Finite Group Databasebeta

← Group #72320758

Character table — Group #72320758

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size1122222222244444444444888888881616161616161616161616161616161616161616161616163232323232323232323232323232323211222222222444444444448888888816161616161616161616161616161616161616161616161632323232323232323232323232323232
order122224444884444888888816161616161616168888161616163232323232323232323232323232323222244488888816161616222224444884444888888816161616161616168888161616163232323232323232323232323232323222244488888816161616
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χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
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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χ12722-2-22-2-222-2-2-2-222-22222-2-222-2-2-2-222000000000000000000000000000000002-2-220000-2-222-222-2-22222-2-22-2-2-2-222-2-22222-2-200000000000000000000000000000000-222-20000
χ12822-2-22-2-222-2-2-2-222-22222-2-222-2-2-2-22200000000000000000000000000000000-222-20000-2-222-222-2-22222-2-22-2-2-2-222-2-22222-2-2000000000000000000000000000000002-2-220000
χ12922-2-22-2-222-2-2-2-222-22222-2-2-2-22222-2-20000000000000000000000002-200-220000000000-2-222-222-2-22222-2-22-2-2-2-22222-2-2-2-222000000000000000000000000-22002-20000000000
χ13022-2-22-2-222-2-2-2-222-22222-2-2-2-22222-2-2000000000000000000000000-22002-20000000000-2-222-222-2-22222-2-22-2-2-2-22222-2-2-2-2220000000000000000000000002-200-220000000000
χ131444444444-4-44444-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000-4-4-4-4-4-4-4-4-444-4-4-4-44444444000000000000000000000000000000000000000000000000
χ132444444444-4-4-4-4-4-4-4-4-44444000000000000000000000000000000000000000000000000-4-4-4-4-4-4-4-4-4444444444-4-4-4-4000000000000000000000000000000000000000000000000
χ13344-44-4-444-4444i−4i−4i4i-4-444i−4i−4i4i000000000000000000000000000000000000000000000000-4-44-444-4-44-4-4−4i4i4i−4i44-4−4i4i4i−4i000000000000000000000000000000000000000000000000
χ13444-44-4-444-444−4i4i4i−4i-4-44−4i4i4i−4i000000000000000000000000000000000000000000000000-4-44-444-4-44-4-44i−4i−4i4i44-44i−4i−4i4i000000000000000000000000000000000000000000000000
χ13588888-8-8-8-80000000000000000000000000000000000000000000000000000000000000-8-8-8-8-888880000000000000000000000000000000000000000000000000000000000000
χ136888-8-8-88-880000000000000000000000000000000000000000000000000000000000000-8-8-8888-88-80000000000000000000000000000000000000000000000000000000000000
χ13788-88-88-8-880000000000000000000000000000000000000000000000000000000000000-8-88-88-888-80000000000000000000000000000000000000000000000000000000000000
χ13888-8-8888-8-80000000000000000000000000000000000000000000000000000000000000-8-888-8-8-8880000000000000000000000000000000000000000000000000000000000000
χ13916-16000000082−8200000000000000000000000000000000000000000000000000000000000-16160000000−828200000000000000000000000000000000000000000000000000000000000
χ14016-160000000−828200000000000000000000000000000000000000000000000000000000000-1616000000082−8200000000000000000000000000000000000000000000000000000000000

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