Finite Group Databasebeta

← Group #13165547

Character table — Group #13165547

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222244444444668888888812121212121212121212181824242424242424242424242424242424243636363636363636363636363636727272108108108
order122236663366666622336666664466661212121244466121212121212121212121212121244881212121212122424242441212488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-11111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-11-1-1
χ311111111111111111111111111-1-11111-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1
χ411111111111111111111111111-1-11111-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1111
χ51111111111111111-1-11111111111-1-1-1-11111111-1-111111111111111-1-1111-1-1-1-111111-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-1-1-1111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111-111
χ71111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1
χ9222222222222222222222222220022220000-2-2022000000000000000000-20000-20000000-200
χ102222222222222222-2-22222222200-2-2-2-20000-2-20-2-2000000000000000000-20000-20000000200
χ112222-1-1-1-12222222200-1-1-1-1-1-1-1-1220000222222200-1-1-1-122-1-1-1-1-1-1-1-10022-10000-1-1-1-1-1000000
χ122222-1-1-1-12222222200-1-1-1-1-1-1-1-1220000222222-200-1-111-2-2-1-1-1-1111100-2-2-10000-11111000000
χ132222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-20000-2-2-2-22220011-1-1221111-1-1-1-100-2-2-10000-11111000000
χ142222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-20000-2-2-2-222-2001111-2-2111111110022-10000-1-1-1-1-1000000
χ1522-2-222-2-22222-2-2-2-22-22222-2-2-2-20022-2-200000002-200000000000000002−200000022−2−200002−2
χ1622-2-222-2-22222-2-2-2-22-22222-2-2-2-20022-2-200000002-20000000000000000−22000000−2−2220000−22
χ1722-2-222-2-22222-2-2-2-2-222222-2-2-2-200-2-2220000000-2200000000000000002−200000022−2−20000−22
χ1822-2-222-2-22222-2-2-2-2-222222-2-2-2-200-2-2220000000-220000000000000000−22000000−2−22200002−2
χ192-2-222-2-2222-2-2-22-220022-2-2-2-2220000000000-22000000000000000002-200222-2-2-20000000000
χ202-2-222-2-2222-2-2-22-220022-2-2-2-2220000000000-2200000000000000000-22002-2-222-20000000000
χ212-2-222-2-2222-2-2-22-220022-2-2-2-2222-2000022-2-22-20002-2000022-2-200000000-2000020000000000
χ222-2-222-2-2222-2-2-22-220022-2-2-2-222-220000-2-2222-2000-220000-2-22200000000-2000020000000000
χ232-2-22-111-122-2-2-22-2200-1-11111-1-12-2000022-2-22-2000-11−i3i300-1-111−i3−i3i3i3000010000-1−i3i3−i3i3000000
χ242-2-22-111-122-2-2-22-2200-1-11111-1-12-2000022-2-22-2000-11i3−i300-1-111i3i3−i3−i3000010000-1i3−i3i3−i3000000
χ252-2-22-111-122-2-2-22-2200-1-11111-1-1-220000-2-2222-20001-1−i3i30011-1-1−i3−i3i3i3000010000-1i3−i3i3−i3000000
χ262-2-22-111-122-2-2-22-2200-1-11111-1-1-220000-2-2222-20001-1i3−i30011-1-1i3i3−i3−i3000010000-1−i3i3−i3i3000000
χ27444444441-21-21-2-21441-21-21-21-2221111-1-1-1-1000-2-2220000-1-1-1-1000022000-1-1-1-100000000000
χ28444444441-21-21-2-21441-21-21-21-2-2-211111111000-2-2-2-2000011110000-2-2000111100000000000
χ29444444441-21-21-2-21-4-41-21-21-21-222-1-1-1-1-1-1-1-100022220000-1-1-1-10000-2-2000111100000000000
χ30444444441-21-21-2-21-4-41-21-21-21-2-2-2-1-1-1-1111100022-2-200001111000022000-1-1-1-100000000000
χ3144444444-21-21-211-244-21-21-21-2100-2-2-2-20000002110022-1-10000-1-1-1-1000000000000002-1-1000
χ3244444444-21-21-211-244-21-21-21-2100-2-2-2-2000000-21100-2-2110000111100000000000000-211000
χ3344444444-21-21-211-2-4-4-21-21-21-210022220000002-1-10022-1-10000-1-1-1-100000000000000-211000
χ3444444444-21-21-211-2-4-4-21-21-21-21002222000000-2-1-100-2-21100001111000000000000002-1-1000
χ354444-2-2-2-24444444400-2-2-2-2-2-2-2-20000000000-4-40000000000000000000002000020000000000
χ3644-4-444-4-41-21-2-122-14-41-21-2-12-120011-1-13−33−3000-220000003−33−30000000003−33−300000000000
χ3744-4-444-4-41-21-2-122-14-41-21-2-12-120011-1-1−33−33000-22000000−33−33000000000−33−3300000000000
χ3844-4-444-4-41-21-2-122-1-441-21-2-12-1200-1-1113−33−30002-20000003−33−3000000000−33−3300000000000
χ3944-4-444-4-41-21-2-122-1-441-21-2-12-1200-1-111−33−330002-2000000−33−330000000003−33−300000000000
χ4044-4-444-4-4-21-212-1-124-4-21-212-12-100-2-22200000001-100003−300003−33−30000000000000003−3000
χ4144-4-444-4-4-21-212-1-124-4-21-212-12-100-2-22200000001-10000−330000−33−33000000000000000−33000
χ4244-4-444-4-4-21-212-1-12-44-21-212-12-10022-2-20000000-1100003−300003−33−3000000000000000−33000
χ4344-4-444-4-4-21-212-1-12-44-21-212-12-10022-2-20000000-110000−330000−33−330000000000000003−3000
χ4444-4-4-2-2224444-4-4-4-400-2-2-2-22222000000000000000000000000000000022−22000000−2−222000000
χ4544-4-4-2-2224444-4-4-4-400-2-2-2-222220000000000000000000000000000000−222200000022−2−2000000
χ464-44-44-44-41-2-1212-2-1001-2-121-2-12003-33-33−3−33000000000003−3−330000000003−3−3300000000000
χ474-44-44-44-41-2-1212-2-1001-2-121-2-12003-33-3−333−300000000000−333−3000000000−333−300000000000
χ484-44-44-44-41-2-1212-2-1001-2-121-2-1200-33-333−3−33000000000003−3−33000000000−333−300000000000
χ494-44-44-44-41-2-1212-2-1001-2-121-2-1200-33-33−333−300000000000−333−30000000003−3−3300000000000
χ504-44-44-44-444-4-44-44-40044-4-444-4-40000000000000000000000000000000000000000000000000
χ514-44-4-22-2244-4-44-44-400-2-222-2-222000000000000000000000000000000000000000i6−i6−i6i6000000
χ524-44-4-22-2244-4-44-44-400-2-222-2-222000000000000000000000000000000000000000−i6i6i6−i6000000
χ534-4-444-4-441-2-12-1-221001-2-12-121-22-23-3-33-1-111000002-20000-1-11100002-2000-1-11100000000000
χ544-4-444-4-441-2-12-1-221001-2-12-121-22-2-333-3-1-111000002-20000-1-1110000-2200011-1-100000000000
χ554-4-444-4-441-2-12-1-221001-2-12-121-2-223-3-3311-1-100000-22000011-1-10000-2200011-1-100000000000
χ564-4-444-4-441-2-12-1-221001-2-12-121-2-22-333-311-1-100000-22000011-1-100002-2000-1-11100000000000
χ574-4-44-222-244-4-4-44-4400-2-22222-2-20000000000-44000000000000000000000-2000020000000000
χ588888-4-4-4-42-42-42-4-4200-12-12-12-12440000-2-2-2-200000-2-200001111000000000000000000000000
χ598888-4-4-4-42-42-42-4-4200-12-12-12-12-4-40000222200000220000-1-1-1-1000000000000000000000000
χ608888-4-4-4-4-42-42-422-4002-12-12-12-100000000000040000-2-2-2-20000111100000000000000000000
χ618888-4-4-4-4-42-42-422-4002-12-12-12-1000000000000-4000022220000-1-1-1-100000000000000000000
χ6288-8-8-4-4442-42-4-244-200-12-121-21-200000023−2323−2300000000000−33−33000000000000000000000000
χ6388-8-8-4-4442-42-4-244-200-12-121-21-2000000−2323−2323000000000003−33−3000000000000000000000000
χ6488-8-8-4-444-42-424-2-24002-12-1-21-21000000000000000000023−230000−33−3300000000000000000000
χ6588-8-8-4-444-42-424-2-24002-12-1-21-210000000000000000000−232300003−33−300000000000000000000
χ668-88-88-88-8-424-2-4-22400-424-2-424-20000000000000000000000000000000000000000000000000
χ678-88-8-44-442-4-2424-4-200-121-2-121-200000023−23−232300000000000−333−3000000000000000000000000
χ688-88-8-44-442-4-2424-4-200-121-2-121-2000000−232323−23000000000003−3−33000000000000000000000000
χ698-88-8-44-44-424-2-4-224002-1-212-1-2100000000000000000000000003i−3i−3i3i00000000000000000000
χ708-88-8-44-44-424-2-4-224002-1-212-1-210000000000000000000000000−3i3i3i−3i00000000000000000000
χ718-8-888-8-88-424-242-2-400-424-24-2-420000000000000000000000000000000000000000000000000
χ728-8-88-444-42-4-24-2-44200-121-21-2-124-40000-2-22200000-22000011-1-1000000000000000000000000
χ738-8-88-444-42-4-24-2-44200-121-21-2-12-44000022-2-2000002-20000-1-111000000000000000000000000
χ748-8-88-444-4-424-242-2-4002-1-21-212-100000000000000000−2i32i3000000i3i3−i3−i300000000000000000000
χ758-8-88-444-4-424-242-2-4002-1-21-212-1000000000000000002i3−2i3000000−i3−i3i3i300000000000000000000

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