Finite Group Databasebeta

← Group #11785488

Character table — Group #11785488

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444444444444444444444444444444444444444444444444444444181818183636363636367272727272727272
order124424888823346666666666666688121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424224424888844444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111-111-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ61111111111-111-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ71111111111-111-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii
χ81111111111-111-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i
χ9111111-1-1-1-1111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-11-11-11-1
χ10111111-1-1-1-1111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-11-11-11
χ11111111-1-1-1-1111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ12111111-1-1-1-1111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ13111111-1-1-1-1-111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1111-1-111-1-11
χ14111111-1-1-1-1-111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-111-1-111-1
χ15111111-1-1-1-1-111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1i−i−ii−iii−i
χ16111111-1-1-1-1-111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1−iii−ii−i−ii
χ172222-2-200000220-2-2-2-200000000222i−2i222200000000-2-2-2-200000000000000002i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2-22-200002i−2i00000000
χ182222-2-200000220-2-2-2-200000000222i−2i222200000000-2-2-2-200000000000000002i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i-22-220000−2i2i00000000
χ192222-2-200000220-2-2-2-20000000022−2i2i222200000000-2-2-2-20000000000000000−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i2-22-20000−2i2i00000000
χ202222-2-200000220-2-2-2-20000000022−2i2i222200000000-2-2-2-20000000000000000−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i-22-2200002i−2i00000000
χ2122-2-22-20000222-22222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022-2-2-22000000000000
χ2222-2-22-20000222-22222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2222-2000000000000
χ2322-2-22-20000-22222222-2-2-2-2-2-2-2-22200-2-2-2-222222222-2-2-2-20000000000000000000000000000000022-2-22-2000000000000
χ2422-2-22-20000-22222222-2-2-2-2-2-2-2-22200-2-2-2-222222222-2-2-2-200000000000000000000000000000000-2-222-22000000000000
χ2522-2-2-2222-2-20220-2-2-2-2000000002200-2-2-2-200000000222222222222-2-2-2-2-2-2-2-200000000000000002-2-22002-20000000000
χ2622-2-2-2222-2-20220-2-2-2-2000000002200-2-2-2-200000000222222222222-2-2-2-2-2-2-2-20000000000000000-222-200-220000000000
χ2722-2-2-22-2-2220220-2-2-2-2000000002200-2-2-2-2000000002222-2-2-2-2-2-2-2-22222222200000000000000002-2-2200-220000000000
χ2822-2-2-22-2-2220220-2-2-2-2000000002200-2-2-2-2000000002222-2-2-2-2-2-2-2-2222222220000000000000000-222-2002-20000000000
χ29444444444441-2411-2-21111-2-2-2-21-24411-2-21111-2-2-2-211-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-2000000000000000000
χ3044444444444-214-2-211-2-2-2-21111-2144-2-211-2-2-2-21111-2-211-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-21111000000000000000000
χ314444444444-41-2-411-2-2-1-1-1-122221-2-4-411-2-2-1-1-1-1222211-2-21111-2-2-2-21111-2-2-2-2-1-1-1-12222-1-1-1-12222000000000000000000
χ324444444444-4-21-4-2-2112222-1-1-1-1-21-4-4-2-2112222-1-1-1-1-2-211-2-2-2-21111-2-2-2-211112222-1-1-1-12222-1-1-1-1000000000000000000
χ33444444-4-4-4-441-2411-2-21111-2-2-2-21-2-4-411-2-21111-2-2-2-211-2-2-1-1-1-12222-1-1-1-12222-1-1-1-12222-1-1-1-12222000000000000000000
χ34444444-4-4-4-44-214-2-211-2-2-2-21111-21-4-4-2-211-2-2-2-21111-2-2112222-1-1-1-12222-1-1-1-12222-1-1-1-12222-1-1-1-1000000000000000000
χ35444444-4-4-4-4-41-2-411-2-2-1-1-1-122221-24411-2-2-1-1-1-1222211-2-2-1-1-1-12222-1-1-1-122221111-2-2-2-21111-2-2-2-2000000000000000000
χ36444444-4-4-4-4-4-21-4-2-2112222-1-1-1-1-2144-2-2112222-1-1-1-1-2-2112222-1-1-1-12222-1-1-1-1-2-2-2-21111-2-2-2-21111000000000000000000
χ374444-4-4000001-20-1-12233-3-300001-24i−4i11-2-233-3-30000-1-1223i3i−3i−3i00003i3i−3i−3i0000iiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i000000000000000000
χ384444-4-4000001-20-1-12233-3-300001-2−4i4i11-2-233-3-30000-1-122−3i−3i3i3i0000−3i−3i3i3i0000−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i000000000000000000
χ394444-4-4000001-20-1-122-3-33300001-24i−4i11-2-2-3-3330000-1-122−3i−3i3i3i0000−3i−3i3i3i0000iiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i000000000000000000
χ404444-4-4000001-20-1-122-3-33300001-2−4i4i11-2-2-3-3330000-1-1223i3i−3i−3i00003i3i−3i−3i0000−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i000000000000000000
χ414444-4-400000-21022-1-1000033-3-3-214i−4i-2-211000033-3-322-1-100003i3i−3i−3i00003i3i−3i−3i−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000
χ424444-4-400000-21022-1-1000033-3-3-21−4i4i-2-211000033-3-322-1-10000−3i−3i3i3i0000−3i−3i3i3i2i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000
χ434444-4-400000-21022-1-10000-3-333-214i−4i-2-2110000-3-33322-1-10000−3i−3i3i3i0000−3i−3i3i3i−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000
χ444444-4-400000-21022-1-10000-3-333-21−4i4i-2-2110000-3-33322-1-100003i3i−3i−3i00003i3i−3i−3i2i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000
χ4544-4-44-4000041-2-411-2-21111-2-2-2-21-200-1-122-1-1-1-12222-1-1223i3i−3i−3i0000−3i−3i3i3i00003i3i−3i−3i00003i3i−3i−3i0000000000000000000000
χ4644-4-44-4000041-2-411-2-21111-2-2-2-21-200-1-122-1-1-1-12222-1-122−3i−3i3i3i00003i3i−3i−3i0000−3i−3i3i3i0000−3i−3i3i3i0000000000000000000000
χ4744-4-44-400004-21-4-2-211-2-2-2-21111-210022-1-12222-1-1-1-122-1-100003i3i−3i−3i0000−3i−3i3i3i00003i3i−3i−3i00003i3i−3i−3i000000000000000000
χ4844-4-44-400004-21-4-2-211-2-2-2-21111-210022-1-12222-1-1-1-122-1-10000−3i−3i3i3i00003i3i−3i−3i0000−3i−3i3i3i0000−3i−3i3i3i000000000000000000
χ4944-4-44-40000-41-2411-2-2-1-1-1-122221-200-1-1221111-2-2-2-2-1-1223i3i−3i−3i0000−3i−3i3i3i0000−3i−3i3i3i0000−3i−3i3i3i0000000000000000000000
χ5044-4-44-40000-41-2411-2-2-1-1-1-122221-200-1-1221111-2-2-2-2-1-122−3i−3i3i3i00003i3i−3i−3i00003i3i−3i−3i00003i3i−3i−3i0000000000000000000000
χ5144-4-44-40000-4-214-2-2112222-1-1-1-1-210022-1-1-2-2-2-2111122-1-100003i3i−3i−3i0000−3i−3i3i3i0000−3i−3i3i3i0000−3i−3i3i3i000000000000000000
χ5244-4-44-40000-4-214-2-2112222-1-1-1-1-210022-1-1-2-2-2-2111122-1-10000−3i−3i3i3i00003i3i−3i−3i00003i3i−3i−3i00003i3i−3i−3i000000000000000000
χ5344-4-4-4444-4-401-20-1-12233-3-300001-200-1-122-3-333000011-2-21111-2-2-2-2-1-1-1-1222233-3-30000-3-3330000000000000000000000
χ5444-4-4-4444-4-401-20-1-122-3-33300001-200-1-12233-3-3000011-2-21111-2-2-2-2-1-1-1-12222-3-333000033-3-30000000000000000000000
χ5544-4-4-4444-4-40-21022-1-1000033-3-3-210022-1-10000-3-333-2-211-2-2-2-211112222-1-1-1-1000033-3-30000-3-333000000000000000000
χ5644-4-4-4444-4-40-21022-1-10000-3-333-210022-1-1000033-3-3-2-211-2-2-2-211112222-1-1-1-10000-3-333000033-3-3000000000000000000
χ5744-4-4-44-4-44401-20-1-12233-3-300001-200-1-122-3-333000011-2-2-1-1-1-122221111-2-2-2-2-3-333000033-3-30000000000000000000000
χ5844-4-4-44-4-44401-20-1-122-3-33300001-200-1-12233-3-3000011-2-2-1-1-1-122221111-2-2-2-233-3-30000-3-3330000000000000000000000
χ5944-4-4-44-4-4440-21022-1-1000033-3-3-210022-1-10000-3-333-2-2112222-1-1-1-1-2-2-2-211110000-3-333000033-3-3000000000000000000
χ6044-4-4-44-4-4440-21022-1-10000-3-333-210022-1-1000033-3-3-2-2112222-1-1-1-1-2-2-2-21111000033-3-30000-3-333000000000000000000
χ614-44i−4i0022−22−2i22i201-203-300−i3i3−i3i300−2i32i3-1200i−i2i−2i3−33−30023−233i−3i00−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ232−22−2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−i2i2−i2i2ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.