Finite Group Databasebeta

← Group #72342732

Character table — Group #72342732

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222233334466666666668888888888881212161616161616161616161616242424242424242424242424242424242424242432323232323232324848484848484848
order12224444448888222288444444888822344666121212128812121212242424242424242422441616161616161616161616161616161666661212121288888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111-1-1111111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ61111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111-1-1111111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ71111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ81111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ911-1-1i−i1-1i−iii−i−i11-1-11-11-1i−ii−iii−i−i1-11i−i1-1-1ii−i−i1-1i−i1-111-1-1ii−i−i1-1i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1311-1-1ii−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1011-1-1i−i1-1i−iii−i−i11-1-11-11-1i−ii−iii−i−i1-11i−i1-1-1ii−i−i1-1i−i1-111-1-1ii−i−i1-1i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1311-1-1ii−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1111-1-1i−i1-1i−iii−i−i11-1-11-11-1i−ii−iii−i−i-111−ii1-1-1ii−i−i1-1i−i1-111-1-1ii−i−i-11−iiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13-1-111−i−iii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1211-1-1i−i1-1i−iii−i−i11-1-11-11-1i−ii−iii−i−i-111−ii1-1-1ii−i−i1-1i−i1-111-1-1ii−i−i-11−ii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13-1-111−i−iiiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1311-1-1−ii1-1−ii−i−iii11-1-11-11-1−ii−ii−i−iii1-11−ii1-1-1−i−iii1-1−ii1-111-1-1−i−iii1-1−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2311-1-1−i−iii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1411-1-1−ii1-1−ii−i−iii11-1-11-11-1−ii−ii−i−iii1-11−ii1-1-1−i−iii1-1−ii1-111-1-1−i−iii1-1−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2311-1-1−i−iiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1511-1-1−ii1-1−ii−i−iii11-1-11-11-1−ii−ii−i−iii-111i−i1-1-1−i−iii1-1−ii1-111-1-1−i−iii-11i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23-1-111ii−i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1611-1-1−ii1-1−ii−i−iii11-1-11-11-1−ii−ii−i−iii-111i−i1-1-1−i−iii1-1−ii1-111-1-1−i−iii-11i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23-1-111ii−i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1722222222222222222222222222222222-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000000000000000-1-1-1-1-1-1-1-100000000
χ18222222222222222222222222222222-2-2-1-2-2-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000000001111111100000000
χ192222222222-2-2-2-22222-2-2222222-2-2-2-2002002222222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ202222222222-2-2-2-22222-2-2222222-2-2-2-200-100-1-1-1-1-1-1-1-2-2-1-1-1-11111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ212222222222-2-2-2-22222-2-2222222-2-2-2-200-100-1-1-1-1-1-1-1-2-2-1-1-1-11111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ22222222-2-2-2-20000222200-2-222-2-2000000200222222200-2-2-2-2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ23222222-2-2-2-20000222200-2-222-2-2000000200222222200-2-2-2-2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ242222-2-222-2-222222222-2-222-2-2-2-2222200200222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000000000000000
χ252222-2-222-2-222222222-2-222-2-2-2-2222200-100-1-1-11111-2-211-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ262222-2-222-2-222222222-2-222-2-2-2-2222200-100-1-1-11111-2-211-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ272222-2-222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222-1-2-2-1-1-111112211-1-1-1-1-1-1111122-2-20000000000000000-1-1-1-1111100000000
χ282222-2-222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-122-1-1-111112211-1-1-1-1-1-11111-2-22200000000000000001111-1-1-1-100000000
χ292222-2-2-2-2220000222200-2-2-2-222000000200222-2-2-2-20022-2-20000000000002−22−2−22−222−22−2−22−220000000000000000
χ302222-2-2-2-2220000222200-2-2-2-222000000200222-2-2-2-20022-2-2000000000000−22−222−22−2−22−222−22−20000000000000000
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χ3222-2-22i−2i2-22i−2i2i2i−2i−2i22-2-22-22-22i−2i2i−2i2i2i−2i−2i-22-1−2i2i-111−i−iii2-2−ii-11-1-111−i−iii-22−2i2i000000000000000011-1-1ii−i−i00000000
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χ3422-2-22i−2i2-22i−2i−2i−2i2i2i22-2-2-222-22i−2i2i−2i−2i−2i2i2i00-100-111−i−iii-22−ii-1111-1-1ii−i−i00000000000000000000−i3i3i3−i33−3−3300000000
χ3522-2-22i−2i2-22i−2i−2i−2i2i2i22-2-2-222-22i−2i2i−2i−2i−2i2i2i00-100-111−i−iii-22−ii-1111-1-1ii−i−i00000000000000000000i3−i3−i3i3−333−300000000
χ3622-2-22i−2i-22−2i2i000022-2-200-222i−2i−2i2i0000002002-2-22i2i−2i−2i00−2i2i-220000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ3722-2-22i−2i-22−2i2i000022-2-200-222i−2i−2i2i0000002002-2-22i2i−2i−2i00−2i2i-22000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ3822-2-2−2i2i2-2−2i2i2i2i−2i−2i22-2-2-222-2−2i2i−2i2i2i2i−2i−2i002002-2-2−2i−2i2i2i-22−2i2i2-2-2-2222i2i−2i−2i000000000000000000000000000000000000
χ3922-2-2−2i2i2-2−2i2i2i2i−2i−2i22-2-2-222-2−2i2i−2i2i2i2i−2i−2i00-100-111ii−i−i-22i−i-1111-1-1−i−iii00000000000000000000−i3i3i3−i3−333−300000000
χ4022-2-2−2i2i2-2−2i2i2i2i−2i−2i22-2-2-222-2−2i2i−2i2i2i2i−2i−2i00-100-111ii−i−i-22i−i-1111-1-1−i−iii00000000000000000000i3−i3−i3i33−3−3300000000
χ4122-2-2−2i2i2-2−2i2i−2i−2i2i2i22-2-22-22-2−2i2i−2i2i−2i−2i2i2i2-2-1−2i2i-111ii−i−i2-2i−i-11-1-111ii−i−i2-2−2i2i0000000000000000-1-111ii−i−i00000000
χ4222-2-2−2i2i2-2−2i2i−2i−2i2i2i22-2-22-22-2−2i2i−2i2i−2i−2i2i2i-22-12i−2i-111ii−i−i2-2i−i-11-1-111ii−i−i-222i−2i000000000000000011-1-1−i−iii00000000
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χ4533333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1330330000000-1-1000000000000-1-1-1-111111111-1-1-1-1-1-1-1-1000000001111-1-1-1-1
χ4633333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1330330000000-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-11111111100000000-1-1-1-11111
χ4733333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1-3-30-3-30000000-1-1000000000000111111111111-1-1-1-1-1-1-1-100000000-1-1-1-11111
χ4833333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1-3-30-3-30000000-1-10000000000001111-1-1-1-1-1-1-1-111111111000000001111-1-1-1-1
χ493333-3-333-3-3-3-3-3-3-1-1-1-133-1-111111111330-3-30000000-1-1000000000000-1-111iiii−i−i−i−i−i−i−i−iiiii00000000ii−i−i−i−iii
χ503333-3-333-3-3-3-3-3-3-1-1-1-133-1-111111111330-3-30000000-1-1000000000000-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000−i−iiiii−i−i
χ513333-3-333-3-3-3-3-3-3-1-1-1-133-1-111111111-3-30330000000-1-100000000000011-1-1iiii−i−i−i−i−i−i−i−iiiii00000000−i−iiiii−i−i
χ523333-3-333-3-3-3-3-3-3-1-1-1-133-1-111111111-3-30330000000-1-100000000000011-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000ii−i−i−i−iii
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χ5933-3-3−3i3i3-3−3i3i−3i−3i3i3i-1-1113-3-11i−ii−iii−i−i-3303i−3i0000000-110000000000001-1−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
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χ61444444-4-4-4-40000444400-4-444-4-4000000-200-2-2-2-2-2-2-200222200000000000000000000000000000000000000000000
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χ714-4-4400000022−22−22224-4-440000000022−22−222200400-4-440000000000000022−22−2222000000000000000000000000000000000000
χ724-4-4400000022−22−22224-4-440000000022−22−222200-20022-2−2i32i32i3−2i3000000−i6i6i6−i6−222−2000000000000000000000000000000000000
χ734-4-4400000022−22−22224-4-440000000022−22−222200-20022-22i3−2i3−2i32i3000000i6−i6−i6i6−222−2000000000000000000000000000000000000
χ744-4-44000000−222222−224-4-4400000000−222222−2200400-4-4400000000000000−222222−22000000000000000000000000000000000000
χ754-4-44000000−222222−224-4-4400000000−222222−2200-20022-2−2i32i32i3−2i3000000i6−i6−i6i62−2−22000000000000000000000000000000000000
χ764-4-44000000−222222−224-4-4400000000−222222−2200-20022-22i3−2i3−2i32i3000000−i6i6i6−i62−2−22000000000000000000000000000000000000
χ776666666666-6-6-6-6-2-2-2-2-6-6-2-2-2-2-2-2222200000000000022000000000000000000000000000000000000000000000000
χ78666666-6-6-6-60000-2-2-2-20022-2-2220000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ79666666-6-6-6-60000-2-2-2-20022-2-2220000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ806666-6-666-6-66666-2-2-2-2-6-6-2-22222-2-2-2-200000000000022000000000000000000000000000000000000000000000000
χ816666-6-6-6-6660000-2-2-2-2002222-2-200000000000000000000000000000000002−22−2−22−22−22−222−22−20000000000000000
χ826666-6-6-6-6660000-2-2-2-2002222-2-20000000000000000000000000000000000−22−222−22−22−22−2−22−220000000000000000
χ8366-6-66i−6i6-66i−6i−6i−6i6i6i-2-222-66-22−2i2i−2i2i2i2i−2i−2i0000000000002-2000000000000000000000000000000000000000000000000
χ8466-6-66i−6i-66−6i6i0000-2-222002-2−2i2i2i−2i00000000000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ8566-6-66i−6i-66−6i6i0000-2-222002-2−2i2i2i−2i0000000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ8666-6-6−6i6i6-6−6i6i6i6i−6i−6i-2-222-66-222i−2i2i−2i−2i−2i2i2i0000000000002-2000000000000000000000000000000000000000000000000
χ8766-6-6−6i6i-666i−6i0000-2-222002-22i−2i−2i2i00000000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ8866-6-6−6i6i-666i−6i0000-2-222002-22i−2i−2i2i0000000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ8912-1212-12000000−6i26i2−6i26i2-44-44000000002i2−2i22i2−2i200000000000000000000000000000000000000000000000000000000000000
χ9012-1212-120000006i2−6i26i2−6i2-44-4400000000−2i22i2−2i22i200000000000000000000000000000000000000000000000000000000000000
χ9112-12-121200000062−62−6262-444-400000000−222222−2200000000000000000000000000000000000000000000000000000000000000
χ9212-12-1212000000−626262−62-444-40000000022−22−222200000000000000000000000000000000000000000000000000000000000000

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