Finite Group Databasebeta

← Group #11774508

Character table — Group #11774508

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222244444444444444444444444488881212121212121212121212121212121212121212121212121818181824242424242424242424242436363636363636363636
order1222444444443366666612121212121212121212121212121212121212128888888824242424242424242424242424242424444422446666121212122488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ511111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-111-1-111-1-1-1-11111-1-1-1-1
χ611111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-111-1-111-1-1-1-1-1-11111
χ711111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-11-111-1-111-1-1-1-1-1-1-1-11111
χ811111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-11-11-1-111-1-111-1-11111-1-1-1-1
χ91111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-11111-1-1-1-1-11ii−i−iii−i−i
χ101111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111-1-1-1-11111-11−i−iii−i−iii
χ111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-11111-1-1-1-1-11−i−iii−i−iii
χ121111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111-1-1-1-11111-11ii−i−iii−i−i
χ131111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-11-1-1111-1-1-1-1111-1ii−i−i−i−iii
χ141111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-111-1-1-11111-1-11-1−i−iiiii−i−i
χ151111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-11-1-1111-1-1-1-1111-1−i−iiiii−i−i
χ161111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-111-1-1-11111-1-11-1ii−i−i−i−iii
χ172222222222222222222222222222222222222222000000000000000000000000-2-2-2-2000000000000-2-200000000
χ1822222222-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000-2-2-2-20000000000002200000000
χ192222-2-2-2-222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000000000000000000000-2-2220000000000002-200000000
χ202222-2-2-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222000000000000000000000000-2-222000000000000-2200000000
χ2122-2-22i2i−2i−2i0000222-2-22-2-2000000002i2i−2i−2i2i2i−2i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232-22i−2i0000000000000000000000
χ2222-2-22i2i−2i−2i0000222-2-22-2-2000000002i2i−2i−2i2i2i−2i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232-22i−2i0000000000000000000000
χ2322-2-22i2i−2i−2i0000222-2-22-2-2000000002i2i−2i−2i2i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300000000-22−2i2i0000000000000000000000
χ2422-2-22i2i−2i−2i0000222-2-22-2-2000000002i2i−2i−2i2i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300000000-22−2i2i0000000000000000000000
χ2522-2-2−2i−2i2i2i0000222-2-22-2-200000000−2i−2i2i2i−2i−2i2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132-2−2i2i0000000000000000000000
χ2622-2-2−2i−2i2i2i0000222-2-22-2-200000000−2i−2i2i2i−2i−2i2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132-2−2i2i0000000000000000000000
χ2722-2-2−2i−2i2i2i0000222-2-22-2-200000000−2i−2i2i2i−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000-222i−2i0000000000000000000000
χ2822-2-2−2i−2i2i2i0000222-2-22-2-200000000−2i−2i2i2i−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000-222i−2i0000000000000000000000
χ292-22-22i−2i2i−2i2-22i−2i22-22-2-22-222-2-22i2i−2i−2i2i−2i2i−2i2i−2i2i−2i2-22i−2i0000000000000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ302-22-22i−2i2i−2i2-22i−2i22-22-2-22-222-2-22i2i−2i−2i2i−2i2i−2i2i−2i2i−2i2-22i−2i000000000000000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ312-22-22i−2i2i−2i-22−2i2i22-22-2-22-2-2-222−2i−2i2i2i2i−2i2i−2i2i−2i2i−2i-22−2i2i0000000000000000000000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ322-22-22i−2i2i−2i-22−2i2i22-22-2-22-2-2-222−2i−2i2i2i2i−2i2i−2i2i−2i2i−2i-22−2i2i000000000000000000000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ332-22-2−2i2i−2i2i2-2−2i2i22-22-2-22-222-2-2−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i2-2−2i2i0000000000000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ342-22-2−2i2i−2i2i2-2−2i2i22-22-2-22-222-2-2−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i2-2−2i2i000000000000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ352-22-2−2i2i−2i2i-222i−2i22-22-2-22-2-2-2222i2i−2i−2i−2i2i−2i2i−2i2i−2i2i-222i−2i0000000000000000000000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ362-22-2−2i2i−2i2i-222i−2i22-22-2-22-2-2-2222i2i−2i−2i−2i2i−2i2i−2i2i−2i2i-222i−2i000000000000000000000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ374444444444441-2111-2-2-211111111-2-2-2-21111-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ384444444444441-2111-2-2-211111111-2-2-2-21111-2-2-2-2-2-2-2-2-2-2-2-2111111111111111100000000000000000000000000
χ39444444444444-21-2-2-2111-2-2-2-2-2-2-2-21111-2-2-2-2111100000000000000000000000000002222-1-1-1-1-1-1-1-10000000000
χ40444444444444-21-2-2-2111-2-2-2-2-2-2-2-21111-2-2-2-211110000000000000000000000000000-2-2-2-2111111110000000000
χ4144444444-4-4-4-41-2111-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2111122222222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000000000
χ4244444444-4-4-4-41-2111-2-2-2-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000000000
χ4344444444-4-4-4-4-21-2-2-2111222222221111-2-2-2-2-1-1-1-100000000000000000000000000002-22-2-1-111-1-1110000000000
χ4444444444-4-4-4-4-21-2-2-2111222222221111-2-2-2-2-1-1-1-10000000000000000000000000000-22-2211-1-111-1-10000000000
χ454444-4-4-4-444-4-41-2111-2-2-21111-1-1-1-12222-1-1-1-1-2-2222i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii00000000000000000000000000
χ464444-4-4-4-444-4-41-2111-2-2-21111-1-1-1-12222-1-1-1-1-2-222−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000000000000000000000
χ474444-4-4-4-444-4-4-21-2-2-2111-2-2-2-22222-1-1-1-1222211-1-1000000000000000000000000000022-2-2-1-1-1-111110000000000
χ484444-4-4-4-444-4-4-21-2-2-2111-2-2-2-22222-1-1-1-1222211-1-10000000000000000000000000000-2-2221111-1-1-1-10000000000
χ494444-4-4-4-4-4-4441-2111-2-2-2-1-1-1-111112222-1-1-1-122-2-22i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000000000
χ504444-4-4-4-4-4-4441-2111-2-2-2-1-1-1-111112222-1-1-1-122-2-2−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii00000000000000000000000000
χ514444-4-4-4-4-4-444-21-2-2-21112222-2-2-2-2-1-1-1-12222-1-11100000000000000000000000000002-2-22-1-11111-1-10000000000
χ524444-4-4-4-4-4-444-21-2-2-21112222-2-2-2-2-1-1-1-12222-1-1110000000000000000000000000000-222-211-1-1-1-1110000000000
χ5344-4-44i4i−4i−4i00001-21-1-1-2223i−3i3i−3i3-33-3−2i−2i2i2iii−i−i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000000000000000000000
χ5444-4-44i4i−4i−4i00001-21-1-1-2223i−3i3i−3i3-33-3−2i−2i2i2iii−i−i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000000000000000000000
χ5544-4-44i4i−4i−4i00001-21-1-1-222−3i3i−3i3i-33-33−2i−2i2i2iii−i−i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000000000000000000000
χ5644-4-44i4i−4i−4i00001-21-1-1-222−3i3i−3i3i-33-33−2i−2i2i2iii−i−i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000000000000000000000
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χ634-44-44i−4i4i−4i4-44i−4i-212-22-11-1-2-222−2i−2i2i2ii−ii−i−2i2i−2i2i1-1i−i00000000000000000000000000000000−i3i3−i3i33−33−30000000000
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χ654-44-44i−4i4i−4i-44−4i4i1-2-11-12-22-1-111−i−iii−2i2i−2i2ii−ii−i2-22i−2i00000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000000000000000000000
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χ674-44-44i−4i4i−4i-44−4i4i-212-22-11-122-2-22i2i−2i−2ii−ii−i−2i2i−2i2i-11−ii00000000000000000000000000000000−i3i3i3−i33−3−330000000000
χ684-44-44i−4i4i−4i-44−4i4i-212-22-11-122-2-22i2i−2i−2ii−ii−i−2i2i−2i2i-11−ii00000000000000000000000000000000i3−i3−i3i3−333−30000000000
χ694-44-4−4i4i−4i4i4-4−4i4i1-2-11-12-2211-1-1−i−iii2i−2i2i−2i−ii−ii-222i−2i00000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000000000000000000000
χ704-44-4−4i4i−4i4i4-4−4i4i1-2-11-12-2211-1-1−i−iii2i−2i2i−2i−ii−ii-222i−2i00000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000000000000000000000
χ714-44-4−4i4i−4i4i4-4−4i4i-212-22-11-1-2-2222i2i−2i−2i−ii−ii2i−2i2i−2i1-1−ii00000000000000000000000000000000−i3i3−i3i3−33−330000000000
χ724-44-4−4i4i−4i4i4-4−4i4i-212-22-11-1-2-2222i2i−2i−2i−ii−ii2i−2i2i−2i1-1−ii00000000000000000000000000000000i3−i3i3−i33−33−30000000000
χ734-44-4−4i4i−4i4i-444i−4i1-2-11-12-22-1-111ii−i−i2i−2i2i−2i−ii−ii2-2−2i2i00000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000000000000000000000
χ744-44-4−4i4i−4i4i-444i−4i1-2-11-12-22-1-111ii−i−i2i−2i2i−2i−ii−ii2-2−2i2i00000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000000000000000000000
χ754-44-4−4i4i−4i4i-444i−4i-212-22-11-122-2-2−2i−2i2i2i−ii−ii2i−2i2i−2i-11i−i00000000000000000000000000000000−i3i3i3−i3−333−30000000000
χ764-44-4−4i4i−4i4i-444i−4i-212-22-11-122-2-2−2i−2i2i2i−ii−ii2i−2i2i−2i-11i−i00000000000000000000000000000000i3−i3−i3i33−3−330000000000
χ774-4-444-4-4400001-2-1-1122-23i−3i−3i3i−3i3i3i−3i-222-21-1-11000000000000−i3i3i3−i3i3−i3−i3i3−333−3−333−300000000000000000000000000
χ784-4-444-4-4400001-2-1-1122-23i−3i−3i3i−3i3i3i−3i-222-21-1-11000000000000i3−i3−i3i3−i3i3i3−i33−3−333−3−3300000000000000000000000000
χ794-4-444-4-4400001-2-1-1122-2−3i3i3i−3i3i−3i−3i3i-222-21-1-11000000000000−i3i3i3−i3i3−i3−i3i33−3−333−3−3300000000000000000000000000
χ804-4-444-4-4400001-2-1-1122-2−3i3i3i−3i3i−3i−3i3i-222-21-1-11000000000000i3−i3−i3i3−i3i3i3−i3−333−3−333−300000000000000000000000000
χ814-4-444-4-44000044-4-44-4-44000000004-4-444-4-44000000000000000000000000000000000000000000000000000000
χ824-4-44-444-400001-2-1-1122-23i−3i−3i3i3i−3i−3i3i2-2-22-111-10000000000003−3−333−3−33−i3i3i3−i3i3−i3−i3i300000000000000000000000000
χ834-4-44-444-400001-2-1-1122-23i−3i−3i3i3i−3i−3i3i2-2-22-111-1000000000000−333−3−333−3i3−i3−i3i3−i3i3i3−i300000000000000000000000000
χ844-4-44-444-400001-2-1-1122-2−3i3i3i−3i−3i3i3i−3i2-2-22-111-10000000000003−3−333−3−33i3−i3−i3i3−i3i3i3−i300000000000000000000000000
χ854-4-44-444-400001-2-1-1122-2−3i3i3i−3i−3i3i3i−3i2-2-22-111-1000000000000−333−3−333−3−i3i3i3−i3i3−i3−i3i300000000000000000000000000
χ864-4-44-444-4000044-4-44-4-4400000000-444-4-444-4000000000000000000000000000000000000000000000000000000
χ8788-8-88i8i−8i−8i0000-42-4442-2-2000000002i2i−2i−2i−4i−4i4i4i000000000000000000000000000000000000000000000000000000
χ8888-8-8−8i−8i8i8i0000-42-4442-2-200000000−2i−2i2i2i4i4i−4i−4i000000000000000000000000000000000000000000000000000000
χ898-8-888-8-880000-4244-4-2-22000000002-2-22-444-4000000000000000000000000000000000000000000000000000000
χ908-8-88-888-80000-4244-4-2-2200000000-222-24-4-44000000000000000000000000000000000000000000000000000000

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