Finite Group Databasebeta

← Group #13175872

Character table — Group #13175872

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135
size1111222222222222222222224444444444444444444444444444466668888888888888888888888888888888888121212121212121212121212121212121212181818182424242424242424363636363636545454547272108108
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1111-1-11111-11-1-1
χ611111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11-1-1-111-1-1-1-11-111
χ711111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1111-1-1-1-1-1-1-1111
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χ10111111111111111111111111-111111-1111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-11-1-111-1-111-11-11
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χ1922222222-1-1222222222222-1-12-1-1-1-1-2-2-1-1-1-1-1-1-1-1-1-1-1-111-2-2-2-2-2-2-2-200002222-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111100000000000000000022-2-200000000-22-1-11100001-100
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χ572-22-222222-22-22-22-22-2-2-2-2-2-220222200-2-2-2-22-22-22-22-20000000000002i−2i0000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000002-20000000000002-2002i−2i0000
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χ794444-2-2-24-2-2-2-2-2-2-2-244-2-2-24-2-2-4111-24-4111-2111111-2-222-2-2-2-2-2-2440000222-42-1-1-1-1-1-122222-4-2111111-2-2-1-1-1-1-1-12200000000000000000000000000000000000000000000
χ804444-2-2-24-2-2-2-2-2-2-2-244-2-2-24-2-2-4111-2-44111-2111111-2-2-2-2222222-4-40000222-42-1-1-1-1-1-122-2-2-242-1-1-1-1-1-122111111-2-200000000000000000000000000000000000000000000
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χ9344-4-4-24-2-2-2222-4-42222-24-2-2-2201-211001-211-1-122-1-1-1-123−23−232300−232323−23000000000-3300-333-3000003−3003−3−33−3323−23−33−3300000000000000000000000000000000000000000000
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χ9944-4-4-2-24-2-222222-4-422-2-24-2-22011-210011-21-1-1-1-122-1-123−23−232323−2300−2323000000000-333-300-33000003−3−33003−3−33−3323−23−3300000000000000000000000000000000000000000000
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χ1084-44-44444-224-44-44-44-4-4-4-4-42-20-2-2-2-2002222-22-22-22-22000000000000000000000000000000000000000000000000000000000000000000004-4000000000000-2200000000
χ1094-44-44444-224-44-44-44-4-4-4-4-42-20-2-2-2-2002222-22-22-22-2200000000000000000000000000000000000000000000000000000000000000000000-440000000000002-200000000
χ1104-44-44-2-2-24-44-4-22-22-22-4222-4404-2-2-200-42224-4-22-22-220000000000004i−4i0000000000000000000000000000000000004i−4i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ1114-44-44-2-2-24-44-4-22-22-22-4222-4404-2-2-200-42224-4-22-22-22000000000000−4i4i000000000000000000000000000000000000−4i4i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ1124-44-4-24-2-24-4-224-4-22-222-422-440-24-2-2002-422-224-4-22-220000000000004i−4i000000000000000000000000000000000000−2i2i4i−4i−2i2i−2i2i0000000000000000000000000000000000
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χ1144-44-4-2-24-24-4-22-224-4-2222-42-440-2-24-20022-42-22-224-4-220000000000004i−4i000000000000000000000000000000000000−2i2i−2i2i4i−4i−2i2i0000000000000000000000000000000000
χ1154-44-4-2-24-24-4-22-224-4-2222-42-440-2-24-20022-42-22-224-4-22000000000000−4i4i0000000000000000000000000000000000002i−2i2i−2i−4i4i2i−2i0000000000000000000000000000000000
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χ1184-4-444444-2-2-44-44-44-44-4-4-4-4220-2-2-2-20022222-22-22-22-20000000000000000000000000000000000000000000000000000000000000000004i−4i000000000000−2i2i0000000000
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χ1204-4-444-2-2-244-442-22-22-2-4222-4-404-2-2-200-4222-442-22-22-200000000004i−4i00000000000000000000000000000000000000000000004i−4i−2i2i−2i2i−2i2i00000000000000000000000000
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χ1254-4-44-2-24-2442-22-2-442-222-42-4-40-2-24-20022-422-22-2-442-20000000000−4i4i00000000000000000000000000000000000000000000002i−2i2i−2i−4i4i2i−2i00000000000000000000000000
χ1264-4-44-2-2-24442-22-22-2-44222-4-4-40-2-2-2400222-42-22-22-2-4400000000004i−4i0000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i4i−4i00000000000000000000000000
χ1274-4-44-2-2-24442-22-22-2-44222-4-4-40-2-2-2400222-42-22-22-2-440000000000−4i4i00000000000000000000000000000000000000000000002i−2i2i−2i2i−2i−4i4i00000000000000000000000000
χ1288-88-88-4-4-4-448-8-44-44-44-84444-40-4222004-2-2-2-442-22-22-200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1298-88-8-48-4-4-44-448-8-44-444-8444-402-42200-24-2-22-2-442-22-200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1308-88-8-4-48-4-44-44-448-8-4444-844-4022-4200-2-24-22-22-2-442-200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1318-88-8-4-4-48-44-44-44-448-8444-84-40222-400-2-2-242-22-22-2-4400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1328-8-888-4-4-4-4-4-884-44-44-4-8444440-4222004-2-2-24-4-22-22-2200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1338-8-88-48-4-4-4-44-4-884-44-44-8444402-42200-24-2-2-224-4-22-2200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1348-8-88-4-48-4-4-44-44-4-884-444-8444022-4200-2-24-2-22-224-4-2200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1358-8-88-4-4-48-4-44-44-44-4-88444-8440222-400-2-2-24-22-22-224-400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).