Finite Group Databasebeta

← Group #10844988

Character table — Group #10844988

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444444444466888888888888888881212121212161616161616161616162424242424242424244848
order122222344446666688888812121212242424244444448881212121224242424242444488266812122424242444448888828
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1
χ3111111111111111111111111111111-1-111111111111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111111111-1-11111-1-1-1-111-1-11111-1-1-1-1-11111-1-1111-1-1-1-1-1-11111-1-1-111-111-111-1-1
χ611111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-11111-1-1-1-111-1-1-1-111-1-1-111
χ711111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-11-1-11-1-11-1-111
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1111111-1-1111-1-1
χ91111111111111111-1-1-1-1111111111111-1-111-1-11-1-1-1-1-1-1-1-11111111111-111-1-1-1-1-111-1-1-11-1-11-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111111-1-1-11-1-11111-1-1-1-1-1-1111-11
χ111111111111111111-1-1-1-11111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1111-111-1-1-1-11-1-1111-111-11
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11111111111-1-1-11-1
χ131111111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1111-1-1111111-1-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-11111-1-1-1-1-1-1111-1-1111-1-1-111-1-11-1-11-1-1-1111-1
χ151111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-11111-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-111-1111-1-1-11
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
χ21222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1002222222-1-1-1-1-1-1-1-1-1-1000002-1-12-1-1-1-1-1-100000000000
χ22222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-10022-2-2-2-22-1-1-1-1-1-1-1-1-1-100000-211-211111100000000000
χ23222222-12222-1-1-1-1-12222-2-2-1-1-1-1111100-2-22222-21111-1-1-1-11100000-211-2-1-1-1-11100000000000
χ24222222-12222-1-1-1-1-12222-2-2-1-1-1-1111100-2-2-2-2-2-2-21111-1-1-1-111000002-1-121111-1-100000000000
χ25222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-100-2-222-2-2211111111-1-1000002-1-1-2-1-1111100000000000
χ26222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-100-2-2-2-222211111111-1-100000-211211-1-1-1-100000000000
χ27222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111002222-2-2-2-1-1-1-111111100000-2112-1-111-1-100000000000
χ28222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-111110022-2-222-2-1-1-1-1111111000002-1-1-211-1-11100000000000
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
χ332222-2-22-22-22222-2-2000000-2-2220000222-20000022-2-2000000-2-22000000000000200-20000000
χ342222-2-22-22-22222-2-2000000-2-222000022-2200000-2-222000000-2-22000000000000-20020000000
χ352222-2-22-22-22222-2-2000000-2-2220000-2-22-20000022-2-200000022-2000000000000-20020000000
χ362222-2-22-22-22222-2-2000000-2-2220000-2-2-2200000-2-22200000022-2000000000000200-20000000
χ3722-2-22-222-2-222-2-22-22-22-2002-22-2000000002i−2i2i−2i000002-22-2000000000002i−2i2i−2i0000000000000
χ3822-2-22-222-2-222-2-22-22-22-2002-22-200000000−2i2i−2i2i000002-22-200000000000−2i2i−2i2i0000000000000
χ3922-2-22-222-2-222-2-22-2-22-22002-22-2000000002i−2i−2i2i00000-22-22000000000002i−2i−2i2i0000000000000
χ4022-2-22-222-2-222-2-22-2-22-22002-22-200000000−2i2i2i−2i00000-22-2200000000000−2i2i2i−2i0000000000000
χ4122-2-22-22-222-22-2-22-22i−2i−2i2i00-22-22000000000000000002i−2i−2i2i0000000000000000002-200002i−2i00
χ4222-2-22-22-222-22-2-22-22i−2i−2i2i00-22-22000000000000000002i−2i−2i2i000000000000000000-220000−2i2i00
χ4322-2-22-22-222-22-2-22-2−2i2i2i−2i00-22-2200000000000000000−2i2i2i−2i0000000000000000002-20000−2i2i00
χ4422-2-22-22-222-22-2-22-2−2i2i2i−2i00-22-2200000000000000000−2i2i2i−2i000000000000000000-2200002i−2i00
χ4522-2-22-2-12-2-22-111-112-22-200-11-1133−3−300002i−2i2i−2i03−33−3-11-113−3000000−i3i30−ii−ii−i3i300000000000
χ4622-2-22-2-12-2-22-111-112-22-200-11-1133−3−30000−2i2i−2i2i03−33−3-11-113−3000000i3−i30i−ii−ii3−i300000000000
χ4722-2-22-2-12-2-22-111-112-22-200-11-11−3−33300002i−2i2i−2i0−33−33-11-11−33000000i3−i30−ii−iii3−i300000000000
χ4822-2-22-2-12-2-22-111-112-22-200-11-11−3−3330000−2i2i−2i2i0−33−33-11-11−33000000−i3i30i−ii−i−i3i300000000000
χ4922-2-22-2-12-2-22-111-11-22-2200-11-1133−3−300002i−2i−2i2i0−33−331-11-13−3000000−i3i30−iii−ii3−i300000000000
χ5022-2-22-2-12-2-22-111-11-22-2200-11-1133−3−30000−2i2i2i−2i0−33−331-11-13−3000000i3−i30i−i−ii−i3i300000000000
χ5122-2-22-2-12-2-22-111-11-22-2200-11-11−3−33300002i−2i−2i2i03−33−31-11-1−33000000i3−i30−iii−i−i3i300000000000
χ5222-2-22-2-12-2-22-111-11-22-2200-11-11−3−3330000−2i2i2i−2i03−33−31-11-1−33000000−i3i30i−i−iii3−i300000000000
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
χ574444-4-4-2-44-44-2-2-22200000022-2-20000004-400000-2-22200000000000000000000000000000000
χ584444-4-4-2-44-44-2-2-22200000022-2-2000000-440000022-2-200000000000000000000000000000000
χ5944-4-44-4-2-444-4-222-224i−4i−4i4i002-22-200000000000000000−2i2i2i−2i0000000000000000000000000000
χ6044-4-44-4-2-444-4-222-22−4i4i4i−4i002-22-2000000000000000002i−2i−2i2i0000000000000000000000000000
χ6144-4-4-44444-4-44-4-4-440000004-4-440000000000000000000000000000000000000000000000000
χ6244-4-4-444-4-4444-4-4-44000000-444-40000000000000000000000000000000000000000000000000
χ6344-4-4-44-244-4-4-2222-2000000-222-22323−23−2300000000000000000−232300000000000000000000000000
χ6444-4-4-44-244-4-4-2222-2000000-222-2−23−2323230000000000000000023−2300000000000000000000000000
χ6544-4-4-44-2-4-444-2222-20000002-2-22000000000000023−23−232300000000000000000000000000000000
χ6644-4-4-44-2-4-444-2222-20000002-2-220000000000000−232323−2300000000000000000000000000000000
χ674-44-40040000-44-4000000−2i22i20000−2i22i2−2i22i24-400000000000000000000−2i22i2000000000000000000000
χ684-44-40040000-44-4000000−2i22i20000−2i22i2−2i22i2-44000000000000000000002i2−2i2000000000000000000000
χ694-44-40040000-44-40000002i2−2i200002i2−2i22i2−2i24-4000000000000000000002i2−2i2000000000000000000000
χ704-44-40040000-44-40000002i2−2i200002i2−2i22i2−2i2-4400000000000000000000−2i22i2000000000000000000000
χ718-88-800-400004-44000000−4i24i200002i2−2i22i2−2i2000000000000000000000000000000000000000000000
χ728-88-800-400004-440000004i2−4i20000−2i22i2−2i22i2000000000000000000000000000000000000000000000
χ738-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000
χ748-8-8800-4000044-40000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ758-8-8800-4000044-4000000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000

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