Finite Group Databasebeta

← Group #13161371

Character table — Group #13161371

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size1111222222222222222222222233334444444444444444444444444444444444444444444466666666666666666688888888888888888888888888121212121212121212121212121212121212121212121212121218181818363636363636545454547272108108
order124423333346666612121212121212121212888823333466666666666666666121212121212121212121212121212121212121212882424242424242424242424242424242466666666666661212121212121212121212121288242424242424242424242424242424242424242424242424444488121212128888242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-11111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111111111111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ4111111111111111111111111111111-11111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111111111111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1111111-1-1
χ911-1-1-111111111111-1-1-1-1-1-1-1-1-1-1ii−i−i11111-1-1-1-1-1111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iii−i−ii−iii−i−i11-1-1i−i1-1
χ1011-1-1-111111111111-1-1-1-1-1-1-1-1-1-1ii−i−i11111-1-1-1-1-1111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−iii−ii−i−iii-1-111−ii-11
χ1111-1-1-111111111111-1-1-1-1-1-1-1-1-1-1ii−i−i-111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111111111111-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111−iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−iiii−i−i11-1-1−ii-11
χ1211-1-1-111111111111-1-1-1-1-1-1-1-1-1-1ii−i−i-111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111111111111-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111−iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−iiii−i−i−iii-1-111i−i1-1
χ1311-1-1-111111111111-1-1-1-1-1-1-1-1-1-1−i−iii11111-1-1-1-1-1111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiii−i−ii−iii−i−i-1-111i−i-11
χ1411-1-1-111111111111-1-1-1-1-1-1-1-1-1-1−i−iii11111-1-1-1-1-1111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−iii−ii−i−iii11-1-1−ii1-1
χ1511-1-1-111111111111-1-1-1-1-1-1-1-1-1-1−i−iii-111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111111111111-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iii−i−i−iiii−i−i-1-111−ii1-1
χ1611-1-1-111111111111-1-1-1-1-1-1-1-1-1-1−i−iii-111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111111111111-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−iiii−i−i−iii11-1-1i−i-11
χ17222222222-122222-122222222-1-100002-1-1-1-12222222222222-1-1-1-1-12222-122222222-1-1-1-1-1-1-1-1000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000222222-1-1-1-10000-1-100
χ18222222222-122222-122222222-1-100002-1-1-1-12222222222222-1-1-1-1-12222-122222222-1-1-1-1-1-1-1-1000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-2-2-2-2-2111100001100
χ19222222222-122222-122222222-1-10000-2-1-1-1-1-22222-2-2-2-2-2-2-2-2-1-1-1-1-12222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000000000000000001-1-1-1-1111111111-1-1-1-111111111000000000000000000000000002222-2-2-1-1-1-100001100
χ20222222222-122222-122222222-1-10000-2-1-1-1-1-22222-2-2-2-2-2-2-2-2-1-1-1-1-12222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000000000000000001-1-1-1-1111111111-1-1-1-11111111100000000000000000000000000-2-2-2-22211110000-1-100
χ21222222-1-1-1222-1-1-1222-1-1-1-1-1-122222222-1-1-122-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000
χ22222222-1-1-1222-1-1-1222-1-1-1-1-1-1222222-22-1-1-1-22-1-1-1-2-21111112-1-1-122-1-1-12-2-211111122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-22-1-1-1-2-2111111-22-1-1-1-2-2111111-2-22-1-1-12-1-1-1-2-2111111-2-2111111000000000000000000
χ23222222-1-1-1222-1-1-1222-1-1-1-1-1-122-2-2-2-222-1-1-122-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111-2-211111122-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1-2-2-2111-2111-2-2111111-2-2111111000000000000000000
χ24222222-1-1-1222-1-1-1222-1-1-1-1-1-122-2-2-2-2-22-1-1-1-22-1-1-1-2-21111112-1-1-122-1-1-12-2-211111122-1-1-1-1-1-1-2-2-2-2111111-2-2111111-22-1-1-1-2-2111111-22-1-1-1-2-211111122-2111-211122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000
χ2522222-12-1-122-12-1-12-1-122-1-1-1-12222222-12-1-12-12-1-1-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000
χ2622222-12-1-122-12-1-12-1-122-1-1-1-1222222-2-12-1-1-2-12-1-111-2-21111-12-1-12-12-1-1211-2-21111-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-2-12-1-111-2-21111-2-12-1-111-2-21111-2-2-12-1-1-12-1-111-2-2111111-2-21111000000000000000000
χ2722222-12-1-122-12-1-12-1-122-1-1-1-122-2-2-2-22-12-1-12-12-1-1-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-1-122-1-1-1-1-2-211-2-2111111-2-211112-12-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-1-1-2-21-2111-21111-2-2111111-2-21111000000000000000000
χ2822222-12-1-122-12-1-12-1-122-1-1-1-122-2-2-2-2-2-12-1-1-2-12-1-111-2-21111-12-1-12-12-1-1211-2-21111-1-122-1-1-1-1-2-211-2-2111111-2-21111-2-12-1-111-2-21111-2-12-1-111-2-21111221-2111-211-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000
χ2922222-1-12-122-1-12-12-1-1-1-122-1-12222222-1-12-12-1-12-1-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-12-1-12-1-1-1-1-122-1-12-1-12-1-1-1-1-122-1-122-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000
χ3022222-1-12-122-1-12-12-1-1-1-122-1-1222222-2-1-12-1-2-1-12-11111-2-211-1-12-12-1-12-121111-2-211-1-1-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-1-2-1-12-11111-2-211-2-1-12-11111-2-211-2-2-1-12-1-1-12-11111-2-2111111-2-211000000000000000000
χ3122222-1-12-122-1-12-12-1-1-1-122-1-122-2-2-2-22-1-12-12-1-12-1-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-1-1-122-1-1-2-21111-2-2111111-2-2112-1-12-1-1-1-1-122-1-12-1-12-1-1-1-1-122-1-1-2-211-2111-211111-2-2111111-2-211000000000000000000
χ3222222-1-12-122-1-12-12-1-1-1-122-1-122-2-2-2-2-2-1-12-1-2-1-12-11111-2-211-1-12-12-1-12-121111-2-211-1-1-1-122-1-1-2-21111-2-2111111-2-211-2-1-12-11111-2-211-2-1-12-11111-2-2112211-2111-21-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000
χ3322222-1-1-1222-1-1-122-1-1-1-1-1-1222222222-1-1-122-1-1-12-1-1-1-1-1-122-1-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-12-1-1-1-1-1-1222-1-1-12-1-1-1-1-1-12222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000
χ3422222-1-1-1222-1-1-122-1-1-1-1-1-122222222-2-1-1-12-2-1-1-12111111-2-2-1-1-122-1-1-122111111-2-2-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-2-1-1-12111111-2-2-2-1-1-12111111-2-2-2-2-1-1-12-1-1-12111111-2-2111111-2-2000000000000000000
χ3522222-1-1-1222-1-1-122-1-1-1-1-1-12222-2-2-2-22-1-1-122-1-1-12-1-1-1-1-1-122-1-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-2-2111111-2-2111111-2-22-1-1-12-1-1-1-1-1-1222-1-1-12-1-1-1-1-1-122-2-2111-2111-2111111-2-2111111-2-2000000000000000000
χ3622222-1-1-1222-1-1-122-1-1-1-1-1-12222-2-2-2-2-2-1-1-12-2-1-1-12111111-2-2-1-1-122-1-1-122111111-2-2-1-1-1-1-1-122-2-2111111-2-2111111-2-2-2-1-1-12111111-2-2-2-1-1-12111111-2-222111-2111-2-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000
χ372222-222222-22222222222222222222022220-2-2-2-2000000002222-2-2-2-2-2-20000000022222222-2-222222222222222220-2-2-2-2000000000-2-2-2-20000000000-2-2-2-2-2-2-2-20000000000000000000000000000000000
χ382222-222222-2222222222222222-2-2-2-2022220-2-2-2-2000000002222-2-2-2-2-2-2000000002222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20-2-2-2-2000000000-2-2-2-20000000000222222220000000000000000000000000000000000
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χ402222-22-1-1-12-22-1-1-1222-1-1-1-1-1-122222202-1-1-10-211100i3−i3i3−i3i3−i32-1-1-1-2-2111-200i3−i3i3−i3i3−i322-1-1-1-1-1-1-2-222-1-1-1-1-1-122-1-1-1-1-1-10-211100i3−i3i3−i3i3−i30-211100i3−i3i3−i3i3−i300-2111-211100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000
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χ422222-22-1-1-12-22-1-1-1222-1-1-1-1-1-122-2-2-2-202-1-1-10-211100i3−i3i3−i3i3−i32-1-1-1-2-2111-200i3−i3i3−i3i3−i322-1-1-1-1-1-122-2-2111111-2-21111110-211100i3−i3i3−i3i3−i30-211100i3−i3i3−i3i3−i3002-1-1-12-1-1-100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000
χ432222-2-12-1-12-2-12-1-12-1-122-1-1-1-12222220-12-1-101-211−i3i300−i3i3i3−i3-12-1-1-21-211-2−i3i300−i3i3i3−i3-1-122-1-1-1-1-2-2-1-122-1-1-1-1-1-122-1-1-1-101-211−i3i300−i3i3i3−i301-211−i3i300−i3i3i3−i3001-2111-211−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000000
χ442222-2-12-1-12-2-12-1-12-1-122-1-1-1-12222220-12-1-101-211i3−i300i3−i3−i3i3-12-1-1-21-211-2i3−i300i3−i3−i3i3-1-122-1-1-1-1-2-2-1-122-1-1-1-1-1-122-1-1-1-101-211i3−i300i3−i3−i3i301-211i3−i300i3−i3−i3i3001-2111-211i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.