Finite Group Databasebeta

← Group #72321268

Character table — Group #72321268

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152
size11112222222222222222224444444444444444444444444444444444444444444444888888888888888888888888888888888888161616161616161616161616161616161616161616161616161616161616161664646464646464646464646464646464
order12442224448888161616161616161622444444888888888816161616161616161616161632323232323232323232323232323232448816161616161616163232323232323232323232323232323232323232323232326464646464646464646464646464646464646464646464646464646464646464888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111111111-1-1-1-1111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111111111-1-1-1-1111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111111111-1-1-1-1111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111111111111111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111111111111111111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ111111111111111111111111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ121111111111111111111111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ131111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
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χ161111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
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χ12944-4-4-44-444-4-4-4444444-4-4-4-400004i−4i−4i4i40000-44i−4i4i−4i-4-4000000004400000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ13044-4-4-44-444-4-4-4444444-4-4-4-40000−4i4i4i−4i40000-4−4i4i−4i4i-4-40000000044000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ13144-4-4-4-44-44444-4-400000000000044-4-440000-4-444-40000000000002222−22−22−22−222222−22−2222222222−22−220000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000000000000000
χ13244-4-4-4-44-44444-4-400000000000044-4-440000-4-444-4000000000000−22−2222222222−22−222222−22−22−22−22222200000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000000000000000
χ13344-4-4-4-44-44444-4-4000000000000-4-44440000-44-4-440000000000002222−22−22−22−222222−22−2222222222−22−2200000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000000000000000
χ13444-4-4-4-44-44444-4-4000000000000-4-44440000-44-4-44000000000000−22−2222222222−22−222222−22−22−22−2222220000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000000000000000
χ13544-4-4-4-44-444-4-4444444-4-4-4-4000044-4-4-4000044-4-444400000000-4-400000000000000000000-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ13644-4-4-4-44-444-4-4444444-4-4-4-40000-4-444-400004-444-44400000000-4-4000000000000000000004-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ1378-88i−8i0000004i2−4i242−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ54ζ3+4ζ5−4ζ3−4ζ54ζ+4ζ7−4ζ−4ζ74-44i−4i000004ζ2−4ζ24ζ6−4ζ600000004ζ−4ζ4ζ5−4ζ54ζ7−4ζ74ζ3−4ζ3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1388-88i−8i0000004i2−4i242−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ54ζ3+4ζ5−4ζ3−4ζ54ζ+4ζ7−4ζ−4ζ7-44−4i4i00000−4ζ24ζ2−4ζ64ζ60000000−4ζ4ζ−4ζ54ζ5−4ζ74ζ7−4ζ34ζ3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1398-88i−8i0000004i2−4i242−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ5−4ζ3−4ζ54ζ3+4ζ5−4ζ−4ζ74ζ+4ζ74-44i−4i000004ζ2−4ζ24ζ6−4ζ60000000−4ζ4ζ−4ζ54ζ5−4ζ74ζ7−4ζ34ζ3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1408-88i−8i0000004i2−4i242−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ5−4ζ3−4ζ54ζ3+4ζ5−4ζ−4ζ74ζ+4ζ7-44−4i4i00000−4ζ24ζ2−4ζ64ζ600000004ζ−4ζ4ζ5−4ζ54ζ7−4ζ74ζ3−4ζ3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1418-88i−8i000000−4i24i2−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ74ζ+4ζ7−4ζ−4ζ7−4ζ3−4ζ54ζ3+4ζ54-44i−4i00000−4ζ24ζ2−4ζ64ζ60000000−4ζ54ζ54ζ−4ζ−4ζ34ζ34ζ7−4ζ7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1428-88i−8i000000−4i24i2−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ74ζ+4ζ7−4ζ−4ζ7−4ζ3−4ζ54ζ3+4ζ5-44−4i4i000004ζ2−4ζ24ζ6−4ζ600000004ζ5−4ζ5−4ζ4ζ4ζ3−4ζ3−4ζ74ζ7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1438-88i−8i000000−4i24i2−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ7−4ζ−4ζ74ζ+4ζ74ζ3+4ζ5−4ζ3−4ζ54-44i−4i00000−4ζ24ζ2−4ζ64ζ600000004ζ5−4ζ5−4ζ4ζ4ζ3−4ζ3−4ζ74ζ7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1448-88i−8i000000−4i24i2−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ7−4ζ−4ζ74ζ+4ζ74ζ3+4ζ5−4ζ3−4ζ5-44−4i4i000004ζ2−4ζ24ζ6−4ζ60000000−4ζ54ζ54ζ−4ζ−4ζ34ζ34ζ7−4ζ7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1458-8−8i8i0000004i2−4i2−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ7−4ζ−4ζ74ζ+4ζ74ζ3+4ζ5−4ζ3−4ζ54-4−4i4i000004ζ6−4ζ64ζ2−4ζ200000004ζ3−4ζ3−4ζ74ζ74ζ5−4ζ5−4ζ4ζ000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1468-8−8i8i0000004i2−4i2−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ7−4ζ−4ζ74ζ+4ζ74ζ3+4ζ5−4ζ3−4ζ5-444i−4i00000−4ζ64ζ6−4ζ24ζ20000000−4ζ34ζ34ζ7−4ζ7−4ζ54ζ54ζ−4ζ000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1478-8−8i8i0000004i2−4i2−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ74ζ+4ζ7−4ζ−4ζ7−4ζ3−4ζ54ζ3+4ζ54-4−4i4i000004ζ6−4ζ64ζ2−4ζ20000000−4ζ34ζ34ζ7−4ζ7−4ζ54ζ54ζ−4ζ000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1488-8−8i8i0000004i2−4i2−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ74ζ+4ζ7−4ζ−4ζ7−4ζ3−4ζ54ζ3+4ζ5-444i−4i00000−4ζ64ζ6−4ζ24ζ200000004ζ3−4ζ3−4ζ74ζ74ζ5−4ζ5−4ζ4ζ000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1498-8−8i8i000000−4i24i242−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ5−4ζ3−4ζ54ζ3+4ζ5−4ζ−4ζ74ζ+4ζ74-4−4i4i00000−4ζ64ζ6−4ζ24ζ20000000−4ζ74ζ7−4ζ34ζ3−4ζ4ζ−4ζ54ζ5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1508-8−8i8i000000−4i24i242−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ5−4ζ3−4ζ54ζ3+4ζ5−4ζ−4ζ74ζ+4ζ7-444i−4i000004ζ6−4ζ64ζ2−4ζ200000004ζ7−4ζ74ζ3−4ζ34ζ−4ζ4ζ5−4ζ5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1518-8−8i8i000000−4i24i242−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ54ζ3+4ζ5−4ζ3−4ζ54ζ+4ζ7−4ζ−4ζ74-4−4i4i00000−4ζ64ζ6−4ζ24ζ200000004ζ7−4ζ74ζ3−4ζ34ζ−4ζ4ζ5−4ζ5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1528-8−8i8i000000−4i24i242−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ54ζ3+4ζ5−4ζ3−4ζ54ζ+4ζ7−4ζ−4ζ7-444i−4i000004ζ6−4ζ64ζ2−4ζ20000000−4ζ74ζ7−4ζ34ζ3−4ζ4ζ−4ζ54ζ5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.