Finite Group Databasebeta

← Group #72320545

Character table — Group #72320545

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size1111222222444444444444888888881616161616161616161616161616161616161616161616163232323232323232323232323232323211112222224444444444448888888816161616161616161616161616161616161616161616161632323232323232323232323232323232
order124422244444448888888816161616161616168888161616163232323232323232323232323232323222444488888816161616224422244444448888888816161616161616168888161616163232323232323232323232323232323222444488888816161616
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χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111111-1-1-1-1
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χ12622-2-2-2-22-222-2-22222-2-2-2-22200000000-222-20000−222−22−2−222−2−22−222−20000000000000000-2-22222-22-2-222-2-2-2-22222-2-2000000002-2-2200002−2−22−222−2−222−22−2−220000000000000000
χ12722-2-2-2-22-222-2-222-2-22222-2-222-2-2-2-222000000000000000000000000000000002-2-220000-2-22222-22-2-222-2-222-2-2-2-222-2-22222-2-200000000000000000000000000000000-222-20000
χ12822-2-2-2-22-222-2-222-2-22222-2-222-2-2-2-22200000000000000000000000000000000-222-20000-2-22222-22-2-222-2-222-2-2-2-222-2-22222-2-2000000000000000000000000000000002-2-220000
χ12922-2-2-2-22-222-2-222-2-22222-2-2-2-22222-2-200000000000000000000000020-20-220000000000-2-22222-22-2-222-2-222-2-2-2-22222-2-2-2-222000000000000000000000000-20202-20000000000
χ13022-2-2-2-22-222-2-222-2-22222-2-2-2-22222-2-2000000000000000000000000-20202-20000000000-2-22222-22-2-222-2-222-2-2-2-22222-2-2-2-22200000000000000000000000020-20-220000000000
χ13144444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000-4-4-4-4-4-4-4-4-4-4-4-4-4-444444444000000000000000000000000000000000000000000000000
χ1324444444444-4-4-4-4-4-4-4-44444000000000000000000000000000000000000000000000000-4-4-4-4-4-4-4-4-4-444444444-4-4-4-4000000000000000000000000000000000000000000000000
χ13344444-4-4-44-44i−4i4i−4i-44-44−4i4i−4i4i000000000000000000000000000000000000000000000000-4-4-4-4-4444-44−4i4i−4i4i4-44-44i−4i4i−4i000000000000000000000000000000000000000000000000
χ13444444-4-4-44-4−4i4i−4i4i-44-444i−4i4i−4i000000000000000000000000000000000000000000000000-4-4-4-4-4444-444i−4i4i−4i4-44-4−4i4i−4i4i000000000000000000000000000000000000000000000000
χ1358888-88-8-8-88000000000000000000000000000000000000000000000000000000000000-8-8-8-88-8888-8000000000000000000000000000000000000000000000000000000000000
χ1368888-8-888-8-8000000000000000000000000000000000000000000000000000000000000-8-8-8-888-8-888000000000000000000000000000000000000000000000000000000000000
χ13788-8-8888-8-8-8000000000000000000000000000000000000000000000000000000000000-8-888-8-8-8888000000000000000000000000000000000000000000000000000000000000
χ13888-8-88-8-88-88000000000000000000000000000000000000000000000000000000000000-8-888-888-88-8000000000000000000000000000000000000000000000000000000000000
χ13916-1616i−16i000000000000000000000000000000000000000000000000000000000000000000-1616−16i16i000000000000000000000000000000000000000000000000000000000000000000
χ14016-16−16i16i000000000000000000000000000000000000000000000000000000000000000000-161616i−16i000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.