Finite Group Databasebeta

← Group #72271582

Character table — Group #72271582

Order 10240.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111110101010101010101010101020202020202020202040404040404040404040404040404040404080808080160160160160160160160160160160160160320320320320320320320320320512512512512512512512512
order1222222244444444244444444224444444444444444444444448888888828888888855101010101010
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ322222222222222222222222222222222222222222220000000000000000000000000−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52
χ422222222222222222222222222222222222222222220000000000000000000000000−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52
χ544-4-40-40400-4-400440000000000000000000000000002i2i−2i−2i002i−2i00002i2i−2i−2i000000000-1-111-111-1
χ644-4-40-40400-4-40044000000000000000000000000000−2i−2i2i2i00−2i2i0000−2i−2i2i2i000000000-1-111-111-1
χ74-44-4-4040-4-40044000000000000000000000000000002i−2i2i−2i2i−2i002i2i−2i−2i0000000000000-1-11-111-11
χ84-44-4-4040-4-4004400000000000000000000000000000−2i2i−2i2i−2i2i00−2i−2i2i2i0000000000000-1-11-111-11
χ9555511111-31-31-31-351-31-311551-3111-3111-311111-3-3-31111-1-1-1-11-11-11-11-111-11-111-1-100000000
χ10555511111-31-31-31-351-31-311551-3111-3111-311111-3-3-3-1-1-1-11111-11-11-11-11-1-11-11-1-11100000000
χ11555511111-3-311-3-31-351155-3111111-3-31-3-311111-311-31111-1-1-1-11-11-1-11-1111-1-11-1-11100000000
χ12555511111-3-311-3-31-351155-3111111-3-31-3-311111-311-3-1-1-1-11111-11-111-11-1-1-111-111-1-100000000
χ1355551111-311-3-311-3-31551-351111-3-311-311-31111-311-31111-1-1-1-1-11-111-11-11-111-1-1-11100000000
χ1455551111-311-3-311-3-31551-351111-3-311-311-31111-311-3-1-1-1-111111-11-1-11-11-11-1-1111-1-100000000
χ1555551111-31-31-31-315-31-311155-311-31111-3111-3-3-31111111-1-1-1-1-11-11-11-111-11-1111-1-100000000
χ1655551111-31-31-31-315-31-311155-311-31111-3111-3-3-3111-1-1-1-111111-11-11-11-1-11-11-1-1-11100000000
χ17555515151-3551-355111-31-311-31111111-31-31-31-3-31-311111-1-1111-11-11111-1-11-1-11-1-1100000000
χ18555515151-3551-355111-31-311-31111111-31-31-31-3-31-31-1-1-1-111-1-1-11-11-1-1-1-111-111-111-100000000
χ1955551515-3155-31551111-31-3-31111111-31-31-31-311-31-31111-1-111-11-111111-11-1-1-1-111-100000000
χ2055551515-3155-31551111-31-3-31111111-31-31-31-311-31-3-1-1-1-111-1-11-11-1-1-1-1-11-11111-1-1100000000
χ2155551-31-31-3111-3111-355115-311-311-3111-311-31-31-3111111-1-1111-11-1-1-1-1-1-1-1111-111-100000000
χ2255551-31-31-3111-3111-355115-311-311-3111-311-31-31-311-1-1-1-111-1-1-11-11111111-1-1-11-1-1100000000
χ2355551-31-3-3111-311115-315511-3-31-3111111-3-311-31-3111111-1-111-11-11-1-1-1-1-11-1111-1-1100000000
χ2455551-31-3-3111-311115-315511-3-31-3111111-3-311-31-311-1-1-1-111-1-11-11-111111-11-1-1-111-100000000
χ2555555151551-3551-31-31111-31-311-311-311111-3-31-3-311111111-1-111111-11-1-1-1-1-111-11-100000000
χ2655555151551-3551-31-31111-31-311-311-311111-3-31-3-311-1-1-1-1-1-111-1-1-1-1-11-111111-1-11-1100000000
χ275555515155-3155-3111-311-31-31111-3-311111-311-311-3-3111111-1-11111-11-11-1-1-11-1-11-1100000000
χ285555515155-3155-3111-311-31-31111-3-311111-311-311-3-3-1-1-1-1-1-111-1-1-1-11-11-1111-111-11-100000000
χ2955555-35-355115511-311-3-31111-3-31111-3-3-3-311111111111111111111-1-1-1-1111-1-1-1-1-1-100000000
χ3055555-35-355115511-311-3-31111-3-31111-3-3-3-311111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111100000000
χ315555-31-31111-3111-3151-3551-311-31-311-31111-3-3111-31111111-1-1-1-1-1-11-11-1-111-11-11-1100000000
χ325555-31-31111-3111-3151-3551-311-31-311-31111-3-3111-31-1-1-1-1-1-1111111-11-111-1-11-11-11-100000000
χ335555-31-3111-3111-311155-3151-3-31111-31-311-31-3111-31111111-1-1-1-1-1-1-11-11-1111-11-11-100000000
χ345555-31-3111-3111-311155-3151-3-31111-31-311-31-3111-31-1-1-1-1-1-11111111-11-11-1-1-11-11-1100000000
χ355555-35-3511551155-3-3-3111111-3-3-3-3-3-311111111111111111111-1-1-1-111111-1-111-1-1-1-100000000
χ365555-35-3511551155-3-3-3111111-3-3-3-3-3-3111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1111100000000
χ375555-3-3-3-31111111151111-3-35511-31-31-3-311-3-311111111111111-1-1-1-1-1-1-1-11-1-1-1-1111100000000
χ385555-3-3-3-31111111151111-3-35511-31-31-3-311-3-3111111-1-1-1-1-1-1-1-111111111-11111-1-1-1-100000000
χ3988-8-80-80800-8-8008800000000000000000000000000000000000000000000000000001−521+52−1+52−1+521−52−1−52−1−521+52
χ4088-8-80-80800-8-8008800000000000000000000000000000000000000000000000000001+521−52−1−52−1−521+52−1+52−1+521−52
χ418-88-8-8080-8-800880000000000000000000000000000000000000000000000000000001−521+52−1+521−52−1+52−1−521+52−1−52
χ428-88-8-8080-8-800880000000000000000000000000000000000000000000000000000001+521−52−1−521+52−1−52−1+521−52−1+52
χ431010101022222-62-62-62-622222-6-6-622-2-2-22-22-2-2-2-26-2-22226000000000000000000000000000000000
χ441010101022222-62-62-62-6-6-62-622222-26-22-22-2-22222-2-26-2-2-2000000000000000000000000000000000
χ451010101022222-6-622-6-62222-6-622-62-222-2-2-2-226-2-2-222-2-262000000000000000000000000000000000
χ461010101022222-6-622-6-622-6-622222-62-2-2-2262-2-2-2-2-2-26222-2000000000000000000000000000000000
χ47101010102222-622-6-622-6222-6-6222-62-2-2-22-22-2-26-2-26-2222-2000000000000000000000000000000000
χ48101010102222-622-6-622-62-6-62222-62-2226-2-2-22-2-2-2-222-26-22000000000000000000000000000000000
χ49101010102222-62-62-62-6222222-6-62-6-222-2-2-2-22-2-26-2226-2-22000000000000000000000000000000000
χ50101010102222-62-62-62-62-62-62-622226-2-22-22-2-22222-2-2-2-2-26000000000000000000000000000000000
χ51101010102-62-62-6222-6222222-62-62-6-2-2-22-22-262222-2-2-26-2-2000000000000000000000000000000000
χ52101010102-62-62-6222-622-62-622-6222-222-26-2-22-26-2-222-2-2-22000000000000000000000000000000000
χ53101010102-62-6-6222-6222222-62-62-62-2-2-22-226-22222-26-2-2-2-2000000000000000000000000000000000
χ54101010102-62-6-6222-6222-6-62222-6222-26-22-22-26-2-2-2-2-2222-2000000000000000000000000000000000
χ5510101010-62-62222-6222-622-622-622-6-2-262-22-2-22222-2-2-2-26-2000000000000000000000000000000000
χ5610101010-62-62222-6222-6-6222-62-622-222-2-2662-2-2-2-222-2-2-22000000000000000000000000000000000
χ5710101010-62-6222-6222-622-62222-6-62-2-2-2262-2-222226-2-2-2-2-2000000000000000000000000000000000
χ5810101010-62-6222-6222-62-622-62-62222-2-262-226-2-2-2-2-2-2222-2000000000000000000000000000000000
χ5910101010-6-6-6-62222222222-62-622-6226-2-22-22-2-2-26-2-2-2222-2000000000000000000000000000000000
χ6010101010-6-6-6-6222222222-62-62222-6622-2-2-2-22-2-2-2622-2-2-22000000000000000000000000000000000
χ6116-16-16160000000000000000000000000000000000000004-4-44000000000000000000000111-1-11-1-1
χ6216-16-1616000000000000000000000000000000000000000-444-4000000000000000000000111-1-11-1-1
χ632020-20-200120-1200-4-400440000000000000000000000000002i2i−2i−2i002i−2i0000−2i−2i2i2i00000000000000000
χ642020-20-200120-1200-4-40044000000000000000000000000000−2i−2i2i2i00−2i2i00002i2i−2i−2i00000000000000000
χ652020-20-200-4040012-400-1240000000000000000000000000002i2i−2i−2i00−2i2i0000−2i2i2i−2i00000000000000000
χ662020-20-200-4040012-400-124000000000000000000000000000−2i−2i2i2i002i−2i00002i−2i−2i2i00000000000000000
χ672020-20-200-40400-412004-120000000000000000000000000002i2i−2i−2i00−2i2i00002i−2i−2i2i00000000000000000
χ682020-20-200-40400-412004-12000000000000000000000000000−2i−2i2i2i002i−2i0000−2i2i2i−2i00000000000000000
χ6920-2020-20120-120-4-40044000000000000000000000000000002i−2i2i−2i2i−2i00−2i−2i2i2i000000000000000000000
χ7020-2020-20120-120-4-4004400000000000000000000000000000−2i2i−2i2i−2i2i002i2i−2i−2i000000000000000000000
χ7120-2020-20-404012-400-124000000000000000000000000000002i−2i2i−2i−2i2i00−2i2i2i−2i000000000000000000000
χ7220-2020-20-404012-400-12400000000000000000000000000000−2i2i−2i2i2i−2i002i−2i−2i2i000000000000000000000
χ7320-2020-20-4040-412004-12000000000000000000000000000002i−2i2i−2i−2i2i002i−2i−2i2i000000000000000000000
χ7420-2020-20-4040-412004-1200000000000000000000000000000−2i2i−2i2i2i−2i00−2i2i2i−2i000000000000000000000
χ7532-32-32320000000000000000000000000000000000000000000000000000000000000000−1+52−1−52−1+521−521−52−1−521+521+52
χ7632-32-32320000000000000000000000000000000000000000000000000000000000000000−1−52−1+52−1−521+521+52−1+521−521−52

Here i is the imaginary unit (i² = −1).