Finite Group Databasebeta

← Group #11797387

Character table — Group #11797387

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444444444444444444444444444444444444444444444444444444181818183636363636367272727272727272
order12442444442334446666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121288888888881616161616161616
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
χ51111111111-111-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ61111111111-111-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ71111111111-111-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii
χ81111111111-111-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i
χ911111-1-1-1-111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-11-11-11-1
χ1011111-1-1-1-111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-11-11-11
χ1111111-1-1-1-111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ1211111-1-1-1-111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ1311111-1-1-1-11-111-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1111-1-111-1-11
χ1411111-1-1-1-11-111-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-111-1-111-1
χ1511111-1-1-1-11-111-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1i−i−ii−iii−i
χ1611111-1-1-1-11-111-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1−iii−ii−i−ii
χ172222-20000-202202i−2i0000000022-2-2-2-22222-2-2-2-20000000000000000000000002i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i22-2-200002i−2i00000000
χ182222-20000-202202i−2i0000000022-2-2-2-22222-2-2-2-20000000000000000000000002i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i-2-2220000−2i2i00000000
χ192222-20000-20220−2i2i0000000022-2-2-2-22222-2-2-2-2000000000000000000000000−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i22-2-20000−2i2i00000000
χ202222-20000-20220−2i2i0000000022-2-2-2-22222-2-2-2-2000000000000000000000000−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i-2-22200002i−2i00000000
χ2122-2-220000-2222-20022222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-200000000000000002i−2i2i−2i2i−2i000000000000
χ2222-2-220000-2222-20022222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-20000000000000000−2i2i−2i2i−2i2i000000000000
χ2322-2-220000-2-222200-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-200000000000000002222222200000000000000002i−2i2i−2i−2i2i000000000000
χ2422-2-220000-2-222200-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000222222220000000000000000−2i2i−2i2i2i−2i000000000000
χ2522-2-2-22i2i−2i−2i20220000000000022-2-2-2-2-2-2-2-222222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i0000000000000000000000002i−2i−2i2i002-20000000000
χ2622-2-2-22i2i−2i−2i20220000000000022-2-2-2-2-2-2-2-222222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i000000000000000000000000−2i2i2i−2i00-220000000000
χ2722-2-2-2−2i−2i2i2i20220000000000022-2-2-2-2-2-2-2-22222−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i0000000000000000000000002i−2i−2i2i00-220000000000
χ2822-2-2-2−2i−2i2i2i20220000000000022-2-2-2-2-2-2-2-22222−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i000000000000000000000000−2i2i2i−2i002-20000000000
χ29444444444441-24441111-2-2-2-21-211-2-211-2-211-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-2000000000000000000
χ3044444444444-21444-2-2-2-21111-21-2-211-2-211-2-211-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-21111000000000000000000
χ314444444444-41-2-4-4-4-1-1-1-122221-211-2-211-2-211-2-21111-2-2-2-21111-2-2-2-2-1-1-1-12222-1-1-1-12222-1-1-1-12222000000000000000000
χ324444444444-4-21-4-4-42222-1-1-1-1-21-2-211-2-211-2-211-2-2-2-21111-2-2-2-211112222-1-1-1-12222-1-1-1-12222-1-1-1-1000000000000000000
χ3344444-4-4-4-4441-24-4-41111-2-2-2-21-211-2-211-2-211-2-2-1-1-1-12222-1-1-1-122221111-2-2-2-2-1-1-1-12222-1-1-1-12222000000000000000000
χ3444444-4-4-4-444-214-4-4-2-2-2-21111-21-2-211-2-211-2-2112222-1-1-1-12222-1-1-1-1-2-2-2-211112222-1-1-1-12222-1-1-1-1000000000000000000
χ3544444-4-4-4-44-41-2-444-1-1-1-122221-211-2-211-2-211-2-2-1-1-1-12222-1-1-1-12222-1-1-1-122221111-2-2-2-21111-2-2-2-2000000000000000000
χ3644444-4-4-4-44-4-21-4442222-1-1-1-1-21-2-211-2-211-2-2112222-1-1-1-12222-1-1-1-12222-1-1-1-1-2-2-2-21111-2-2-2-21111000000000000000000
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χ384444-40000-401-204i−4i-3-33300001-2-1-12211-2-2-1-122−3i−3i3i3i0000−3i−3i3i3i0000-3-3330000iiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i000000000000000000
χ394444-40000-401-20−4i4i33-3-300001-2-1-12211-2-2-1-122−3i−3i3i3i0000−3i−3i3i3i000033-3-30000−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i000000000000000000
χ404444-40000-401-20−4i4i-3-33300001-2-1-12211-2-2-1-1223i3i−3i−3i00003i3i−3i−3i0000-3-3330000−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i000000000000000000
χ414444-40000-40-2104i−4i000033-3-3-2122-1-1-2-21122-1-100003i3i−3i−3i00003i3i−3i−3i000033-3-3−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000
χ424444-40000-40-2104i−4i0000-3-333-2122-1-1-2-21122-1-10000−3i−3i3i3i0000−3i−3i3i3i0000-3-333−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000
χ434444-40000-40-210−4i4i000033-3-3-2122-1-1-2-21122-1-10000−3i−3i3i3i0000−3i−3i3i3i000033-3-32i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000
χ444444-40000-40-210−4i4i0000-3-333-2122-1-1-2-21122-1-100003i3i−3i−3i00003i3i−3i−3i0000-3-3332i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000
χ4544-4-440000-441-2-4001111-2-2-2-21-211-2-2-1-122-1-12233-3-30000-3-3330000-1-1-1-1222233-3-3000033-3-30000000000000000000000
χ4644-4-440000-441-2-4001111-2-2-2-21-211-2-2-1-122-1-122-3-333000033-3-30000-1-1-1-12222-3-3330000-3-3330000000000000000000000
χ4744-4-440000-44-21-400-2-2-2-21111-21-2-21122-1-122-1-1000033-3-30000-3-3332222-1-1-1-1000033-3-3000033-3-3000000000000000000
χ4844-4-440000-44-21-400-2-2-2-21111-21-2-21122-1-122-1-10000-3-333000033-3-32222-1-1-1-10000-3-3330000-3-333000000000000000000
χ4944-4-440000-4-41-2400-1-1-1-122221-211-2-2-1-122-1-12233-3-30000-3-33300001111-2-2-2-2-3-3330000-3-3330000000000000000000000
χ5044-4-440000-4-41-2400-1-1-1-122221-211-2-2-1-122-1-122-3-333000033-3-300001111-2-2-2-233-3-3000033-3-30000000000000000000000
χ5144-4-440000-4-4-214002222-1-1-1-1-21-2-21122-1-122-1-1000033-3-30000-3-333-2-2-2-211110000-3-3330000-3-333000000000000000000
χ5244-4-440000-4-4-214002222-1-1-1-1-21-2-21122-1-122-1-10000-3-333000033-3-3-2-2-2-21111000033-3-3000033-3-3000000000000000000
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χ5444-4-4-44i4i−4i−4i401-2000-3-33300001-2-1-122-1-12211-2-2iiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i33-3-30000−3i−3i3i3i00003i3i−3i−3i0000000000000000000000
χ5544-4-4-44i4i−4i−4i40-21000000033-3-3-2122-1-122-1-1-2-211−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000-3-33300003i3i−3i−3i0000−3i−3i3i3i000000000000000000
χ5644-4-4-44i4i−4i−4i40-210000000-3-333-2122-1-122-1-1-2-211−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000033-3-30000−3i−3i3i3i00003i3i−3i−3i000000000000000000
χ5744-4-4-4−4i−4i4i4i401-200033-3-300001-2-1-122-1-12211-2-2−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i-3-3330000−3i−3i3i3i00003i3i−3i−3i0000000000000000000000
χ5844-4-4-4−4i−4i4i4i401-2000-3-33300001-2-1-122-1-12211-2-2−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i33-3-300003i3i−3i−3i0000−3i−3i3i3i0000000000000000000000
χ5944-4-4-4−4i−4i4i4i40-21000000033-3-3-2122-1-122-1-1-2-2112i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000-3-3330000−3i−3i3i3i00003i3i−3i−3i000000000000000000
χ6044-4-4-4−4i−4i4i4i40-210000000-3-333-2122-1-122-1-1-2-2112i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000033-3-300003i3i−3i−3i0000−3i−3i3i3i000000000000000000
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χ664-44i−4i02+2i−2−2i2−2i−2+2i00-2100000−2i32i3−i3i3i3−i32-1003-3−2i2i−ii003i−3i1+i−1−i−1−i1+i−2+i2−i1−2i−1+2i−1+i1−i1−i−1+i1+2i−1−2i−2−i2+i0023−233−3−33−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ113−3i3−i3−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−33i3−i3000000000000000000
χ674-44i−4i02+2i−2−2i2−2i−2+2i00-21000002i3−2i3i3−i3−i3i32-1003-3−2i2i−ii003i−3i1+i−1−i−1−i1+i−2+i2−i1−2i−1+2i−1+i1−i1−i−1+i1+2i−1−2i−2−i2+i00−2323−333−3ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−33−i3i3ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ113−3−i3i3000000000000000000
χ684-44i−4i02+2i−2−2i2−2i−2+2i00-21000−2i32i300i3−i3i3−i32-100-33−2i2i−ii00−3i3i1+i−1−i−1−i1+i1−2i−1+2i−2+i2−i−1+i1−i1−i−1+i−2−i2+i1+2i−1−2i23−2300−33−33−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11i3−i3−33−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11i3−i33−3000000000000000000
χ694-44i−4i02+2i−2−2i2−2i−2+2i00-210002i3−2i300−i3i3−i3i32-100-33−2i2i−ii00−3i3i1+i−1−i−1−i1+i1−2i−1+2i−2+i2−i−1+i1−i1−i−1+i−2−i2+i1+2i−1−2i−2323003−33−3ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−i3i33−3ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−i3i3−33000000000000000000
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χ964-4−4i4i0−2+2i2−2i−2−2i2+2i00-210002i3−2i300−i3i3−i3i32-100-332i−2ii−i003i−3i−1+i1−i1−i−1+i−1−2i1+2i2+i−2−i1+i−1−i−1−i1+i2−i−2+i−1+2i1−2i23−2300−33−33−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11i3−i33−3−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11i3−i3−33000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.