Finite Group Databasebeta

← Group #72222535

Character table — Group #72222535

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size1111222222222222222222444444444444444444444444444444444444444444444488888888888888888888888888888888888888888888999918181818181818181818242424242424242424242424242424243636363636363636363648484848484848484848484848484848
order124423346688888888121212123446666612121212121216161616161616162424242424242424242424242424242424242424242424241212121212121212242424244848484848484848484848484848484848484848484848484848484848484848224424888888881616161616161616161616161616161644161616161616161648484848484848484848484848484848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-111111-1-1111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111-1-1-1-111111-1-1111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−iii−i−iii−i−iii−i−iii-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111111-1-1-1-111111-1-1111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii11-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111-1-1-1-111111-1-1111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i11-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111-1-1-1-111111-1-111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111-1-1-1-111111-1-111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111-1-1-1-111111-1-111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111-1-1-1-111111-1-111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1711-1-1-11111111-1-1ii−i−i-1-1-1-11i−i-1-11-1-11111-1-111-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-11ii−i−i11-1-1ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3i−i11-1-1ii−i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ1811-1-1-11111111-1-1ii−i−i-1-1-1-11i−i-1-11-1-11111-1-111-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-11ii−i−i11-1-1−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3i−i11-1-1ii−i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ1911-1-1-11111111-1-1ii−i−i-1-1-1-11i−i-1-11-1-11111-1-111-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1111-1−i−iii-1-111ζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ii-1-111−i−iiiζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ2011-1-1-11111111-1-1ii−i−i-1-1-1-11i−i-1-11-1-11111-1-111-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1111-1−i−iii-1-111−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3−ii-1-111−i−iii−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ2111-1-1-11111111-1-1ii−i−i-1-1-1-11i−i-1-11-1-11111-1-1-1-111−i−iii11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-11ii−i−i11-1-1ζ−ζζ3−ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3i−i-1-111−i−iiiζ−ζζ3−ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ2211-1-1-11111111-1-1ii−i−i-1-1-1-11i−i-1-11-1-11111-1-1-1-111−i−iii11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-11ii−i−i11-1-1−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3i−i-1-111−i−iii−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ2311-1-1-11111111-1-1ii−i−i-1-1-1-11i−i-1-11-1-11111-1-1-1-111−i−iii11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-1111-1−i−iii-1-111ζ−ζζ3−ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ii11-1-1ii−i−iζ−ζζ3−ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ2411-1-1-11111111-1-1ii−i−i-1-1-1-11i−i-1-11-1-11111-1-1-1-111−i−iii11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-1111-1−i−iii-1-111−ζζ−ζ3ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3−ii11-1-1ii−i−i−ζζ−ζ3ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ2511-1-1-11111111-1-1−i−iii-1-1-1-11−ii-1-11-1-11111-1-111-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-11−i−iii11-1-1ζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ii11-1-1−i−iiiζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ2611-1-1-11111111-1-1−i−iii-1-1-1-11−ii-1-11-1-11111-1-111-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-11−i−iii11-1-1−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ii11-1-1−i−iii−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ2711-1-1-11111111-1-1−i−iii-1-1-1-11−ii-1-11-1-11111-1-111-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1111-1ii−i−i-1-111ζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ−ζ3ζ3−ζζi−i-1-111ii−i−iζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ2811-1-1-11111111-1-1−i−iii-1-1-1-11−ii-1-11-1-11111-1-111-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1111-1ii−i−i-1-111−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3−ζ3ζ−ζζ3−ζ3ζ−ζi−i-1-111ii−i−i−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ2911-1-1-11111111-1-1−i−iii-1-1-1-11−ii-1-11-1-11111-1-1-1-111ii−i−i11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-11−i−iii11-1-1ζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ−ii-1-111ii−i−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ3011-1-1-11111111-1-1−i−iii-1-1-1-11−ii-1-11-1-11111-1-1-1-111ii−i−i11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-11−i−iii11-1-1−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ii-1-111ii−i−i−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ3111-1-1-11111111-1-1−i−iii-1-1-1-11−ii-1-11-1-11111-1-1-1-111ii−i−i11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-1111-1ii−i−i-1-111ζ3−ζ3ζ−ζ−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3−ζ3ζ−ζi−i11-1-1−i−iiiζ3−ζ3ζ−ζ−ζ3ζ3−ζζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ3211-1-1-11111111-1-1−i−iii-1-1-1-11−ii-1-11-1-11111-1-1-1-111ii−i−i11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-1111-1ii−i−i-1-111−ζ3ζ3−ζζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3ζ3−ζζi−i11-1-1−i−iii−ζ3ζ3−ζζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ332222222222-2-2-2-2222222222-2-22222222222200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000000000002222222222-2-2-2-20000000000000000-2-2000000000000000000000000
χ342222222222-2-2-2-2222222222-2-22222222222200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2-2-2-2-2-2-2-2-2-22222000000000000000022000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-222222222222222222200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000222222-2-2-2-2-2-2-2-2000000000000000022000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-222222222222222222200000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000-2-2-2-2-2-2222222220000000000000000-2-2000000000000000000000000
χ37222222-122-12222222222-1-1-1222-1-1-1-12-1-1-1-1-12222222222-1-1-1-1-1-122-1-1-1-1-1-122-1-122-1-12-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000022222222000000000000000000-1-1-1-1-1-1-1-1
χ38222222-122-12222222222-1-1-1222-1-1-1-12-1-1-1-1-12222222222-1-1-1-1-1-122-1-1-1-1-1-122-1-122-1-12-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000000000-2-2-2-2-2-2-2-200000000000000000011111111
χ39222222-122-12222222222-1-1-1222-1-1-1-12-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-122-1-122-1-12-1-1-12-1-1-1-1-1-1-1-2-2111111-2-2111111-2-2111111-2-211111100000000000000000000002222-2-2-2-2000000000000000000-1-1-1-11111
χ40222222-122-12222222222-1-1-1222-1-1-1-12-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-122-1-122-1-12-1-1-12-1-1-1-1-1-1-1-2-2111111-2-2111111-2-2111111-2-21111110000000000000000000000-2-2-2-222220000000000000000001111-1-1-1-1
χ41222222-122-12222-2-2-2-222-1-1-1-2-22-1-1-1-12-1-1-1-1-12222-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-1-2-211-2-211-2111-2111111122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-211111100000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000−i−iii−i−iii
χ42222222-122-12222-2-2-2-222-1-1-1-2-22-1-1-1-12-1-1-1-1-12222-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-1-2-211-2-211-2111-2111111122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-21111110000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000ii−i−iii−i−i
χ43222222-122-12222-2-2-2-222-1-1-1-2-22-1-1-1-12-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-122-1-1-1-1-1-1-2-211-2-211-2111-21111111-2-2111111-2-211111122-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000−i−iiiii−i−i
χ44222222-122-12222-2-2-2-222-1-1-1-2-22-1-1-1-12-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-122-1-1-1-1-1-1-2-211-2-211-2111-21111111-2-2111111-2-211111122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000ii−i−i−i−iii
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.