Finite Group Databasebeta

← Group #72254117

Character table — Group #72254117

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444448888888888888888888888881616161616161616161616161616161616161616161616161616161616162424242424242424484848484848484848484848
order122222344446661212121222222244444466121222446666666666121212121212121212124444448888121212121212121212121212242424242424242422222244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
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χ1111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-11111-111-1-1-11111-1-1-1−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii
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χ914-44-4-444-444-4-4-44-4-4440000000000004-44-400000000000000000000000000000000000000000000000000000000004-400000000000000
χ924-44-4-444-444-4-4-44-4-4440000000000004-44-40000000000000000000000000000000000000000000000000000000000-4400000000000000
χ938888-8-8-48-88-8-4-4-4-4-4-4-4000000000000444400000000000000000000000000000000000000000000000000000000000000000000000000
χ948888-8-8-4-88-88-4-4-4444400000000000044-4-400000000000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-800800008-8-800000000000000000000004i−4i0000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000000
χ9688-8-800800008-8-80000000000000000000000−4i4i000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000
χ9788-8-800-40000-44443−4343−430000000000000000004i−4i00000−2i32i3−2i32i3000000−2i2i−2i2i000000000000000000000000000000000000000000000000000
χ9888-8-800-40000-44443−4343−43000000000000000000−4i4i000002i3−2i32i3−2i30000002i−2i2i−2i000000000000000000000000000000000000000000000000000
χ9988-8-800-40000-444−4343−43430000000000000000004i−4i000002i3−2i32i3−2i3000000−2i2i−2i2i000000000000000000000000000000000000000000000000000
χ10088-8-800-40000-444−4343−4343000000000000000000−4i4i00000−2i32i3−2i32i30000002i−2i2i−2i000000000000000000000000000000000000000000000000000
χ1018-88-8-88-48-8-8844-4-4-444000000000000-444-400000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-88-4-888-844-444-4-4000000000000-44-4400000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-880080000-88-8000000000000000000004-400000004-4-440000000000000000000000000000000000000000000000000000000000000
χ1048-8-880080000-88-800000000000000000000-440000000-444-40000000000000000000000000000000000000000000000000000000000000
χ1058-8-8800-400004-4443−43−434300000000000000004-40000000-222-200000023−23−2323000000000000000000000000000000000000000000000000000
χ1068-8-8800-400004-4443−43−43430000000000000000-4400000002-2-22000000−232323−23000000000000000000000000000000000000000000000000000
χ1078-8-8800-400004-44−434343−4300000000000000004-40000000-222-2000000−232323−23000000000000000000000000000000000000000000000000000
χ1088-8-8800-400004-44−434343−430000000000000000-4400000002-2-2200000023−23−2323000000000000000000000000000000000000000000000000000

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