χ1611−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14ζ22ζ22ζ34ζ34−ζ22−ζ34−ζ22−ζ34ζ26ζ26−ζ14−ζ26−ζ14−ζ26ζ14ζ14
χ1711−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26−ζ22−ζ34−ζ22−ζ34ζ22ζ22ζ34ζ34−ζ14−ζ26−ζ14−ζ26ζ14ζ14ζ26ζ26
χ1811−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26ζ34ζ34−ζ22−ζ34−ζ22−ζ34ζ22ζ22ζ14ζ14ζ26ζ26−ζ14−ζ26−ζ14−ζ26
χ192-222-2-2-22-2-2222i−2i2i−2i2i−2i000000000000-1-1-1-1-1-1111111i−ii−ii−ii−ii−ii−i
χ202-222-2-2-22-2-2222i−2i2i−2i2i−2i0000000000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−ζ15ζ15−ζ15ζ15−ζ15ζ15−ζ3ζ3−ζ3ζ3−ζ3ζ3
χ212-222-2-2-22-2-2222i−2i2i−2i2i−2i0000000000001−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−ζ3ζ3−ζ3ζ3−ζ3ζ3−ζ15ζ15−ζ15ζ15−ζ15ζ15
χ222-222-2-2-22-2-222−2i2i−2i2i−2i2i000000000000-1-1-1-1-1-1111111−ii−ii−ii−ii−ii−ii
χ232-222-2-2-22-2-222−2i2i−2i2i−2i2i0000000000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32ζ15−ζ15ζ15−ζ15ζ15−ζ15ζ3−ζ3ζ3−ζ3ζ3−ζ3
χ242-222-2-2-22-2-222−2i2i−2i2i−2i2i0000000000001−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32ζ3−ζ3ζ3−ζ3ζ3−ζ3ζ15−ζ15ζ15−ζ15ζ15−ζ15
χ252-2−1−i3−1+i31+i31−i3-221+i31−i3−1−i3−1+i32i−2i−2ζ152ζ15−2ζ32ζ3000000000000−ζ14−ζ26ζ26ζ14ζ22−ζ22−ζ34ζ34ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34ζ23+ζ35−ζ23−ζ35−ζ35ζ35−ζ23ζ23−ζ31ζ31ζ7+ζ31−ζ7−ζ31−ζ7ζ7
χ262-2−1−i3−1+i31+i31−i3-221+i31−i3−1−i3−1+i32i−2i−2ζ152ζ15−2ζ32ζ3000000000000ζ26ζ14−ζ14−ζ26ζ34ζ22−ζ22−ζ34−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34−ζ35ζ35−ζ23ζ23ζ23+ζ35−ζ23−ζ35−ζ7ζ7−ζ31ζ31ζ7+ζ31−ζ7−ζ31
χ272-2−1−i3−1+i31+i31−i3-221+i31−i3−1−i3−1+i32i−2i−2ζ152ζ15−2ζ32ζ3000000000000ζ14−ζ14−ζ26ζ26−ζ22−ζ34ζ34ζ22−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22−ζ23ζ23ζ23+ζ35−ζ23−ζ35−ζ35ζ35ζ7+ζ31−ζ7−ζ31−ζ7ζ7−ζ31ζ31
χ282-2−1−i3−1+i31+i31−i3-221+i31−i3−1−i3−1+i3−2i2i2ζ15−2ζ152ζ3−2ζ3000000000000−ζ14−ζ26ζ26ζ14ζ22−ζ22−ζ34ζ34ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34−ζ23−ζ35ζ23+ζ35ζ35−ζ35ζ23−ζ23ζ31−ζ31−ζ7−ζ31ζ7+ζ31ζ7−ζ7
χ292-2−1−i3−1+i31+i31−i3-221+i31−i3−1−i3−1+i3−2i2i2ζ15−2ζ152ζ3−2ζ3000000000000ζ26ζ14−ζ14−ζ26ζ34ζ22−ζ22−ζ34−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34ζ35−ζ35ζ23−ζ23−ζ23−ζ35ζ23+ζ35ζ7−ζ7ζ31−ζ31−ζ7−ζ31ζ7+ζ31
χ302-2−1−i3−1+i31+i31−i3-221+i31−i3−1−i3−1+i3−2i2i2ζ15−2ζ152ζ3−2ζ3000000000000ζ14−ζ14−ζ26ζ26−ζ22−ζ34ζ34ζ22−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22ζ23−ζ23−ζ23−ζ35ζ23+ζ35ζ35−ζ35−ζ7−ζ31ζ7+ζ31ζ7−ζ7ζ31−ζ31
χ312-2−1+i3−1−i31−i31+i3-221−i31+i3−1+i3−1−i32i−2i−2ζ32ζ3−2ζ152ζ15000000000000ζ22ζ34−ζ22−ζ34ζ26−ζ14−ζ26ζ14−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14−ζ31ζ31−ζ7ζ7ζ7+ζ31−ζ7−ζ31−ζ35ζ35ζ23+ζ35−ζ23−ζ35−ζ23ζ23
χ322-2−1+i3−1−i31−i31+i3-221−i31+i3−1+i3−1−i32i−2i−2ζ32ζ3−2ζ152ζ15000000000000−ζ22−ζ34ζ22ζ34−ζ14−ζ26ζ14ζ26ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26ζ7+ζ31−ζ7−ζ31−ζ31ζ31−ζ7ζ7ζ23+ζ35−ζ23−ζ35−ζ23ζ23−ζ35ζ35
χ332-2−1+i3−1−i31−i31+i3-221−i31+i3−1+i3−1−i32i−2i−2ζ32ζ3−2ζ152ζ15000000000000ζ34−ζ22−ζ34ζ22ζ14ζ26−ζ14−ζ26−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26−ζ7ζ7ζ7+ζ31−ζ7−ζ31−ζ31ζ31−ζ23ζ23−ζ35ζ35ζ23+ζ35−ζ23−ζ35
χ342-2−1+i3−1−i31−i31+i3-221−i31+i3−1+i3−1−i3−2i2i2ζ3−2ζ32ζ15−2ζ15000000000000ζ22ζ34−ζ22−ζ34ζ26−ζ14−ζ26ζ14−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14ζ31−ζ31ζ7−ζ7−ζ7−ζ31ζ7+ζ31ζ35−ζ35−ζ23−ζ35ζ23+ζ35ζ23−ζ23
χ352-2−1+i3−1−i31−i31+i3-221−i31+i3−1+i3−1−i3−2i2i2ζ3−2ζ32ζ15−2ζ15000000000000−ζ22−ζ34ζ22ζ34−ζ14−ζ26ζ14ζ26ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26−ζ7−ζ31ζ7+ζ31ζ31−ζ31ζ7−ζ7−ζ23−ζ35ζ23+ζ35ζ23−ζ23ζ35−ζ35
χ362-2−1+i3−1−i31−i31+i3-221−i31+i3−1+i3−1−i3−2i2i2ζ3−2ζ32ζ15−2ζ15000000000000ζ34−ζ22−ζ34ζ22ζ14ζ26−ζ14−ζ26−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26ζ7−ζ7−ζ7−ζ31ζ7+ζ31ζ31−ζ31ζ23−ζ23ζ35−ζ35−ζ23−ζ35ζ23+ζ35
χ37333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ38333333333333-3-3-3-3-3-3-1-111-1-1-1-11111000000000000000000000000
χ3933−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3−3i32−3+3i32−3+3i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32000000000000000000000000
χ4033−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323+3i323−3i323−3i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32000000000000000000000000
χ4133−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3+3i32−3−3i32−3−3i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32000000000000000000000000
χ4233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323−3i323+3i323+3i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32000000000000000000000000
χ43666666-2-2-2-2-2-20000002-2002-22-20000000000000000000000000000
χ44666666-2-2-2-2-2-2000000-2200-22-220000000000000000000000000000
χ4566−3−3i3−3+3i3−3−3i3−3+3i3-2-21+i31−i31+i31−i30000002-200−1−i31+i3−1+i31−i30000000000000000000000000000
χ4666−3−3i3−3+3i3−3−3i3−3+3i3-2-21+i31−i31+i31−i3000000-22001+i3−1−i31−i3−1+i30000000000000000000000000000
χ4766−3+3i3−3−3i3−3+3i3−3−3i3-2-21−i31+i31−i31+i30000002-200−1+i31−i3−1−i31+i30000000000000000000000000000
χ4866−3+3i3−3−3i3−3+3i3−3−3i3-2-21−i31+i31−i31+i3000000-22001−i3−1+i31+i3−1−i30000000000000000000000000000
χ496-666-6-62-222-2-2000000002-200002-22-2000000000000000000000000
χ506-666-6-62-222-2-200000000-220000-22-22000000000000000000000000
χ516-6−3−3i3−3+3i33+3i33−3i32-2−1−i3−1+i31+i31−i3000000002-20000−1−i31+i3−1+i31−i3000000000000000000000000
χ526-6−3−3i3−3+3i33+3i33−3i32-2−1−i3−1+i31+i31−i300000000-2200001+i3−1−i31−i3−1+i3000000000000000000000000
χ536-6−3+3i3−3−3i33−3i33+3i32-2−1+i3−1−i31−i31+i3000000002-20000−1+i31−i3−1−i31+i3000000000000000000000000
χ546-6−3+3i3−3−3i33−3i33+3i32-2−1+i3−1−i31−i31+i300000000-2200001−i3−1+i31+i3−1−i3000000000000000000000000

Here ζ is a primitive root of unity of order 36 (ζ36 = 1); i = ζ9.