Finite Group Databasebeta

← Group #10847363

Character table — Group #10847363

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444444444466888888888888888881212121212161616161616161616162424242424242424244848
order12222234444666668888881212121224242424444444888121212122424242424244448848121212122424242444448888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1
χ3111111111111111111111111111111-1-111111111111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111
χ511111111111111111111-1-11111-1-1-1-11111-1-111-1-1-1-1-11111-1-1111-1-1-1-111-1-111-1-1-1-11111-111-1-1
χ611111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-111-1-111-1-111-1-1-1-111-1-1-111
χ711111111111111111111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-11111-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11-1-111
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1-1111111-1-1111-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-111-1-11-1-11-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111111-11-1-1-1-11111-1-1-1-1-1-1111-11
χ111111111111111111-1-1-1-11111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-11-11111-1-1-1-111-1-111-111-11
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-11111111111-1-1-11-1
χ131111111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1111-1-1-1111-1-1-1-1111111-1-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-11111-1-1-1-1-1-1111-1-11-1-1-11111-1-111-1-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-111-1111-1-1-1-111-1-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-111111-1-1-11
χ172222222-2-2-2-2222222i2i−2i−2i00-2-2-2-2000022000000000002i2i−2i−2i002-2-200000000000000002i−2i00000
χ182222222-2-2-2-2222222i2i−2i−2i00-2-2-2-20000-2-2000000000002i2i−2i−2i00-2220000000000000000−2i2i00000
χ192222222-2-2-2-222222−2i−2i2i2i00-2-2-2-200002200000000000−2i−2i2i2i002-2-20000000000000000−2i2i00000
χ202222222-2-2-2-222222−2i−2i2i2i00-2-2-2-20000-2-200000000000−2i−2i2i2i00-22200000000000000002i−2i00000
χ21222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1002222222-1-1-1-1-1-1-1-1-1-10000022-1-1-1-1-1-1-1-100000000000
χ22222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-100-2-222-2-22-1-1-1-1-1-1-1-1-1-100000-2-21111111100000000000
χ23222222-12222-1-1-1-1-12222-2-2-1-1-1-111110022-2-222-21111-1-1-1-11100000-2-2-1-111-1-11100000000000
χ24222222-12222-1-1-1-1-12222-2-2-1-1-1-1111100-2-2-2-2-2-2-21111-1-1-1-111000002211-1-111-1-100000000000
χ25222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-10022-2-2-2-2211111111-1-1000002-2-1-1-1-1111100000000000
χ26222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-100-2-2-2-222211111111-1-100000-221111-1-1-1-100000000000
χ27222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111002222-2-2-2-1-1-1-111111100000-22-1-11111-1-100000000000
χ28222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1111100-2-22222-2-1-1-1-1111111000002-211-1-1-1-11100000000000
χ292222-2-222-22-2222-2-200002222-2-2222222000000-200000000-2-2-22-2220000000000000000-20000
χ302222-2-222-22-2222-2-200002222-2-22222-2-2000000-200000000-2-22-22-2-2000000000000000020000
χ312222-2-222-22-2222-2-20000-2-222-2-2-2-2-2-22200000020000000022-22-2-2-2000000000000000020000
χ322222-2-222-22-2222-2-20000-2-222-2-2-2-2-2-2-2-2000000200000000222-22220000000000000000-20000
χ332222-2-22-22-22222-2-2000000-2-222000022002-200022-2-2000000-2-22000000000000-22000000000
χ342222-2-22-22-22222-2-2000000-2-22200002200-22000-2-222000000-2-220000000000002-2000000000
χ352222-2-22-22-22222-2-2000000-2-2220000-2-2002-200022-2-200000022-20000000000002-2000000000
χ362222-2-22-22-22222-2-2000000-2-2220000-2-200-22000-2-22200000022-2000000000000-22000000000
χ3722-2-22-2222-2-2-22-22-22-22-2002-22-20000002-2002-2000002-22-20000000002-2002-20000000000000
χ3822-2-22-2222-2-2-22-22-22-22-2002-22-2000000-2200-22000002-22-2000000000-2200-220000000000000
χ3922-2-22-2222-2-2-22-22-2-22-22002-22-20000002-200-2200000-22-220000000002-200-220000000000000
χ4022-2-22-2222-2-2-22-22-2-22-22002-22-2000000-22002-200000-22-22000000000-22002-20000000000000
χ4122-2-22-22-2-222-22-22-22i−2i−2i2i00-22-22000000000000000002i−2i−2i2i00000000000000000002i−2i0002-200
χ4222-2-22-22-2-222-22-22-22i−2i−2i2i00-22-22000000000000000002i−2i−2i2i0000000000000000000−2i2i000-2200
χ4322-2-22-22-2-222-22-22-2−2i2i2i−2i00-22-2200000000000000000−2i2i2i−2i00000000000000000002i−2i000-2200
χ4422-2-22-22-2-222-22-22-2−2i2i2i−2i00-22-2200000000000000000−2i2i2i−2i0000000000000000000−2i2i0002-200
χ4522-2-22-2-122-2-21-11-112-22-200-11-1133−3−3002-2002-203−33−3-11-113−30000000-113−3-113−300000000000
χ4622-2-22-2-122-2-21-11-112-22-200-11-1133−3−300-2200-2203−33−3-11-113−300000001-1−331-1−3300000000000
χ4722-2-22-2-122-2-21-11-112-22-200-11-11−3−333002-2002-20−33−33-11-11−330000000-11−33-11−3300000000000
χ4822-2-22-2-122-2-21-11-112-22-200-11-11−3−33300-2200-220−33−33-11-11−3300000001-13−31-13−300000000000
χ4922-2-22-2-122-2-21-11-11-22-2200-11-1133−3−3002-200-220−33−331-11-13−30000000-113−31-1−3300000000000
χ5022-2-22-2-122-2-21-11-11-22-2200-11-1133−3−300-22002-20−33−331-11-13−300000001-1−33-113−300000000000
χ5122-2-22-2-122-2-21-11-11-22-2200-11-11−3−333002-200-2203−33−31-11-1−330000000-11−331-13−300000000000
χ5222-2-22-2-122-2-21-11-11-22-2200-11-11−3−33300-22002-203−33−31-11-1−3300000001-13−3-11−3300000000000
χ53444444-2-4-4-4-4-2-2-2-2-24i4i−4i−4i00222200000000000000000−2i−2i2i2i0000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-2−4i−4i4i4i002222000000000000000002i2i−2i−2i0000000000000000000000000000
χ554444-4-4-24-44-4-2-2-222000044-2-222-2-2-2-200000000-4000000002200000000000000000000000000
χ564444-4-4-24-44-4-2-2-2220000-4-4-2-222222200000000400000000-2-200000000000000000000000000
χ574444-4-4-2-44-44-2-2-22200000022-2-2000000004-4000-2-22200000000000000000000000000000000
χ584444-4-4-2-44-44-2-2-22200000022-2-200000000-4400022-2-200000000000000000000000000000000
χ5944-4-44-4-2-4-4442-22-224i−4i−4i4i002-22-200000000000000000−2i2i2i−2i0000000000000000000000000000
χ6044-4-44-4-2-4-4442-22-22−4i4i4i−4i002-22-2000000000000000002i−2i−2i2i0000000000000000000000000000
χ6144-4-4-4444-4-44-44-4-440000004-4-440000000000000000000000000000000000000000000000000
χ6244-4-4-444-444-4-44-4-44000000-444-40000000000000000000000000000000000000000000000000
χ6344-4-4-44-24-4-442-222-2000000-222-22323−23−2300000000000000000−232300000000000000000000000000
χ6444-4-4-44-24-4-442-222-2000000-222-2−23−2323230000000000000000023−2300000000000000000000000000
χ6544-4-4-44-2-444-42-222-20000002-2-22000000000000023−23−232300000000000000000000000000000000
χ6644-4-4-44-2-444-42-222-20000002-2-220000000000000−232323−2300000000000000000000000000000000
χ674-4-440040000-4-44000000−2i22i20000−2i22i2−2i22i24i−4i0000000000000000000022−22000000000000000000000
χ684-4-440040000-4-44000000−2i22i20000−2i22i2−2i22i2−4i4i00000000000000000000−2222000000000000000000000
χ694-4-440040000-4-440000002i2−2i200002i2−2i22i2−2i24i−4i00000000000000000000−2222000000000000000000000
χ704-4-440040000-4-440000002i2−2i200002i2−2i22i2−2i2−4i4i0000000000000000000022−22000000000000000000000
χ718-88-800800008-8-80000000000000000000000000000000000000000000000000000000000000
χ728-88-800-40000-4440000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ738-88-800-40000-444000000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000
χ748-8-8800-4000044-4000000−4i24i200002i2−2i22i2−2i2000000000000000000000000000000000000000000000
χ758-8-8800-4000044-40000004i2−4i20000−2i22i2−2i22i2000000000000000000000000000000000000000000000

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