Finite Group Databasebeta

← Group #72230964

Character table — Group #72230964

Order 4800.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11222444444444444448888888888888888888161616161616161616161616161616161616161616161616202020202020202025254040404040404040404040404040505050808080808080100100150150150150200300300300300300300
order1234625510101215151515303030305561010151515152020303030306060606010101010101020203030303030303030303030306060606022882424242422664040404012012012012012012012012046610103030303021244446444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-11-111-1-1-1-11-111-1-11111-1-1-1-1-1-1-11-111-1-1-1-1ii−i−i-1ii−i−ii−i
χ4111111111111111111111111111111111111111111111111111111111111111-11-111-1-1-1-11-111-1-11111-1-1-1-1-1-1-11-111-1-1-1-1−i−iii-1−i−iii−ii
χ511111111111111111111111111111111111111111111111111111111111111-11-11-1-111-1-1-11-1-111-1-1-1-11111-1-1-1-11-1-111-1-1ii−i−i-1i−ii−i−ii
χ611111111111111111111111111111111111111111111111111111111111111-11-11-1-111-1-1-11-1-111-1-1-1-11111-1-1-1-11-1-111-1-1−i−iii-1−ii−iii−i
χ711111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-11-1-1
χ811111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-111-111
χ911111-1111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111111-1-111-1-1-1
χ1011111-1111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-11-1-1111
χ1111111-1111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-11-1-1-111-1-1-1-11111-1-1-11-111-1-11-1ii−i−i1−ii−ii−ii
χ1211111-1111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-11-1-1-111-1-1-1-11111-1-1-11-111-1-11-1−i−iii1i−ii−ii−i
χ1311111-1111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11-1-1111-1ii−i−i1−i−iiii−i
χ1411111-1111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11-1-1111-1−i−iii1ii−i−i−ii
χ1511111-1111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1111111111111111-1-1-1-1-1-1-111111-1-1-1-1-111
χ1611111-1111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1111111111111111-1-1-1-1-1-1-11-1-1-1-1-11111-1-1
χ17222-2202222-222222222220222222-2-22222-2-2-2-2000000-2-2000000000000-2-2-2-2000000002200000000000000-2220000000-22-22-20000000
χ18222-2202222-222222222220222222-2-22222-2-2-2-2000000-2-2000000000000-2-2-2-2000000002200000000000000-2220000000-2-22-220000000
χ19222-2202222-222222222220222222-2-22222-2-2-2-2000000-2-2000000000000-2-2-2-200000000-2-2000000000000002-2-2000000022i−2i−2i2i0000000
χ20222-2202222-222222222220222222-2-22222-2-2-2-2000000-2-2000000000000-2-2-2-200000000-2-2000000000000002-2-200000002−2i2i2i−2i0000000
χ2122-12-122222-1-1-1-1-1-1-1-1-122-122-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-12-10000-1000000
χ2222-12-122222-1-1-1-1-1-1-1-1-122-122-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-22-2-1-111-2-2-1122-2-2-1-1-1-11111-2112-2-1-111-2100001000000
χ2322-12-122222-1-1-1-1-1-1-1-1-122-122-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-2211-1-1-2-21-1-2-2221111-1-1-1-1-211-2211-1-1-2100001000000
χ2422-12-122222-1-1-1-1-1-1-1-1-122-122-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112211-2-2-2-2111111112-1-1-2-211112-10000-1000000
χ2522-12-1-22222-1-1-1-1-1-1-1-1-122122-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-122-2-2111122-1-1-2-2-2-2111111112-1-122-1-1-1-1-2-100001000000
χ2622-12-1-22222-1-1-1-1-1-1-1-1-122122-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-12-2-2211-1-1-2-2-11-2-2221111-1-1-1-1-2112-2-1-111210000-1000000
χ2722-12-1-22222-1-1-1-1-1-1-1-1-122122-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-1-222-2-1-111-2-21-122-2-2-1-1-1-11111-211-2211-1-1210000-1000000
χ2822-12-1-22222-1-1-1-1-1-1-1-1-122122-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-1-2-222-1-1-1-122112222-1-1-1-1-1-1-1-12-1-1-2-21111-2-100001000000
χ294444444-14-1444-1-144-1-1-1-14-1-1-1-1-1-14-1-1-1-1-144-1-14-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-104040044000400-1-10000-1-1-1-10000-100-1-10000000000000
χ304444444-14-1444-1-144-1-1-1-14-1-1-1-1-1-14-1-1-1-1-144-1-14-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-10-40-400-4-4000-40011000011110000100110000000000000
χ31444444-14-144-1-144-1-144-1-14-1-1-1-1-1-1-14-1-1-1-1-1-144-14-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1404044000040-1-100-1-1-1-10000000-10-1-1000000000000000
χ32444444-14-144-1-144-1-144-1-14-1-1-1-1-1-1-14-1-1-1-1-1-144-14-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-40-40-4-40000-401100111100000001011000000000000000
χ3344444-44-14-1444-1-144-1-1-1-1-4-1-1-1-1-1-14-1-1-1-1-144-1-1-411111-1-1-4-41111111111-1-1-1-1040-400-4-400040011000011110000-100-1-10000000000000
χ3444444-44-14-1444-1-144-1-1-1-1-4-1-1-1-1-1-14-1-1-1-1-144-1-1-411111-1-1-4-41111111111-1-1-1-10-4040044000-400-1-10000-1-1-1-10000100110000000000000
χ3544444-4-14-144-1-144-1-144-1-1-4-1-1-1-1-1-1-14-1-1-1-1-1-1441-41111-1-111-4-411111111-1-1-1-140-40-4-4000040110011110000000-10-1-1000000000000000
χ3644444-4-14-144-1-144-1-144-1-1-4-1-1-1-1-1-1-14-1-1-1-1-1-1441-41111-1-111-4-411111111-1-1-1-1-4040440000-40-1-100-1-1-1-100000001011000000000000000
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χ3844-24-244-14-1-2-2-21−i1521+i152-2-21−i1521+i152-1-1-2-1-11−i1521−i1521+i1521+i1524-11−i1521−i1521+i1521+i152-2-21−i1521+i1524-1-1-1-1-1-1-1-2-21−i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521+i1521+i1520-40-40022000200110000−1+i152−1+i152−1−i152−1−i1520000100−1+i152−1−i1520000000000000
χ3944-24-244-14-1-2-2-21+i1521−i152-2-21+i1521−i152-1-1-2-1-11+i1521+i1521−i1521−i1524-11+i1521+i1521−i1521−i152-2-21+i1521−i1524-1-1-1-1-1-1-1-2-21+i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521−i1521−i152040400-2-2000-200-1-100001+i1521+i1521−i1521−i1520000-1001+i1521−i1520000000000000
χ4044-24-244-14-1-2-2-21+i1521−i152-2-21+i1521−i152-1-1-2-1-11+i1521+i1521−i1521−i1524-11+i1521+i1521−i1521−i152-2-21+i1521−i1524-1-1-1-1-1-1-1-2-21+i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521−i1521−i1520-40-40022000200110000−1−i152−1−i152−1+i152−1+i1520000100−1−i152−1+i1520000000000000
χ4144-24-24-14-14-21−i1521+i152-2-21−i1521+i152-2-2-1-1-2-1-11−i1521+i1521−i1521+i152-141−i1521+i1521−i1521+i1521−i1521+i152-2-2-14-1-1-1-1-1-11−i1521+i152-2-21−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521+i1524040-2-20000-20-1-1001−i1521−i1521+i1521+i1520000000-101−i1521+i152000000000000000
χ4244-24-24-14-14-21−i1521+i152-2-21−i1521+i152-2-2-1-1-2-1-11−i1521+i1521−i1521+i152-141−i1521+i1521−i1521+i1521−i1521+i152-2-2-14-1-1-1-1-1-11−i1521+i152-2-21−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521+i1521−i1521+i152-40-40220000201100−1+i152−1+i152−1−i152−1−i152000000010−1+i152−1−i152000000000000000
χ4344-24-24-14-14-21+i1521−i152-2-21+i1521−i152-2-2-1-1-2-1-11+i1521−i1521+i1521−i152-141+i1521−i1521+i1521−i1521+i1521−i152-2-2-14-1-1-1-1-1-11+i1521−i152-2-21+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521−i1524040-2-20000-20-1-1001+i1521+i1521−i1521−i1520000000-101+i1521−i152000000000000000
χ4444-24-24-14-14-21+i1521−i152-2-21+i1521−i152-2-2-1-1-2-1-11+i1521−i1521+i1521−i152-141+i1521−i1521+i1521−i1521+i1521−i152-2-2-14-1-1-1-1-1-11+i1521−i152-2-21+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521−i1521+i1521−i152-40-40220000201100−1−i152−1−i152−1+i152−1+i152000000010−1−i152−1+i152000000000000000
χ4544-24-2-44-14-1-2-2-21−i1521+i152-2-21−i1521+i152-1-12-1-11−i1521−i1521+i1521+i1524-11−i1521−i1521+i1521+i152-2-21−i1521+i152-411111-1-122−1+i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i1521−i1521−i1521+i1521+i152040-40022000-200110000−1+i152−1+i152−1−i152−1−i1520000-1001−i1521+i1520000000000000
χ4644-24-2-44-14-1-2-2-21−i1521+i152-2-21−i1521+i152-1-12-1-11−i1521−i1521+i1521+i1524-11−i1521−i1521+i1521+i152-2-21−i1521+i152-411111-1-122−1+i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i1521−i1521−i1521+i1521+i1520-40400-2-2000200-1-100001−i1521−i1521+i1521+i1520000100−1+i152−1−i1520000000000000
χ4744-24-2-44-14-1-2-2-21+i1521−i152-2-21+i1521−i152-1-12-1-11+i1521+i1521−i1521−i1524-11+i1521+i1521−i1521−i152-2-21+i1521−i152-411111-1-122−1−i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i1521+i1521+i1521−i1521−i152040-40022000-200110000−1−i152−1−i152−1+i152−1+i1520000-1001+i1521−i1520000000000000
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χ4944-24-2-4-14-14-21−i1521+i152-2-21−i1521+i152-2-2-1-12-1-11−i1521+i1521−i1521+i152-141−i1521+i1521−i1521+i1521−i1521+i152-2-21-41111-1-1−1+i152−1−i15222−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i1521−i1521+i1521−i1521+i15240-40220000-201100−1+i152−1+i152−1−i152−1−i1520000000-101−i1521+i152000000000000000
χ5044-24-2-4-14-14-21−i1521+i152-2-21−i1521+i152-2-2-1-12-1-11−i1521+i1521−i1521+i152-141−i1521+i1521−i1521+i1521−i1521+i152-2-21-41111-1-1−1+i152−1−i15222−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i1521−i1521+i1521−i1521+i152-4040-2-2000020-1-1001−i1521−i1521+i1521+i152000000010−1+i152−1−i152000000000000000
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χ5244-24-2-4-14-14-21+i1521−i152-2-21+i1521−i152-2-2-1-12-1-11+i1521−i1521+i1521−i152-141+i1521−i1521+i1521−i1521+i1521−i152-2-21-41111-1-1−1−i152−1+i15222−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i1521+i1521−i1521+i1521−i152-4040-2-2000020-1-1001+i1521+i1521−i1521−i152000000010−1−i152−1+i152000000000000000
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χ5444-2-4-2044442-2-2-2-2-2-2-2-244044-2-2-2-2-4-4-2-2-2-22222000000-4-4000000000000222200000000-4-4000000000000004220000000-200000000000
χ554-440-4044-4-404444-4-4-4-4440-4-4444400-4-4-4-40000000000000000000000000000000000004-40000000000000004-40000000000000000000
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χ6488888-8-2-2-2-28-2-2-2-2-2-2-2-2-23-8-23-233-2-2-2-233-2-2-2-2-22222-3-3-23222222-3-3-3-322-233-20000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.