Finite Group Databasebeta

← Group #72246932

Character table — Group #72246932

Order 3024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1122222444444666699121212121833666661212121212121818181827273636363654336666612121212121218181818272736363636547714141414142828282828284242424263638484848412677141414141428282828282842424242636384848484126
order12334663612121212222222666647142121284242214284848484141414141414424242422871421212842422142848484841414141414144242424228363312663612121212666666666612363312663612121212666666666612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111-1-1-1-111-1-1-1111111111111111-1-1-1-111-1-1-1111111111111111-1-1-1-111-1-1-1111111111111111-1-1-1-111-1-1-1111111111111111-1-1-1-111-1-1-1
χ31111111111111-1-111-1-1-1-111-11111111111111-1-111-1-1-1-111-11111111111111-1-111-1-1-1-111-11111111111111-1-111-1-1-1-111-11111111111111-1-111-1-1-1-111-1
χ41111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-11
χ51111-11111-1-1-1-11-11-1111-11-1-11111-11111-1-1-1-11-11-1111-11-1-11111-11111-1-1-1-11-11-1111-11-1-11111-11111-1-1-1-11-11-1111-11-1-11111-11111-1-1-1-11-11-1111-11-1-1
χ61111-11111-1-1-1-11-1-11-1-11-1-1111111-11111-1-1-1-11-1-11-1-11-1-1111111-11111-1-1-1-11-1-11-1-11-1-1111111-11111-1-1-1-11-1-11-1-11-1-1111111-11111-1-1-1-11-1-11-1-11-1-111
χ71111-11111-1-1-1-1-111-1-1-1-111-111111-11111-1-1-1-1-111-1-1-1-111-111111-11111-1-1-1-1-111-1-1-1-111-111111-11111-1-1-1-1-111-1-1-1-111-111111-11111-1-1-1-1-111-1-1-1-111-11
χ81111-11111-1-1-1-1-11-1111-11-11-11111-11111-1-1-1-1-11-1111-11-11-11111-11111-1-1-1-1-11-1111-11-11-11111-11111-1-1-1-1-11-1111-11-11-11111-11111-1-1-1-1-11-1111-11-11-1
χ9222-122-1-1-12-1-1-100220000-1-10222-122-1-1-12-1-1-100220000-1-10222-122-1-1-12-1-1-100220000-1-10222-122-1-1-12-1-1-100220000-1-10222-122-1-1-12-1-1-100220000-1-10
χ10222-122-1-1-12-1-1-100-2-20000110222-122-1-1-12-1-1-100-2-20000110222-122-1-1-12-1-1-100-2-20000110222-122-1-1-12-1-1-100-2-20000110222-122-1-1-12-1-1-100-2-20000110
χ11222-1-22-1-1-1-2111002-20000-110222-1-22-1-1-1-2111002-20000-110222-1-22-1-1-1-2111002-20000-110222-1-22-1-1-1-2111002-20000-110222-1-22-1-1-1-2111002-20000-110
χ12222-1-22-1-1-1-211100-2200001-10222-1-22-1-1-1-211100-2200001-10222-1-22-1-1-1-211100-2200001-10222-1-22-1-1-1-211100-2200001-10222-1-22-1-1-1-211100-2200001-10
χ1322-122-12-1-1-12-1-1220000-1-100022-122-12-1-1-12-1-1220000-1-100022-122-12-1-1-12-1-1220000-1-100022-122-12-1-1-12-1-1220000-1-100022-122-12-1-1-12-1-1220000-1-1000
χ1422-122-12-1-1-12-1-1-2-200001100022-122-12-1-1-12-1-1-2-200001100022-122-12-1-1-12-1-1-2-200001100022-122-12-1-1-12-1-1-2-200001100022-122-12-1-1-12-1-1-2-2000011000
χ1522-12-2-12-1-11-2112-20000-1100022-12-2-12-1-11-2112-20000-1100022-12-2-12-1-11-2112-20000-1100022-12-2-12-1-11-2112-20000-1100022-12-2-12-1-11-2112-20000-11000
χ1622-12-2-12-1-11-211-2200001-100022-12-2-12-1-11-211-2200001-100022-12-2-12-1-11-211-2200001-100022-12-2-12-1-11-211-2200001-100022-12-2-12-1-11-211-2200001-1000
χ172-2220-2-22-2000000002-2000002-2220-2-22-2000000002-2000002-2220-2-22-2000000002-2000002-2220-2-22-2000000002-2000002-2220-2-22-2000000002-200000
χ182-2220-2-22-200000000-22000002-2220-2-22-200000000-22000002-2220-2-22-200000000-22000002-2220-2-22-200000000-22000002-2220-2-22-200000000-2200000
χ1944-2-24-2-211-2-2110000000000044-2-24-2-211-2-2110000000000044-2-24-2-211-2-2110000000000044-2-24-2-211-2-2110000000000044-2-24-2-211-2-21100000000000
χ2044-2-2-4-2-21122-1-10000000000044-2-2-4-2-21122-1-10000000000044-2-2-4-2-21122-1-10000000000044-2-2-4-2-21122-1-10000000000044-2-2-4-2-21122-1-100000000000
χ214-44-20-42-220000000000000004-44-20-42-220000000000000004-44-20-42-220000000000000004-44-20-42-220000000000000004-44-20-42-22000000000000000
χ224-4-2402-4-220000000000000004-4-2402-4-220000000000000004-4-2402-4-220000000000000004-4-2402-4-220000000000000004-4-2402-4-22000000000000000
χ234-4-2-20221-1003i−3i000000000004-4-2-20221-1003i−3i000000000004-4-2-20221-1003i−3i000000000004-4-2-20221-1003i−3i000000000004-4-2-20221-1003i−3i00000000000
χ244-4-2-20221-100−3i3i000000000004-4-2-20221-100−3i3i000000000004-4-2-20221-100−3i3i000000000004-4-2-20221-100−3i3i000000000004-4-2-20221-100−3i3i00000000000
χ25111111111111111111111111111111111111111111111111111111111111111111111111−1+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−i32−1−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
χ26111111111111111-1-1-1-111-1-1-1111111111111111-1-1-1-111-1-1-1111111111111111-1-1-1-111-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−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−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32
χ271111111111111-1-111-1-1-1-111-11111111111111-1-111-1-1-1-111-11111111111111-1-111-1-1-1-111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−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−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32
χ281111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−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−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32
χ291111-11111-1-1-1-11-11-1111-11-1-11111-11111-1-1-1-11-11-1111-11-1-11111-11111-1-1-1-11-11-1111-11-1-1−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32
χ301111-11111-1-1-1-11-1-11-1-11-1-1111111-11111-1-1-1-11-1-11-1-11-1-1111111-11111-1-1-1-11-1-11-1-11-1-111−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32
χ311111-11111-1-1-1-1-111-1-1-1-111-111111-11111-1-1-1-1-111-1-1-1-111-111111-11111-1-1-1-1-111-1-1-1-111-11−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ321111-11111-1-1-1-1-11-1111-11-11-11111-11111-1-1-1-1-11-1111-11-11-11111-11111-1-1-1-1-11-1111-11-11-1−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i32
χ33222-122-1-1-12-1-1-100220000-1-10222-122-1-1-12-1-1-100220000-1-10222-122-1-1-12-1-1-100220000-1-10−1+i3−1+i3−1+i31−i32−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i3200−1+i3−1+i300001−i321−i320−1−i3−1−i3−1−i31+i32−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i3200−1−i3−1−i300001+i321+i320
χ34222-122-1-1-12-1-1-100-2-20000110222-122-1-1-12-1-1-100-2-20000110222-122-1-1-12-1-1-100-2-20000110−1+i3−1+i3−1+i31−i32−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i32001−i31−i30000−1+i32−1+i320−1−i3−1−i3−1−i31+i32−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i32001+i31+i30000−1−i32−1−i320
χ35222-1-22-1-1-1-2111002-20000-110222-1-22-1-1-1-2111002-20000-110222-1-22-1-1-1-2111002-20000-110−1+i3−1+i3−1+i31−i321−i3−1+i31−i321−i321−i321−i3−1+i32−1+i32−1+i3200−1+i31−i300001−i32−1+i320−1−i3−1−i3−1−i31+i321+i3−1−i31+i321+i321+i321+i3−1−i32−1−i32−1−i3200−1−i31+i300001+i32−1−i320
χ36222-1-22-1-1-1-211100-2200001-10222-1-22-1-1-1-211100-2200001-10222-1-22-1-1-1-211100-2200001-10−1+i3−1+i3−1+i31−i321−i3−1+i31−i321−i321−i321−i3−1+i32−1+i32−1+i32001−i3−1+i30000−1+i321−i320−1−i3−1−i3−1−i31+i321+i3−1−i31+i321+i321+i321+i3−1−i32−1−i32−1−i32001+i3−1−i30000−1−i321+i320
χ3722-122-12-1-1-12-1-1220000-1-100022-122-12-1-1-12-1-1220000-1-100022-122-12-1-1-12-1-1220000-1-1000−1+i3−1+i31−i32−1+i3−1+i31−i32−1+i31−i321−i321−i32−1+i31−i321−i32−1+i3−1+i300001−i321−i32000−1−i3−1−i31+i32−1−i3−1−i31+i32−1−i31+i321+i321+i32−1−i31+i321+i32−1−i3−1−i300001+i321+i32000
χ3822-122-12-1-1-12-1-1-2-200001100022-122-12-1-1-12-1-1-2-200001100022-122-12-1-1-12-1-1-2-2000011000−1+i3−1+i31−i32−1+i3−1+i31−i32−1+i31−i321−i321−i32−1+i31−i321−i321−i31−i30000−1+i32−1+i32000−1−i3−1−i31+i32−1−i3−1−i31+i32−1−i31+i321+i321+i32−1−i31+i321+i321+i31+i30000−1−i32−1−i32000
χ3922-12-2-12-1-11-2112-20000-1100022-12-2-12-1-11-2112-20000-1100022-12-2-12-1-11-2112-20000-11000−1+i3−1+i31−i32−1+i31−i31−i32−1+i31−i321−i32−1+i321−i3−1+i32−1+i32−1+i31−i300001−i32−1+i32000−1−i3−1−i31+i32−1−i31+i31+i32−1−i31+i321+i32−1−i321+i3−1−i32−1−i32−1−i31+i300001+i32−1−i32000
χ4022-12-2-12-1-11-211-2200001-100022-12-2-12-1-11-211-2200001-100022-12-2-12-1-11-211-2200001-1000−1+i3−1+i31−i32−1+i31−i31−i32−1+i31−i321−i32−1+i321−i3−1+i32−1+i321−i3−1+i30000−1+i321−i32000−1−i3−1−i31+i32−1−i31+i31+i32−1−i31+i321+i32−1−i321+i3−1−i32−1−i321+i3−1−i30000−1−i321+i32000
χ412-2220-2-22-2000000002-2000002-2220-2-22-2000000002-2000002-2220-2-22-2000000002-200000−1+i31−i3−1+i3−1+i301−i31−i3−1+i31−i300000000−1+i31−i300000−1−i31+i3−1−i3−1−i301+i31+i3−1−i31+i300000000−1−i31+i300000
χ422-2220-2-22-200000000-22000002-2220-2-22-200000000-22000002-2220-2-22-200000000-2200000−1+i31−i3−1+i3−1+i301−i31−i3−1+i31−i3000000001−i3−1+i300000−1−i31+i3−1−i3−1−i301+i31+i3−1−i31+i3000000001+i3−1−i300000
χ4344-2-24-2-211-2-2110000000000044-2-24-2-211-2-2110000000000044-2-24-2-211-2-21100000000000−2+2i3−2+2i31−i31−i3−2+2i31−i31−i3−1+i32−1+i321−i31−i3−1+i32−1+i3200000000000−2−2i3−2−2i31+i31+i3−2−2i31+i31+i3−1−i32−1−i321+i31+i3−1−i32−1−i3200000000000
χ4444-2-2-4-2-21122-1-10000000000044-2-2-4-2-21122-1-10000000000044-2-2-4-2-21122-1-100000000000−2+2i3−2+2i31−i31−i32−2i31−i31−i3−1+i32−1+i32−1+i3−1+i31−i321−i3200000000000−2−2i3−2−2i31+i31+i32+2i31+i31+i3−1−i32−1−i32−1−i3−1−i31+i321+i3200000000000
χ454-44-20-42-220000000000000004-44-20-42-220000000000000004-44-20-42-22000000000000000−2+2i32−2i3−2+2i31−i302−2i3−1+i31−i3−1+i3000000000000000−2−2i32+2i3−2−2i31+i302+2i3−1−i31+i3−1−i3000000000000000
χ464-4-2402-4-220000000000000004-4-2402-4-220000000000000004-4-2402-4-22000000000000000−2+2i32−2i31−i3−2+2i30−1+i32−2i31−i3−1+i3000000000000000−2−2i32+2i31+i3−2−2i30−1−i32+2i31+i3−1−i3000000000000000
χ474-4-2-20221-1003i−3i000000000004-4-2-20221-1003i−3i000000000004-4-2-20221-1003i−3i00000000000−2+2i32−2i31−i31−i30−1+i3−1+i3−1+i321−i32003ζ19+3ζ31+3ζ43+3ζ55+3ζ67+3ζ79−3ζ19−3ζ31−3ζ43−3ζ55−3ζ67−3ζ7900000000000−2−2i32+2i31+i31+i30−1−i3−1−i3−1−i321+i32003ζ11+3ζ23+3ζ47+3ζ59+3ζ71+3ζ83−3ζ11−3ζ23−3ζ47−3ζ59−3ζ71−3ζ8300000000000
χ484-4-2-20221-100−3i3i000000000004-4-2-20221-100−3i3i000000000004-4-2-20221-100−3i3i00000000000−2+2i32−2i31−i31−i30−1+i3−1+i3−1+i321−i3200−3ζ19−3ζ31−3ζ43−3ζ55−3ζ67−3ζ793ζ19+3ζ31+3ζ43+3ζ55+3ζ67+3ζ7900000000000−2−2i32+2i31+i31+i30−1−i3−1−i3−1−i321+i3200−3ζ11−3ζ23−3ζ47−3ζ59−3ζ71−3ζ833ζ11+3ζ23+3ζ47+3ζ59+3ζ71+3ζ8300000000000
χ49111111111111111111111111111111111111111111111111111111111111111111111111−1−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+i32−1+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
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.