Finite Group Databasebeta

← Group #13135092

Character table — Group #13135092

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1244234688881212242424246122424336666121212121212242424243666612121212122424242424242424242424242424246688121216161616161616162424242448484848484848484848484848484848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii
χ811111111-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i
χ911-1-111-11ii−i−i-1-1ii−i−i1-1i−i111111-1-1-1-1-1-1ii−i−i11111-1-1-1-1-1i−iii−i−iiiii−i−i−i−i1-111i−i-1-1ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ1011-1-111-11ii−i−i-1-1ii−i−i1-1i−i111111-1-1-1-1-1-1ii−i−i11111-1-1-1-1-1i−iii−i−iiiii−i−i−i−i1-111i−i-1-1−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ1111-1-111-11ii−i−i-1-1ii−i−i1-1i−i111111-1-1-1-1-1-1ii−i−i11111-1-1-1-1-1i−iii−i−iiiii−i−i−i−i-11-1-1−ii11ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ1211-1-111-11ii−i−i-1-1ii−i−i1-1i−i111111-1-1-1-1-1-1ii−i−i11111-1-1-1-1-1i−iii−i−iiiii−i−i−i−i-11-1-1−ii11−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ1311-1-111-11−i−iii-1-1−i−iii1-1−ii111111-1-1-1-1-1-1−i−iii11111-1-1-1-1-1−ii−i−iii−i−i−i−iiiii1-111−ii-1-1−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ1411-1-111-11−i−iii-1-1−i−iii1-1−ii111111-1-1-1-1-1-1−i−iii11111-1-1-1-1-1−ii−i−iii−i−i−i−iiiii1-111−ii-1-1ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ1511-1-111-11−i−iii-1-1−i−iii1-1−ii111111-1-1-1-1-1-1−i−iii11111-1-1-1-1-1−ii−i−iii−i−i−i−iiiii-11-1-1i−i11−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ1611-1-111-11−i−iii-1-1−i−iii1-1−ii111111-1-1-1-1-1-1−i−iii11111-1-1-1-1-1−ii−i−iii−i−i−i−iiiii-11-1-1i−i11ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ1722222222222222222222222-1-1-12-1-1-122-1-12222-12-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-100000000-1-1-1-10000000000000000
χ1822222222222222222222222-1-1-12-1-1-122-1-12222-12-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2110000000011110000000000000000
χ192222222222222222222222-1222-1222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000002222000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-1222-1222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000-2-2-2-200000000000011111111
χ2122222222-2-2-2-222-2-2-2-222-2-22-1-1-12-1-1-122-1-1-2-2-2-2-12-1-1-12-1-1-1-1-2-211111111111122-1-1-2-2-1-10000000011110000000000000000
χ2222222222-2-2-2-222-2-2-2-222-2-22-1-1-12-1-1-122-1-1-2-2-2-2-12-1-1-12-1-1-1-1-2-2111111111111-2-211221100000000-1-1-1-10000000000000000
χ2322222222-2-2-2-222-2-2-2-222-2-2-1222-1222-1-1221111-1-1-1-1-1-1-1-1-1-111-2-2-2-2111111110000000000002i2i−2i−2i000000000000−i−i−i−iiiii
χ2422222222-2-2-2-222-2-2-2-222-2-2-1222-1222-1-1221111-1-1-1-1-1-1-1-1-1-111-2-2-2-211111111000000000000−2i−2i2i2i000000000000iiii−i−i−i−i
χ252222-22-222-22-2222222-2-2-2-222-2-222-2-22222-2-2-2-22-2-2-22-2-2-222222-22-222-2-222-2-2000000000000000000000000000000000000
χ262222-22-222-22-2222222-2-2-2-22-1112-11122-1-1-2-2-2-2-1-211-1-211-1-122-11-11-1-111-1-11100−i3i300−i3i300000000−i3i3−i3i30000000000000000
χ272222-22-222-22-2222222-2-2-2-22-1112-11122-1-1-2-2-2-2-1-211-1-211-1-122-11-11-1-111-1-11100i3−i300i3−i300000000i3−i3i3−i30000000000000000
χ282222-22-222-22-2222222-2-2-2-2-12-2-2-12-2-2-1-1221111-1111-1111-1-1-1-12-22-2-1-111-1-11100000000000000000000000000003−33−33−33−3
χ292222-22-222-22-2222222-2-2-2-2-12-2-2-12-2-2-1-1221111-1111-1111-1-1-1-12-22-2-1-111-1-1110000000000000000000000000000−33−33−33−33
χ302222-22-22-22-2222-2-2-2-2-2-22222-2-222-2-2222222222-2-2-22-2-2-222-2-2-22-22-2-222-2-222000000000000000000000000000000000000
χ312222-22-22-22-2222-2-2-2-2-2-2222-1112-11122-1-12222-1-211-1-211-1-1-2-21-11-111-1-111-1-100−i3i300−i3i300000000i3−i3i3−i30000000000000000
χ322222-22-22-22-2222-2-2-2-2-2-2222-1112-11122-1-12222-1-211-1-211-1-1-2-21-11-111-1-111-1-100i3−i300i3−i300000000−i3i3−i3i30000000000000000
χ332222-22-22-22-2222-2-2-2-2-2-222-12-2-2-12-2-2-1-122-1-1-1-1-1111-1111-1-111-22-2211-1-111-1-10000000000000000000000000000−i3i3−i3i3i3−i3i3−i3
χ342222-22-22-22-2222-2-2-2-2-2-222-12-2-2-12-2-2-1-122-1-1-1-1-1111-1111-1-111-22-2211-1-111-1-10000000000000000000000000000i3−i3i3−i3−i3i3−i3i3
χ3522-2-222-222i2i−2i−2i-2-22i2i−2i−2i2-22i−2i2-1-1-12-111-2-2112i2i−2i−2i-12-1-1-1-211112i−2i−i−iii−i−i−i−iiiii2-2-1-12i−2i1100000000−i−iii0000000000000000
χ3622-2-222-222i2i−2i−2i-2-22i2i−2i−2i2-22i−2i2-1-1-12-111-2-2112i2i−2i−2i-12-1-1-1-211112i−2i−i−iii−i−i−i−iiiii-2211−2i2i-1-100000000ii−i−i0000000000000000
χ3722-2-222-222i2i−2i−2i-2-22i2i−2i−2i2-22i−2i-1222-12-2-211-2-2−i−iii-1-1-1-1-111111−ii2i2i−2i−2i−i−i−i−iiiii0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ3822-2-222-222i2i−2i−2i-2-22i2i−2i−2i2-22i−2i-1222-12-2-211-2-2−i−iii-1-1-1-1-111111−ii2i2i−2i−2i−i−i−i−iiiii000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ3922-2-222-22−2i−2i2i2i-2-2−2i−2i2i2i2-2−2i2i2-1-1-12-111-2-211−2i−2i2i2i-12-1-1-1-21111−2i2iii−i−iiiii−i−i−i−i2-2-1-1−2i2i1100000000ii−i−i0000000000000000
χ4022-2-222-22−2i−2i2i2i-2-2−2i−2i2i2i2-2−2i2i2-1-1-12-111-2-211−2i−2i2i2i-12-1-1-1-21111−2i2iii−i−iiiii−i−i−i−i-22112i−2i-1-100000000−i−iii0000000000000000
χ4122-2-222-22−2i−2i2i2i-2-2−2i−2i2i2i2-2−2i2i-1222-12-2-211-2-2ii−i−i-1-1-1-1-111111i−i−2i−2i2i2iiiii−i−i−i−i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ4222-2-222-22−2i−2i2i2i-2-2−2i−2i2i2i2-2−2i2i-1222-12-2-211-2-2ii−i−i-1-1-1-1-111111i−i−2i−2i2i2iiiii−i−i−i−i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ4322-2-2-22222i−2i−2i2i-2-22i2i−2i−2i-22−2i2i22-2-22222-2-2-2-2−2i−2i2i2i2-2-2-22222-2-22i−2i2i−2i−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ4422-2-2-22222i−2i−2i2i-2-22i2i−2i−2i-22−2i2i2-1112-1-1-1-2-211−2i−2i2i2i-1-211-12-1-1112i−2i−iii−i−i−iiiii−i−i00−i3i300i3−i3000000003−3−330000000000000000
χ4522-2-2-22222i−2i−2i2i-2-22i2i−2i−2i-22−2i2i2-1112-1-1-1-2-211−2i−2i2i2i-1-211-12-1-1112i−2i−iii−i−i−iiiii−i−i00i3−i300−i3i300000000−333−30000000000000000
χ4622-2-2-22222i−2i−2i2i-2-22i2i−2i−2i-22−2i2i-12-2-2-122211-2-2ii−i−i-1111-1-1-1-111−ii2i−2i−2i2i−i−iiiii−i−i0000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23
χ4722-2-2-22222i−2i−2i2i-2-22i2i−2i−2i-22−2i2i-12-2-2-122211-2-2ii−i−i-1111-1-1-1-111−ii2i−2i−2i2i−i−iiiii−i−i0000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23
χ4822-2-2-2222−2i2i2i−2i-2-2−2i−2i2i2i-222i−2i22-2-22222-2-2-2-22i2i−2i−2i2-2-2-22222-2-2−2i2i−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ4922-2-2-2222−2i2i2i−2i-2-2−2i−2i2i2i-222i−2i2-1112-1-1-1-2-2112i2i−2i−2i-1-211-12-1-111−2i2ii−i−iiii−i−i−i−iii00−i3i300i3−i300000000−333−30000000000000000
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χ5222-2-2-2222−2i2i2i−2i-2-2−2i−2i2i2i-222i−2i-12-2-2-122211-2-2−i−iii-1111-1-1-1-111i−i−2i2i2i−2iii−i−i−i−iii0000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2111-21111-2-2-2-2-2-211111111000000000000000000000000000000000000
χ5444444444-4-4-4-444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-222221-2111-21111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ554444-44-444-44-4444444-4-4-4-4-2-222-2-222-2-2-2-2222212-1-112-1-111-2-2-22-2211-1-111-1-1000000000000000000000000000000000000
χ564444-44-44-44-4444-4-4-4-4-4-444-2-222-2-222-2-2-2-2-2-2-2-212-1-112-1-111222-22-2-1-111-1-111000000000000000000000000000000000000
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χ5844-4-444-44−4i−4i4i4i-4-4−4i−4i4i4i4-4−4i4i-2-2-2-2-2-22222222i2i−2i−2i1-21112-1-1-1-12i−2i2i2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000
χ5944-4-4-44444i−4i−4i4i-4-44i4i−4i−4i-44−4i4i-2-222-2-2-2-222222i2i−2i−2i12-1-11-211-1-1−2i2i−2i2i2i−2iii−i−i−i−iii000000000000000000000000000000000000
χ6044-4-4-4444−4i4i4i−4i-4-4−4i−4i4i4i-444i−4i-2-222-2-2-2-22222−2i−2i2i2i12-1-11-211-1-12i−2i2i−2i−2i2i−i−iiiii−i−i000000000000000000000000000000000000
χ614-44i−4i040-400004i−4i000000004400-4-4004i−4i4i−4i00004000-40004i−4i00000000000000000000000000000000000000000000000000
χ624-44i−4i040-400004i−4i000000004-2−2i32i3-4223−234i−4i−2i2i0000-20−2i32i32023−23−2i2i00000000000000000000000000000000000000000000000000
χ634-44i−4i040-400004i−4i000000004-22i3−2i3-42−23234i−4i−2i2i0000-202i3−2i320−2323−2i2i00000000000000000000000000000000000000000000000000
χ644-44i−4i040-400004i−4i00000000-24002-400−2i2i4i−4i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13-20002000−2i2i00000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000000000
χ654-44i−4i040-400004i−4i00000000-24002-400−2i2i4i−4i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13-20002000−2i2i000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000000000
χ664-44i−4i040-400004i−4i00000000-2-2−2i32i32223−23−2i2i−2i2i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ1310i3−i3-10−33i−i0000003ζ7+3ζ23−3ζ7−3ζ23ζ7−ζ23−ζ7+ζ23−3ζ5−3ζ133ζ5+3ζ13−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.