Finite Group Databasebeta

← Group #14514380

Character table — Group #14514380

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111444455556688881616161616161616242430303030303030303030404040406060606011114444555566888816161616161616162424303030303030303030304040404060606060
order1244510202022442436121215153030606060601020248888888866121244442244101020202244246612123030303060606060102024888888886612124444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111-1-1-1-11111111111111111-1-1iiii−i−i−i−i-1-1-1-1ii−i−i11111111-1-1-1-11111111111111111-1-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ411111111-1-1-1-11111111111111111-1-1−i−i−i−iiiii-1-1-1-1−i−iii11111111-1-1-1-11111111111111111-1-1−i−i−i−iiiii-1-1-1-1−i−iii
χ511-1-111-1-111-1-1-1111-1-11111-1-1-1-1-11-1111-1-111-1-111-1-11-11-111-1-111-1-111-1-1-1111-1-11111-1-1-1-1-11-1111-1-111-1-111-1-11-11-1
χ611-1-111-1-111-1-1-1111-1-11111-1-1-1-1-11-11-1-111-1-11111-1-1-11-1111-1-111-1-111-1-1-1111-1-11111-1-1-1-1-11-11-1-111-1-11111-1-1-11-11
χ711-1-111-1-1-1-111-1111-1-11111-1-1-1-1-111-1ii−i−i−i−iii-1-111i−i−ii11-1-111-1-1-1-111-1111-1-11111-1-1-1-1-111-1ii−i−i−i−iii-1-111i−i−ii
χ811-1-111-1-1-1-111-1111-1-11111-1-1-1-1-111-1−i−iiiii−i−i-1-111−iii−i11-1-111-1-1-1-111-1111-1-11111-1-1-1-1-111-1−i−iiiii−i−i-1-111−iii−i
χ922222222222222-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-1000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-10000
χ1022222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-122-2-2000000001111000022222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-122-2-20000000011110000
χ1122-2-222-2-222-2-2-22-1-111-1-1-1-11111-22-2200000000-1-111000022-2-222-2-222-2-2-22-1-111-1-1-1-11111-22-2200000000-1-1110000
χ1222-2-222-2-2-2-222-22-1-111-1-1-1-11111-222-20000000011-1-1000022-2-222-2-2-2-222-22-1-111-1-1-1-11111-222-20000000011-1-10000
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χ142-22i−2i2-22i−2i2-22i−2i00-11i−i-1-111ii−i−i0000−22i2−i2−22i2−i21-1i−i00002-22i−2i2-22i−2i2-22i−2i00-11i−i-1-111ii−i−i0000−22i2−i2−22i2−i21-1i−i0000
χ152-22i−2i2-22i−2i-22−2i2i00-11i−i-1-111ii−i−i0000−i2i2−22i2−i22−2-11−ii00002-22i−2i2-22i−2i-22−2i2i00-11i−i-1-111ii−i−i0000−i2i2−22i2−i22−2-11−ii0000
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χ172-2−2i2i2-2−2i2i2-2−2i2i00-11−ii-1-111−i−iii00002−2i2−i22−2i2−i21-1−ii00002-2−2i2i2-2−2i2i2-2−2i2i00-11−ii-1-111−i−iii00002−2i2−i22−2i2−i21-1−ii0000
χ182-2−2i2i2-2−2i2i2-2−2i2i00-11−ii-1-111−i−iii0000−22−i2i2−22−i2i21-1−ii00002-2−2i2i2-2−2i2i2-2−2i2i00-11−ii-1-111−i−iii0000−22−i2i2−22−i2i21-1−ii0000
χ192-2−2i2i2-2−2i2i-222i−2i00-11−ii-1-111−i−iii0000−i2i22−2i2−i2−22-11i−i00002-2−2i2i2-2−2i2i-222i−2i00-11−ii-1-111−i−iii0000−i2i22−2i2−i2−22-11i−i0000
χ202-2−2i2i2-2−2i2i-222i−2i00-11−ii-1-111−i−iii0000i2−i2−22−i2i22−2-11i−i00002-2−2i2i2-2−2i2i-222i−2i00-11−ii-1-111−i−iii0000i2−i2−22−i2i22−2-11i−i0000
χ21333333333333-1-1000000000000-1-1-1-1111111110000-1-1-1-1333333333333-1-1000000000000-1-1-1-1111111110000-1-1-1-1
χ22333333333333-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-100001111333333333333-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-100001111
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χ2433333333-3-3-3-3-1-1000000000000-1-111−i−i−i−iiiii0000ii−i−i33333333-3-3-3-3-1-1000000000000-1-111−i−i−i−iiiii0000ii−i−i
χ2533-3-333-3-333-3-31-10000000000001-11-111-1-111-1-10000-11-1133-3-333-3-333-3-31-10000000000001-11-111-1-111-1-10000-11-11
χ2633-3-333-3-333-3-31-10000000000001-11-1-1-111-1-11100001-11-133-3-333-3-333-3-31-10000000000001-11-1-1-111-1-11100001-11-1
χ2733-3-333-3-3-3-3331-10000000000001-1-11ii−i−i−i−iii0000−iii−i33-3-333-3-3-3-3331-10000000000001-1-11ii−i−i−i−iii0000−iii−i
χ2833-3-333-3-3-3-3331-10000000000001-1-11−i−iiiii−i−i0000i−i−ii33-3-333-3-3-3-3331-10000000000001-1-11−i−iiiii−i−i0000i−i−ii
χ294444-1-1-1-10000444444-1-1-1-1-1-1-1-1-1-10000000000000000004444-1-1-1-10000444444-1-1-1-1-1-1-1-1-1-1000000000000000000
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χ314444-1-1-1-1000044-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-1-10000000000000000004444-1-1-1-1000044-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-1-1000000000000000000
χ3244-4-4-1-1110000-4444-4-4-1-1-1-111111-100000000000000000044-4-4-1-1110000-4444-4-4-1-1-1-111111-1000000000000000000
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χ364-44i−4i4-44i−4i-44−4i4i001-1−ii11-1-1−i−iii0000000000001-1i−i00004-44i−4i4-44i−4i-44−4i4i001-1−ii11-1-1−i−iii0000000000001-1i−i0000
χ374-4−4i4i4-4−4i4i4-4−4i4i001-1i−i11-1-1ii−i−i000000000000-11i−i00004-4−4i4i4-4−4i4i4-4−4i4i001-1i−i11-1-1ii−i−i000000000000-11i−i0000
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χ418-88i−8i-22−2i2i000000-444i−4i11-1-1−i−iii000000000000000000008-88i−8i-22−2i2i000000-444i−4i11-1-1−i−iii00000000000000000000
χ428-8−8i8i-222i−2i0000002-22i−2i−1−i152−1+i1521+i1521−i152−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118000000000000000000008-8−8i8i-222i−2i0000002-22i−2i−1−i152−1+i1521+i1521−i152−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ11800000000000000000000
χ438-8−8i8i-222i−2i0000002-22i−2i−1+i152−1−i1521−i1521+i152−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94000000000000000000008-8−8i8i-222i−2i0000002-22i−2i−1+i152−1−i1521−i1521+i152−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ9400000000000000000000
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χ4512121212-3-3-3-30000-4-40000000000001100000000000000000012121212-3-3-3-30000-4-400000000000011000000000000000000
χ461212-12-12-3-33300004-4000000000000-110000000000000000001212-12-12-3-33300004-4000000000000-11000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ48111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ4911111111-1-1-1-11111111111111111-1-1iiii−i−i−i−i-1-1-1-1ii−i−i-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1111−i−iii
χ5011111111-1-1-1-11111111111111111-1-1−i−i−i−iiiii-1-1-1-1−i−iii-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1111ii−i−i
χ5111-1-111-1-111-1-1-1111-1-11111-1-1-1-1-11-1111-1-111-1-111-1-11-11-1-1-111-1-111-1-1111-1-1-111-1-1-1-111111-11-1-1-111-1-111-1-111-11-11
χ5211-1-111-1-111-1-1-1111-1-11111-1-1-1-1-11-11-1-111-1-11111-1-1-11-11-1-111-1-111-1-1111-1-1-111-1-1-1-111111-11-111-1-111-1-1-1-1111-11-1
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χ5411-1-111-1-1-1-111-1111-1-11111-1-1-1-1-111-1−i−iiiii−i−i-1-111−iii−i-1-111-1-11111-1-11-1-1-111-1-1-1-111111-1-11ii−i−i−i−iii11-1-1i−i−ii
χ5522222222222222-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-10000-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111-2-2-2-20000000011110000
χ5622222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-122-2-20000000011110000-2-2-2-2-2-2-2-22222-2-2111111111111-2-22200000000-1-1-1-10000
χ5722-2-222-2-222-2-2-22-1-111-1-1-1-11111-22-2200000000-1-1110000-2-222-2-222-2-2222-211-1-11111-1-1-1-12-22-20000000011-1-10000
χ5822-2-222-2-2-2-222-22-1-111-1-1-1-11111-222-20000000011-1-10000-2-222-2-22222-2-22-211-1-11111-1-1-1-12-2-2200000000-1-1110000
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χ7233-3-333-3-333-3-31-10000000000001-11-1-1-111-1-11100001-11-1-3-333-3-333-3-333-11000000000000-11-1111-1-111-1-10000-11-11
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χ814-44i−4i4-44i−4i4-44i−4i001-1−ii11-1-1−i−iii000000000000-11−ii0000-44−4i4i-44−4i4i-44−4i4i00-11i−i-1-111ii−i−i0000000000001-1i−i0000
χ824-44i−4i4-44i−4i-44−4i4i001-1−ii11-1-1−i−iii0000000000001-1i−i0000-44−4i4i-44−4i4i4-44i−4i00-11i−i-1-111ii−i−i000000000000-11−ii0000
χ834-4−4i4i4-4−4i4i4-4−4i4i001-1i−i11-1-1ii−i−i000000000000-11i−i0000-444i−4i-444i−4i-444i−4i00-11−ii-1-111−i−iii0000000000001-1−ii0000
χ844-4−4i4i4-4−4i4i-444i−4i001-1i−i11-1-1ii−i−i0000000000001-1−ii0000-444i−4i-444i−4i4-4−4i4i00-11−ii-1-111−i−iii000000000000-11i−i0000
χ858-88i−8i-22−2i2i0000002-2−2i2i−1−i152−1+i1521+i1521−i152ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ11800000000000000000000-88−8i8i2-22i−2i000000-222i−2i1+i1521−i152−1−i152−1+i152−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ11800000000000000000000
χ868-88i−8i-22−2i2i0000002-2−2i2i−1+i152−1−i1521−i1521+i152ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ9400000000000000000000-88−8i8i2-22i−2i000000-222i−2i1−i1521+i152−1+i152−1−i152−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ9400000000000000000000
χ878-88i−8i-22−2i2i000000-444i−4i11-1-1−i−iii00000000000000000000-88−8i8i2-22i−2i0000004-4−4i4i-1-111ii−i−i00000000000000000000
χ888-8−8i8i-222i−2i0000002-22i−2i−1−i152−1+i1521+i1521−i152−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ11800000000000000000000-888i−8i2-2−2i2i000000-22−2i2i1+i1521−i152−1−i152−1+i152ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ11800000000000000000000
χ898-8−8i8i-222i−2i0000002-22i−2i−1+i152−1−i1521−i1521+i152−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ9400000000000000000000-888i−8i2-2−2i2i000000-22−2i2i1−i1521+i152−1+i152−1−i152ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ9400000000000000000000
χ908-8−8i8i-222i−2i000000-44−4i4i11-1-1ii−i−i00000000000000000000-888i−8i2-2−2i2i0000004-44i−4i-1-111−i−iii00000000000000000000
χ9112121212-3-3-3-30000-4-400000000000011000000000000000000-12-12-12-123333000044000000000000-1-1000000000000000000
χ921212-12-12-3-33300004-4000000000000-11000000000000000000-12-12121233-3-30000-440000000000001-1000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.