Finite Group Databasebeta

← Group #10590570

Character table — Group #10590570

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222444444446666121222224444448888888812121212242433336666661212121212121212181818183636
order1222344666441212121212128888443666312126661212121212121212242424241212222264466644121212121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ31111111111-1-111-1-1-1-11111-1-11111111111-1-111-1-1-1-11111-1-11111111111-1-111-1-1-1-11111-1-1
χ41111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111
χ511-1-11-11-11-1i−i1-1ii−i−i11-1-1i−i11-1-11-11-11-1i−i1-1ii−i−i11-1-1i−i11-1-11-11-11-1i−i1-1ii−i−i11-1-1i−i
χ611-1-11-11-11-1i−i1-1ii−i−i-1-111−ii11-1-11-11-11-1i−i1-1ii−i−i-1-111−ii11-1-11-11-11-1i−i1-1ii−i−i-1-111−ii
χ711-1-11-11-11-1−ii1-1−i−iii11-1-1−ii11-1-11-11-11-1−ii1-1−i−iii11-1-1−ii11-1-11-11-11-1−ii1-1−i−iii11-1-1−ii
χ811-1-11-11-11-1−ii1-1−i−iii-1-111i−i11-1-11-11-11-1−ii1-1−i−iii-1-111i−i11-1-11-11-11-1−ii1-1−i−iii-1-111i−i
χ922222-2-222200-2-2000000000022222-2-222200-2-2000000000022222-2-222200-2-20000000000
χ102222-122-1-1-122-1-1-1-1-1-10000002222-122-1-1-122-1-1-1-1-1-10000002222-122-1-1-122-1-1-1-1-1-1000000
χ112222-122-1-1-1-2-2-1-111110000002222-122-1-1-1-2-2-1-111110000002222-122-1-1-1-2-2-1-11111000000
χ122222-1-2-2-1-1-10011−i3i3−i3i30000002222-1-2-2-1-1-10011−i3i3−i3i30000002222-1-2-2-1-1-10011−i3i3−i3i3000000
χ132222-1-2-2-1-1-10011i3−i3i3−i30000002222-1-2-2-1-1-10011i3−i3i3−i30000002222-1-2-2-1-1-10011i3−i3i3−i3000000
χ1422-2-222-2-22-200-22000000000022-2-222-2-22-200-22000000000022-2-222-2-22-200-220000000000
χ1522-2-2-12-21-11001-13−3−3300000022-2-2-12-21-11001-13−3−3300000022-2-2-12-21-11001-13−3−33000000
χ1622-2-2-12-21-11001-1−333−300000022-2-2-12-21-11001-1−333−300000022-2-2-12-21-11001-1−333−3000000
χ1722-2-2-1-221-112i−2i-11−i−iii00000022-2-2-1-221-112i−2i-11−i−iii00000022-2-2-1-221-112i−2i-11−i−iii000000
χ1822-2-2-1-221-11−2i2i-11ii−i−i00000022-2-2-1-221-11−2i2i-11ii−i−i00000022-2-2-1-221-11−2i2i-11ii−i−i000000
χ192-22-2200-2-2200000000−i2i2−i2i2002-22-2200-2-2200000000−i2i2−i2i2002-22-2200-2-2200000000−i2i2−i2i200
χ202-22-2200-2-2200000000i2−i2i2−i2002-22-2200-2-2200000000i2−i2i2−i2002-22-2200-2-2200000000i2−i2i2−i200
χ212-2-222002-2-200000000−i2i2i2−i2002-2-222002-2-200000000−i2i2i2−i2002-2-222002-2-200000000−i2i2i2−i200
χ222-2-222002-2-200000000i2−i2−i2i2002-2-222002-2-200000000i2−i2−i2i2002-2-222002-2-200000000i2−i2−i2i200
χ234-44-4-20022-2000000000000004-44-4-20022-2000000000000004-44-4-20022-200000000000000
χ244-4-44-200-222000000000000004-4-44-200-222000000000000004-4-44-200-22200000000000000
χ25111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ26111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ271111111111-1-111-1-1-1-11111-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ281111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1
χ2911-1-11-11-11-1i−i1-1ii−i−i11-1-1i−i11-1-11-11-11-1i−i1-1ii−i−i11-1-1i−i-1-111-11-11-11−ii-11−i−iii-1-111−ii
χ3011-1-11-11-11-1i−i1-1ii−i−i-1-111−ii11-1-11-11-11-1i−i1-1ii−i−i-1-111−ii-1-111-11-11-11−ii-11−i−iii11-1-1i−i
χ3111-1-11-11-11-1−ii1-1−i−iii11-1-1−ii11-1-11-11-11-1−ii1-1−i−iii11-1-1−ii-1-111-11-11-11i−i-11ii−i−i-1-111i−i
χ3211-1-11-11-11-1−ii1-1−i−iii-1-111i−i11-1-11-11-11-1−ii1-1−i−iii-1-111i−i-1-111-11-11-11i−i-11ii−i−i11-1-1−ii
χ3322222-2-222200-2-2000000000022222-2-222200-2-20000000000-2-2-2-2-222-2-2-200220000000000
χ342222-122-1-1-122-1-1-1-1-1-10000002222-122-1-1-122-1-1-1-1-1-1000000-2-2-2-21-2-2111-2-2111111000000
χ352222-122-1-1-1-2-2-1-111110000002222-122-1-1-1-2-2-1-11111000000-2-2-2-21-2-21112211-1-1-1-1000000
χ362222-1-2-2-1-1-10011−i3i3−i3i30000002222-1-2-2-1-1-10011−i3i3−i3i3000000-2-2-2-212211100-1-1i3−i3i3−i3000000
χ372222-1-2-2-1-1-10011i3−i3i3−i30000002222-1-2-2-1-1-10011i3−i3i3−i3000000-2-2-2-212211100-1-1−i3i3−i3i3000000
χ3822-2-222-2-22-200-22000000000022-2-222-2-22-200-220000000000-2-222-2-222-22002-20000000000
χ3922-2-2-12-21-11001-13−3−3300000022-2-2-12-21-11001-13−3−33000000-2-2221-22-11-100-11−333−3000000
χ4022-2-2-12-21-11001-1−333−300000022-2-2-12-21-11001-1−333−3000000-2-2221-22-11-100-113−3−33000000
χ4122-2-2-1-221-112i−2i-11−i−iii00000022-2-2-1-221-112i−2i-11−i−iii000000-2-22212-2-11-1−2i2i1-1ii−i−i000000
χ4222-2-2-1-221-11−2i2i-11ii−i−i00000022-2-2-1-221-11−2i2i-11ii−i−i000000-2-22212-2-11-12i−2i1-1−i−iii000000
χ432-22-2200-2-2200000000−i2i2−i2i2002-22-2200-2-2200000000−i2i2−i2i200-22-22-20022-200000000i2−i2i2−i200
χ442-22-2200-2-2200000000i2−i2i2−i2002-22-2200-2-2200000000i2−i2i2−i200-22-22-20022-200000000−i2i2−i2i200
χ452-2-222002-2-200000000−i2i2i2−i2002-2-222002-2-200000000−i2i2i2−i200-222-2-200-22200000000i2−i2−i2i200
χ462-2-222002-2-200000000i2−i2−i2i2002-2-222002-2-200000000i2−i2−i2i200-222-2-200-22200000000−i2i2i2−i200
χ474-44-4-20022-2000000000000004-44-4-20022-200000000000000-44-44200-2-2200000000000000
χ484-4-44-200-222000000000000004-4-44-200-22200000000000000-444-42002-2-200000000000000
χ49222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ50222222222222222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111000000000000000000000000
χ512222222222-2-222-2-2-2-22222-2-2-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111000000000000000000000000
χ522222222222-2-222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1000000000000000000000000
χ5322-2-22-22-22-22i−2i2-22i2i−2i−2i22-2-22i−2i-1-111-11-11-11−ii-11−i−iii-1-111−ii000000000000000000000000
χ5422-2-22-22-22-22i−2i2-22i2i−2i−2i-2-222−2i2i-1-111-11-11-11−ii-11−i−iii11-1-1i−i000000000000000000000000
χ5522-2-22-22-22-2−2i2i2-2−2i−2i2i2i22-2-2−2i2i-1-111-11-11-11i−i-11ii−i−i-1-111i−i000000000000000000000000
χ5622-2-22-22-22-2−2i2i2-2−2i−2i2i2i-2-2222i−2i-1-111-11-11-11i−i-11ii−i−i11-1-1−ii000000000000000000000000
χ5744444-4-444400-4-40000000000-2-2-2-2-222-2-2-200220000000000000000000000000000000000
χ584444-244-2-2-244-2-2-2-2-2-2000000-2-2-2-21-2-2111-2-2111111000000000000000000000000000000
χ594444-244-2-2-2-4-4-2-22222000000-2-2-2-21-2-21112211-1-1-1-1000000000000000000000000000000
χ604444-2-4-4-2-2-20022−2i32i3−2i32i3000000-2-2-2-212211100-1-1i3−i3i3−i3000000000000000000000000000000
χ614444-2-4-4-2-2-200222i3−2i32i3−2i3000000-2-2-2-212211100-1-1−i3i3−i3i3000000000000000000000000000000
χ6244-4-444-4-44-400-440000000000-2-222-2-222-22002-20000000000000000000000000000000000
χ6344-4-4-24-42-22002-223−23−2323000000-2-2221-22-11-100-11−333−3000000000000000000000000000000
χ6444-4-4-24-42-22002-2−232323−23000000-2-2221-22-11-100-113−3−33000000000000000000000000000000
χ6544-4-4-2-442-224i−4i-22−2i−2i2i2i000000-2-22212-2-11-1−2i2i1-1ii−i−i000000000000000000000000000000
χ6644-4-4-2-442-22−4i4i-222i2i−2i−2i000000-2-22212-2-11-12i−2i1-1−i−iii000000000000000000000000000000
χ674-44-4400-4-4400000000−2i22i2−2i22i200-22-22-20022-200000000i2−i2i2−i200000000000000000000000000
χ684-44-4400-4-44000000002i2−2i22i2−2i200-22-22-20022-200000000−i2i2−i2i200000000000000000000000000
χ694-4-444004-4-400000000−2i22i22i2−2i200-222-2-200-22200000000i2−i2−i2i200000000000000000000000000
χ704-4-444004-4-4000000002i2−2i2−2i22i200-222-2-200-22200000000−i2i2i2−i200000000000000000000000000
χ718-88-8-40044-400000000000000-44-44200-2-2200000000000000000000000000000000000000
χ728-8-88-400-44400000000000000-444-42002-2-200000000000000000000000000000000000000

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