Finite Group Databasebeta

← Group #13161372

Character table — Group #13161372

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size11112222222222222222222222444444444444444444444444444444444444444444446666666666666666666688888888888888888888888888121212121212121212121212121212121212121212121212121236363636363636367272108108108108
order124423333346666612121212121212121212233334666666666666666661212121212121212121212121212121212121212128888242424242424242424242424242424246666666666666121212121212121212121212128824242424242424242424242424242424242424242424242444881212121224242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-11111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111111111111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ611111111111111111111111111-11111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111111111111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ711111111111111111111111111-11111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111-1-11111-1-111-1-1
χ811111111111111111111111111-11111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111-1-111
χ911-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−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−ii−ii−iii−i−ii−i1-11-1
χ1011-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−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−ii−ii−i−iii−ii-11-11
χ1111-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−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−iiiiiiiiii−ii−iii−i−ii−i-11-11
χ1211-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−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−ii−ii−i−iii−ii1-11-1
χ1311-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111111111111-1-1-1-1-1-1-1-1ii−i−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−iiiiiiiiii−i−iiii−i−i−ii-111-1
χ1411-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111111111111-1-1-1-1-1-1-1-1ii−i−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−iii−i−i−iiii−i1-1-11
χ1511-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111111111111-1-1-1-1-1-1-1-1−i−iii−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−ii−i−iiii−i−i−ii1-1-11
χ1611-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111111111111-1-1-1-1-1-1-1-1−i−iii−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−iii−i−i−iiii−i-111-1
χ17222222222-122222-122222222-1-12-1-1-1-12222222222222-1-1-1-1-12222-122222222-1-1-1-1-1-1-1-100000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000002222-1-1-1-1-1-10000
χ18222222222-122222-122222222-1-12-1-1-1-12222222222222-1-1-1-1-12222-122222222-1-1-1-1-1-1-1-100000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-2-2-21111110000
χ19222222222-122222-122222222-1-1-2-1-1-1-1-22222-2-2-2-2-2-2-2-2-1-1-1-1-12222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000000000000000001-1-1-1-1111111111-1-1-1-1111111110000000000000000000000000022-2-2-1-1-1-1110000
χ20222222222-122222-122222222-1-1-2-1-1-1-1-22222-2-2-2-2-2-2-2-2-1-1-1-1-12222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000000000000000001-1-1-1-1111111111-1-1-1-11111111100000000000000000000000000-2-2221111-1-10000
χ21222222-1-1-1222-1-1-1222-1-1-1-1-1-12222-1-1-122-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000000000
χ22222222-1-1-1222-1-1-1222-1-1-1-1-1-12222-1-1-122-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2111111-2-211111122-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1-2-2-2111-2111-2-2111111-2-211111100000000000000
χ23222222-1-1-1222-1-1-1222-1-1-1-1-1-122-22-1-1-1-22-1-1-1-2-21111112-1-1-122-1-1-12-2-211111122-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-1-22-1-1-1-2-2111111-22-1-1-1-2-2111111-2-22-1-1-12-1-1-1-2-2111111-2-211111100000000000000
χ24222222-1-1-1222-1-1-1222-1-1-1-1-1-122-22-1-1-1-22-1-1-1-2-21111112-1-1-122-1-1-12-2-211111122-1-1-1-1-1-1-2-2-2-2-2-2111111-2-2111111-22-1-1-1-2-2111111-22-1-1-1-2-211111122-2111-211122-1-1-1-1-1-122-1-1-1-1-1-100000000000000
χ2522222-12-1-122-12-1-12-1-122-1-1-1-1222-12-1-12-12-1-1-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-1-122-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000000000
χ2622222-12-1-122-12-1-12-1-122-1-1-1-1222-12-1-12-12-1-1-1-122-1-1-1-1-12-1-12-12-1-12-1-122-1-1-1-1-1-122-1-1-1-1-2-2-2-211-2-2111111-2-211112-12-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-1-1-2-21-2111-21111-2-2111111-2-2111100000000000000
χ2722222-12-1-122-12-1-12-1-122-1-1-1-122-2-12-1-1-2-12-1-111-2-21111-12-1-12-12-1-1211-2-21111-1-122-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-2-12-1-111-2-21111-2-12-1-111-2-21111-2-2-12-1-1-12-1-111-2-2111111-2-2111100000000000000
χ2822222-12-1-122-12-1-12-1-122-1-1-1-122-2-12-1-1-2-12-1-111-2-21111-12-1-12-12-1-1211-2-21111-1-122-1-1-1-1-2-2-2-211-2-2111111-2-21111-2-12-1-111-2-21111-2-12-1-111-2-21111221-2111-211-1-122-1-1-1-1-1-122-1-1-1-100000000000000
χ2922222-1-12-122-1-12-12-1-1-1-122-1-1222-1-12-12-1-12-1-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-1-1-122-1-12222-1-1-1-122-1-1-1-1-1-122-1-12-1-12-1-1-1-1-122-1-12-1-12-1-1-1-1-122-1-122-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-100000000000000
χ3022222-1-12-122-1-12-12-1-1-1-122-1-1222-1-12-12-1-12-1-1-1-1-122-1-1-1-12-12-1-12-12-1-1-1-122-1-1-1-1-1-122-1-1-2-2-2-21111-2-2111111-2-2112-1-12-1-1-1-1-122-1-12-1-12-1-1-1-1-122-1-1-2-211-2111-211111-2-2111111-2-21100000000000000
χ3122222-1-12-122-1-12-12-1-1-1-122-1-122-2-1-12-1-2-1-12-11111-2-211-1-12-12-1-12-121111-2-211-1-1-1-122-1-12222-1-1-1-122-1-1-1-1-1-122-1-1-2-1-12-11111-2-211-2-1-12-11111-2-211-2-2-1-12-1-1-12-11111-2-2111111-2-21100000000000000
χ3222222-1-12-122-1-12-12-1-1-1-122-1-122-2-1-12-1-2-1-12-11111-2-211-1-12-12-1-12-121111-2-211-1-1-1-122-1-1-2-2-2-21111-2-2111111-2-211-2-1-12-11111-2-211-2-1-12-11111-2-2112211-2111-21-1-1-1-122-1-1-1-1-1-122-1-100000000000000
χ3322222-1-1-1222-1-1-122-1-1-1-1-1-122222-1-1-122-1-1-12-1-1-1-1-1-122-1-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-12-1-1-1-1-1-1222-1-1-12-1-1-1-1-1-12222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12200000000000000
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χ3522222-1-1-1222-1-1-122-1-1-1-1-1-12222-2-1-1-12-2-1-1-12111111-2-2-1-1-122-1-1-122111111-2-2-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-122-2-1-1-12111111-2-2-2-1-1-12111111-2-2-2-2-1-1-12-1-1-12111111-2-2111111-2-200000000000000
χ3622222-1-1-1222-1-1-122-1-1-1-1-1-12222-2-1-1-12-2-1-1-12111111-2-2-1-1-122-1-1-122111111-2-2-1-1-1-1-1-122-2-2-2-2111111-2-2111111-2-2-2-1-1-12111111-2-2-2-1-1-12111111-2-222111-2111-2-1-1-1-1-1-122-1-1-1-1-1-12200000000000000
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χ382222-222222-2222222222222222022220-2-2-2-2000000002222-2-2-2-2-2-20000000022222222-22-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20-2-2-2-2000000000-2-2-2-2000000000022222222000000000000000000000000000000
χ392222-22-1-1-12-22-1-1-1222-1-1-1-1-1-12202-1-1-10-211100−i3i3−i3i3−i3i32-1-1-1-2-2111-200−i3i3−i3i3−i3i322-1-1-1-1-1-12-22-222-1-1-1-1-1-122-1-1-1-1-1-10-211100−i3i3−i3i3−i3i30-211100−i3i3−i3i3−i3i300-2111-211100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300000000000000
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χ442222-2-12-1-12-2-12-1-12-1-122-1-1-1-1220-12-1-101-211−i3i300−i3i3i3−i3-12-1-1-21-211-2−i3i300−i3i3i3−i3-1-122-1-1-1-1-22-2211-2-2111111-2-2111101-211−i3i300−i3i3i3−i301-211−i3i300−i3i3i3−i300-12-1-1-12-1-1i3−i300i3−i3−i3i3i3−i300i3−i3−i3i300000000000000
χ452222-2-12-1-12-2-12-1-12-1-122-1-1-1-1220-12-1-101-211i3−i300i3−i3−i3i3-12-1-1-21-211-2i3−i300i3−i3−i3i3-1-122-1-1-1-12-22-2-1-122-1-1-1-1-1-122-1-1-1-101-211i3−i300i3−i3−i3i301-211i3−i300i3−i3−i3i3001-2111-211i3−i300i3−i3−i3i3i3−i300i3−i3−i3i300000000000000
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χ1464-4−4i4i0-2-24-24022-42-42i−2i2i−2i−4i4i2i−2i−4i4i0-2-24-2000000000000022-42000000000000002i−2i2i−2i−4i4i2i−2i0000−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ1300−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ23002ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000000000000000000000000000000000000000
χ1474-4−4i4i0-2-2-2440222-4-42i−2i2i−2i2i−2i−4i4i−4i4i0-2-2-240000000000000222-4000000000000002i−2i2i−2i2i−2i−4i4i00002ζ5−2ζ13−2ζ5+2ζ132ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ1300−2ζ7+2ζ232ζ7−2ζ23−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000000000000000000000000000000000000000000000
χ1484-4−4i4i0-2-2-2440222-4-42i−2i2i−2i2i−2i−4i4i−4i4i0-2-2-240000000000000222-4000000000000002i−2i2i−2i2i−2i−4i4i0000−2ζ5+2ζ132ζ5−2ζ13−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ13002ζ7−2ζ23−2ζ7+2ζ232ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000000000000000000000000000000000000000000000
χ1498-88i−8i08-4-4-4-40-844448i−8i−4i4i−4i4i−4i4i−4i4i0-422200000000000004-2-2-200000000000000−4i4i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1508-88i−8i0-48-4-4-404-8444−4i4i8i−8i−4i4i−4i4i−4i4i02-4220000000000000-24-2-2000000000000002i−2i−4i4i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1518-88i−8i0-4-48-4-4044-844−4i4i−4i4i8i−8i−4i4i−4i4i022-420000000000000-2-24-2000000000000002i−2i2i−2i−4i4i2i−2i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1528-88i−8i0-4-4-48-40444-84−4i4i−4i4i−4i4i8i−8i−4i4i0222-40000000000000-2-2-24000000000000002i−2i2i−2i2i−2i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1538-8−8i8i08-4-4-4-40-84444−8i8i4i−4i4i−4i4i−4i4i−4i0-422200000000000004-2-2-2000000000000004i−4i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1548-8−8i8i0-48-4-4-404-84444i−4i−8i8i4i−4i4i−4i4i−4i02-4220000000000000-24-2-200000000000000−2i2i4i−4i−2i2i−2i2i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1558-8−8i8i0-4-48-4-4044-8444i−4i4i−4i−8i8i4i−4i4i−4i022-420000000000000-2-24-200000000000000−2i2i−2i2i4i−4i−2i2i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1568-8−8i8i0-4-4-48-40444-844i−4i4i−4i4i−4i−8i8i4i−4i0222-40000000000000-2-2-2400000000000000−2i2i−2i2i−2i2i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.