Finite Group Databasebeta

← Group #72342874

Character table — Group #72342874

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222233334466666666668888888888881212161616161616161616161616242424242424242424242424242424242424242432323232323232324848484848484848
order124424444488882244882444448888234688121224242424886121212121224242424242424888888888888888888661212242424241616161616161616
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
χ3111111111111111111111111111111-11-11-1-111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-1-1-11-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ6111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-1-1-11-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ7111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-111111-1-1-1-1111-1-1-1-11-1-11111-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ8111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-111111-1-1-1-1111-1-1-1-11-1-11111-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ911-1-1-11ii−i−ii−ii−i11-1-11-1-11ii−i−ii−ii−i11-11i−i-1-1ii−i−i1-1-1ii−i−i1i−i11-1-11-1i−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
χ1011-1-1-11ii−i−ii−ii−i11-1-11-1-11ii−i−ii−ii−i11-11i−i-1-1ii−i−i1-1-1ii−i−i1i−i11-1-11-1i−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
χ1111-1-1-11ii−i−ii−ii−i11-1-11-1-11ii−i−ii−ii−i-1111−ii-1-1ii−i−i1-1-1ii−i−i1i−i11-1-1-11−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
χ1211-1-1-11ii−i−ii−ii−i11-1-11-1-11ii−i−ii−ii−i-1111−ii-1-1ii−i−i1-1-1ii−i−i1i−i11-1-1-11−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
χ1311-1-1-11−i−iii−ii−ii11-1-11-1-11−i−iii−ii−ii11-11−ii-1-1−i−iii1-1-1−i−iii1−ii11-1-11-1−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
χ1411-1-1-11−i−iii−ii−ii11-1-11-1-11−i−iii−ii−ii11-11−ii-1-1−i−iii1-1-1−i−iii1−ii11-1-11-1−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
χ1511-1-1-11−i−iii−ii−ii11-1-11-1-11−i−iii−ii−ii-1111i−i-1-1−i−iii1-1-1−i−iii1−ii11-1-1-11i−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
χ1611-1-1-11−i−iii−ii−ii11-1-11-1-11−i−iii−ii−ii-1111i−i-1-1−i−iii1-1-1−i−iii1−ii11-1-1-11i−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
χ172222222222222222222222222222222-12-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000000000000000-1-1-1-1-1-1-1-100000000
χ18222222222222222222222222222222-2-1-2-1-2-2-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000000001111111100000000
χ192222222222-2-2-2-22222-2-2222222-2-2-2-202020022-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000
χ202222222222-2-2-2-22222-2-2222222-2-2-2-20-10-100-1-11111-2-2-1-1-1-1-1-111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ212222222222-2-2-2-22222-2-2222222-2-2-2-20-10-100-1-11111-2-2-1-1-1-1-1-111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ22222222-2-2-2-222222222-2-222-2-2-2-22222020200222222-2-22-2-2-2-2222-2-2-2-2000000000000000000000000000000000000
χ23222222-2-2-2-222222222-2-222-2-2-2-222220-10-100-1-1-1-1-1-1-2-2-11111-1-1-1111100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ24222222-2-2-2-222222222-2-222-2-2-2-222220-10-100-1-1-1-1-1-1-2-2-11111-1-1-1111100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ25222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22-12-1-2-2-1-1111122-11111-111-1-1-1-122-2-20000000000000000-1-1-1-1111100000000
χ26222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-1-2-122-1-1111122-11111-111-1-1-1-1-2-22200000000000000001111-1-1-1-100000000
χ272222-2-2000022-2-2222200-2-2000022-2-202020022222200-20000-2-2-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ282222-2-2000022-2-2222200-2-2000022-2-202020022222200-20000-2-2-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ292222-2-20000-2-222222200-2-20000-2-22202020022-2-2-2-200-20000-222000000002−22−2−22−222−22−2−22−220000000000000000
χ302222-2-20000-2-222222200-2-20000-2-22202020022-2-2-2-200-20000-22200000000−22−222−22−2−22−222−22−20000000000000000
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χ3222-2-22-200002i−2i−2i2i22-2-2002-200002i−2i−2i2i020200-2-22i2i−2i−2i0020000-2−2i2i00000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
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χ3422-2-22-20000−2i2i2i−2i22-2-2002-20000−2i2i2i−2i020200-2-2−2i−2i2i2i0020000-22i−2i00000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ3522-2-2-222i2i−2i−2i2i−2i2i−2i22-2-22-2-222i2i−2i−2i2i−2i2i−2i2-1-2-12i−2i11−i−iii2-21−i−iii-1−ii-1-1112-22i−2i0000000000000000-1-111−i−iii00000000
χ3622-2-2-222i2i−2i−2i2i−2i2i−2i22-2-22-2-222i2i−2i−2i2i−2i2i−2i-2-12-1−2i2i11−i−iii2-21−i−iii-1−ii-1-111-22−2i2i000000000000000011-1-1ii−i−i00000000
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χ3922-2-2-222i2i−2i−2i−2i2i−2i2i22-2-2-22-222i2i−2i−2i−2i2i−2i2i0-10-10011ii−i−i-221−i−iii-1i−i11-1-100000000000000000000i3−i3−i3i3−333−300000000
χ4022-2-2-22−2i−2i2i2i2i−2i2i−2i22-2-2-22-22−2i−2i2i2i2i−2i2i−2i020200-2-22i2i−2i−2i-22-2−2i−2i2i2i22i−2i-2-222000000000000000000000000000000000000
χ4122-2-2-22−2i−2i2i2i2i−2i2i−2i22-2-2-22-22−2i−2i2i2i2i−2i2i−2i0-10-10011−i−iii-221ii−i−i-1−ii11-1-100000000000000000000−i3i3i3−i3−333−300000000
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χ4422-2-2-22−2i−2i2i2i−2i2i−2i2i22-2-22-2-22−2i−2i2i2i−2i2i−2i2i-2-12-12i−2i11ii−i−i2-21ii−i−i-1i−i-1-111-222i−2i000000000000000011-1-1−i−iii00000000
χ4533333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1303033000000-1-1000000000000-1-1-1-111111111-1-1-1-1-1-1-1-1000000001111-1-1-1-1
χ4633333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1303033000000-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-11111111100000000-1-1-1-11111
χ4733333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1-30-30-3-3000000-1-1000000000000111111111111-1-1-1-1-1-1-1-100000000-1-1-1-11111
χ4833333333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1-30-30-3-3000000-1-10000000000001111-1-1-1-1-1-1-1-111111111000000001111-1-1-1-1
χ49333333-3-3-3-3-3-3-3-3-1-1-1-133-1-1111111113030-3-3000000-1-1000000000000-1-111iiii−i−i−i−i−i−i−i−iiiii00000000ii−i−i−i−iii
χ50333333-3-3-3-3-3-3-3-3-1-1-1-133-1-1111111113030-3-3000000-1-1000000000000-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000−i−iiiii−i−i
χ51333333-3-3-3-3-3-3-3-3-1-1-1-133-1-111111111-30-3033000000-1-100000000000011-1-1iiii−i−i−i−i−i−i−i−iiiii00000000−i−iiiii−i−i
χ52333333-3-3-3-3-3-3-3-3-1-1-1-133-1-111111111-30-3033000000-1-100000000000011-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000ii−i−i−i−iii
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χ5933-3-3-33−3i−3i3i3i−3i3i−3i3i-1-1113-31-1ii−i−ii−ii−i-30303i−3i000000-110000000000001-1−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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χ694-44i−4i00−2−2i2+2i−2+2i2−2i00004-44i−4i0000−2−2i2+2i−2+2i2−2i00000-20200−2i2i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ130001+i−1−i1−i−1+i000−i6i6−66000000000000000000000000000000000000
χ704-44i−4i00−2−2i2+2i−2+2i2−2i00004-44i−4i0000−2−2i2+2i−2+2i2−2i00000-20200−2i2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ130001+i−1−i1−i−1+i000i6−i66−6000000000000000000000000000000000000
χ714-4−4i4i002−2i−2+2i2+2i−2−2i00004-4−4i4i00002−2i−2+2i2+2i−2−2i0000040-400−4i4i00000002−2i−2+2i2+2i−2−2i0000000000000000000000000000000000000000000
χ724-4−4i4i002−2i−2+2i2+2i−2−2i00004-4−4i4i00002−2i−2+2i2+2i−2−2i00000-202002i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000−1+i1−i−1−i1+i000−i6i66−6000000000000000000000000000000000000
χ734-4−4i4i002−2i−2+2i2+2i−2−2i00004-4−4i4i00002−2i−2+2i2+2i−2−2i00000-202002i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000−1+i1−i−1−i1+i000i6−i6−66000000000000000000000000000000000000
χ744-4−4i4i00−2+2i2−2i−2−2i2+2i00004-4−4i4i0000−2+2i2−2i−2−2i2+2i0000040-400−4i4i0000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000000000000000000
χ754-4−4i4i00−2+2i2−2i−2−2i2+2i00004-4−4i4i0000−2+2i2−2i−2−2i2+2i00000-202002i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ230001−i−1+i1+i−1−i000i6−i6−66000000000000000000000000000000000000
χ764-4−4i4i00−2+2i2−2i−2−2i2+2i00004-4−4i4i0000−2+2i2−2i−2−2i2+2i00000-202002i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230001−i−1+i1+i−1−i000−i6i66−6000000000000000000000000000000000000
χ776666666666-6-6-6-6-2-2-2-2-6-6-2-2-2-2-2-2222200000000000022000000000000000000000000000000000000000000000000
χ78666666-6-6-6-66666-2-2-2-2-6-6-2-22222-2-2-2-200000000000022000000000000000000000000000000000000000000000000
χ796666-6-6000066-6-6-2-2-2-200220000-2-222000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ806666-6-6000066-6-6-2-2-2-200220000-2-222000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ816666-6-60000-6-666-2-2-2-20022000022-2-20000000000000000000000000000002−22−2−22−22−22−222−22−20000000000000000
χ826666-6-60000-6-666-2-2-2-20022000022-2-2000000000000000000000000000000−22−222−22−22−22−2−22−220000000000000000
χ8366-6-66-600006i−6i−6i6i-2-22200-220000−2i2i2i−2i0000000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ8466-6-66-600006i−6i−6i6i-2-22200-220000−2i2i2i−2i000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ8566-6-66-60000−6i6i6i−6i-2-22200-2200002i−2i−2i2i0000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ8666-6-66-60000−6i6i6i−6i-2-22200-2200002i−2i−2i2i000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ8766-6-6-666i6i−6i−6i−6i6i−6i6i-2-222-662-2−2i−2i2i2i2i−2i2i−2i0000000000002-2000000000000000000000000000000000000000000000000
χ8866-6-6-66−6i−6i6i6i6i−6i6i−6i-2-222-662-22i2i−2i−2i−2i2i−2i2i0000000000002-2000000000000000000000000000000000000000000000000
χ8912-1212i−12i006+6i−6−6i6−6i−6+6i0000-44−4i4i0000−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000000000000000000000000000000000
χ9012-1212i−12i00−6−6i6+6i−6+6i6−6i0000-44−4i4i00002+2i−2−2i2−2i−2+2i000000000000000000000000000000000000000000000000000000000000000000
χ9112-12−12i12i006−6i−6+6i6+6i−6−6i0000-444i−4i0000−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000000000000000000000000000000000
χ9212-12−12i12i00−6+6i6−6i−6−6i6+6i0000-444i−4i00002−2i−2+2i2+2i−2−2i000000000000000000000000000000000000000000000000000000000000000000

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