Finite Group Databasebeta

← Group #72340821

Character table — Group #72340821

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size11233446668121212121212121212161624242424242424242424242424484848484848484848484848484848484848489696969696969696128128128128192192192192192192192192192192256256256256256256
order124222244442222444442222222244444442244444444488888888444488883666444488888866661212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ311111111111111111111-1-111-1-1-1-11111111-1-111-1-11-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111-1-111-1-1-1-11111111-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ511-111-1-1-111111111-1-1111-11111-1-1-1-1-1-1-1111-1-1-11-1111-1-11111-1-1-1-11-11-111-1-11-1-1111-1-11-111-1-111-1-11-1
χ611-111-1-1-111111111-1-1111-11111-1-1-1-1-1-1-1111-1-1-11-1111-1-1-1-1-1-11111-11-11-1-1111-1-11-1-111-11-1-11111-1-11-1
χ711-111-1-1-111111111-1-111-1111-1-111-1-1-1-1-111-11-1-1-111-1-1111111-1-1-1-1-11-1111-1-11-1-1111-1-1-11-1-111-1-1111-1
χ811-111-1-1-111111111-1-111-1111-1-111-1-1-1-1-111-11-1-1-111-1-111-1-1-1-111111-11-1-1-1111-1-11-1-1111-111-1-1-1-1111-1
χ922222222222222222222222222222222222222222222220000000000000000-1-1-1-10000000000-1-1-1-1-1-1
χ1022222222222222222222-2-222-2-2-2-22222222-2-222-2-22-2-2-2-20000000000000000-1-1-1-100000000001111-1-1
χ1122222-2-22-2-2-2-2-2-2-22-2-2-2200220000-2-222222002-200-2000000000000000000002-2-2200000000000000-22
χ1222222-2-22-2-2-2-2-2-2-22-2-2-2200220000-2-222222002-200-200000000000000000000-111-10000000000−i3i3−i3i31-1
χ1322222-2-22-2-2-2-2-2-2-22-2-2-2200220000-2-222222002-200-200000000000000000000-111-10000000000i3−i3i3−i31-1
χ1422-22222-2-2-2-2-2-2-2-2222-220022000022-2-2-22200-2200-200000000000000000000222200000000000000-2-2
χ1522-22222-2-2-2-2-2-2-2-2222-220022000022-2-2-22200-2200-200000000000000000000-1-1-1-10000000000−i3i3i3−i311
χ1622-22222-2-2-2-2-2-2-2-2222-220022000022-2-2-22200-2200-200000000000000000000-1-1-1-10000000000i3−i3−i3i311
χ1722-222-2-2-222222222-2-2222-22222-2-2-2-2-2-2-2222-2-2-22-2222-2-20000000000000000-111-10000000000-1-111-11
χ1822-222-2-2-222222222-2-222-2222-2-222-2-2-2-2-222-22-2-2-222-2-2220000000000000000-111-1000000000011-1-1-11
χ1933333333333-1-1-1-13333333-1-1-1-1-1-1-1-1-1-13-1-133-1-1-1-1-1-1-1-1-111111111111111110000-1-1-1-111-1-1-1-1000000
χ2033333333333-1-1-1-13333333-1-1-1-1-1-1-1-1-1-13-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111-1-11111000000
χ2133333333333-1-1-1-133333-3-3-1-11111-1-1-1-13-1-1-3-3-1-111-1111111111111-1-1-1-111110000-1-1-1-1-1-11111000000
χ2233333333333-1-1-1-133333-3-3-1-11111-1-1-1-13-1-1-3-3-1-111-11111-1-1-1-1-1-1-1-11111-1-1-1-10000111111-1-1-1-1000000
χ2333333333-1-1333-1-1-1-1-1-1-133-1-1-1-1-1-13-13-1-13-1-1-1-1-1-1-1-13-13-111111111-1-1-1-1-1-1-1-100001-11-1111-11-1000000
χ2433333333-1-1333-1-1-1-1-1-1-133-1-1-1-1-1-13-13-1-13-1-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1111111110000-11-11-1-1-11-11000000
χ2533333333-1-1333-1-1-1-1-1-1-1-3-3-1-111113-13-1-13-111-1-111-1-31-31111111111111-1-1-1-100001-11-1-1-1-11-11000000
χ2633333333-1-1333-1-1-1-1-1-1-1-3-3-1-111113-13-1-13-111-1-111-1-31-31-1-1-1-1-1-1-1-1-1-1-1-111110000-11-11111-11-1000000
χ2733333333-1-13-1-133-1-1-1-1-133-1-1-1-1-1-1-13-13-1-13-1-1-1-1-1-1-1-13-1311111111-1-1-1-1-1-1-1-10000-11-1111-11-11000000
χ2833333333-1-13-1-133-1-1-1-1-133-1-1-1-1-1-1-13-13-1-13-1-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-11111111100001-11-1-1-11-11-1000000
χ2933333333-1-13-1-133-1-1-1-1-1-3-3-1-11111-13-13-1-1311-1-111-11-31-3111111111111-1-1-1-10000-11-11-1-11-11-1000000
χ3033333333-1-13-1-133-1-1-1-1-1-3-3-1-11111-13-13-1-1311-1-111-11-31-3-1-1-1-1-1-1-1-1-1-1-1-1111100001-11-111-11-11000000
χ3133-333-3-3-3333-1-1-1-13-3-3333-3-1-1-1-1111111-3-1-13-311-11-1-1-1111111-1-1-1-11-11-111-1-10000-1-1111-1-1-111000000
χ3233-333-3-3-3333-1-1-1-13-3-3333-3-1-1-1-1111111-3-1-13-311-11-1-1-111-1-1-1-11111-11-11-1-111000011-1-1-1111-1-1000000
χ3333-333-3-3-3333-1-1-1-13-3-333-33-1-111-1-11111-3-1-1-33111-1-111-1-11111-1-1-1-1-11-1111-1-10000-1-111-1111-1-1000000
χ3433-333-3-3-3333-1-1-1-13-3-333-33-1-111-1-11111-3-1-1-33111-1-111-1-1-1-1-1-111111-11-1-1-111000011-1-11-1-1-111000000
χ3533-333-3-3-3-1-1333-1-1-111-1-13-3-1-1-1-111-31-3113-1-1111-11-13-1-311111-1-1-1-1-11-11-1-11100001-1-111-11-1-11000000
χ3633-333-3-3-3-1-1333-1-1-111-1-13-3-1-1-1-111-31-3113-1-1111-11-13-1-31-1-1-1-111111-11-111-1-10000-111-1-11-111-1000000
χ3733-333-3-3-3-1-1333-1-1-111-1-1-33-1-111-1-1-31-3113-11-1111-1-1-313-11111-1-1-1-11-11-1-1-11100001-1-11-11-111-1000000
χ3833-333-3-3-3-1-1333-1-1-111-1-1-33-1-111-1-1-31-3113-11-1111-1-1-313-1-1-1-1-11111-11-1111-1-10000-111-11-11-1-11000000
χ3933-333-3-3-3-1-13-1-133-111-1-13-3-1-1-1-1111-31-31-13-1111-11-1-131-31111-1-1-1-1-11-11-1-1110000-111-11-1-111-1000000
χ4033-333-3-3-3-1-13-1-133-111-1-13-3-1-1-1-1111-31-31-13-1111-11-1-131-3-1-1-1-111111-11-111-1-100001-1-11-111-1-11000000
χ4133-333-3-3-3-1-13-1-133-111-1-1-33-1-111-1-11-31-31-131-1111-1-11-3-131111-1-1-1-11-11-1-1-1110000-111-1-111-1-11000000
χ4233-333-3-3-3-1-13-1-133-111-1-1-33-1-111-1-11-31-31-131-1111-1-11-3-13-1-1-1-11111-11-1111-1-100001-1-111-1-111-1000000
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χ4466666666-2-26-2-2-2-2-2-2-2-2-2-6-622-2-2-2-2-2-2-2-2-2-2-22222-2-222222000000000000000000000000000000000000
χ4566666-6-6622-62222-2222-20022444422-2-2-2-2-2002-2-4-4-20000000000000000000000000000000000000000
χ4666666-6-6622-62222-2222-20022-4-4-4-422-2-2-2-2-2002-244-20000000000000000000000000000000000000000
χ4766666-6-6622-622-6-6-2222-200-2-200002-6-26-2-2600-220020000000000000000000000000000000000000000
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χ578-808-88-8000000000000000000000000000000000000000−2i2−2i22i22i2−2i2−2i22i22i20000000022-2-20000000000000000
χ588-808-88-80000000000000000000000000000000000000002i22i2−2i2−2i22i22i2−2i2−2i20000000022-2-20000000000000000
χ598-808-8-88000000000000000000000000000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000002-22-20000000000000000
χ608-808-8-880000000000000000000000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000002-22-20000000000000000
χ61121212-4-400-4440000004-4-4000004-44-40000000000000000002-22-22-22-222-2-2000000000000000000000000
χ62121212-4-400-4440000004-4-4000004-44-4000000000000000000-22-22-22-22-2-222000000000000000000000000
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χ6912-120-440008-804-44-44000-4004-400000000000000000000000000−2i22i22i2−2i2000000−2i22i200000000000000000000
χ7012-120-440008-804-44-44000-4004-4000000000000000000000000002i2−2i2−2i22i20000002i2−2i200000000000000000000
χ7112-120-440008-80-44-444000-400-440000000000000000000000−2i22i22i2−2i200000000−2i22i20000000000000000000000
χ7212-120-440008-80-44-444000-400-4400000000000000000000002i2−2i2−2i22i2000000002i2−2i20000000000000000000000
χ7312-120-44000-8804-44-44000-400-4400000000000000000000000000−2i22i22i2−2i20000002i2−2i200000000000000000000
χ7412-120-44000-8804-44-44000-400-44000000000000000000000000002i2−2i2−2i22i2000000−2i22i200000000000000000000
χ7512-120-44000-880-44-444000-4004-40000000000000000000000−2i22i22i2−2i2000000002i2−2i20000000000000000000000
χ7612-120-44000-880-44-444000-4004-400000000000000000000002i2−2i2−2i22i200000000−2i22i20000000000000000000000
χ7716-16016-1616-160000000000000000000000000000000000000000000000000000000-2-2220000000000000000
χ7816-16016-16-16160000000000000000000000000000000000000000000000000000000-22-220000000000000000
χ79242424-8-800-8-8-8000000-888000000000000000000000000000000000000000000000000000000000000000
χ802424-24-8-8008-8-80000008-88000000000000000000000000000000000000000000000000000000000000000
χ8124-240-880000008-8-88-8000800000000000000000000000000000000000000000000000000000000000000
χ8224-240-88000000-888-8-8000800000000000000000000000000000000000000000000000000000000000000

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