Finite Group Databasebeta

← Group #10827770

Character table — Group #10827770

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222222222244444444444488888888888888888888888121212121616161616161616242424242424242424244848
order12222222236662244446666664444444661212121212121212121212121212444444121212121212222444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11-1-11-1-11111-1-1
χ411111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-111-111-1-1-1-111
χ511111111111111111-1-1111111-11111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-11111-1-1-1-1
χ611111111111111111-1-1111111-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111
χ711111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111
χ811111111111111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111111-1-111-1-1
χ91111111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-1-111-1-1-11-1-11-1-1-1111-1
χ101111111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-1-1-111-1-11-111-1111-1-1-11
χ111111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-11111-1-111111111-11-1-1-1-111-1-11-1-11-1-111-11
χ121111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11-1-1-1-11111-111-111-1-11-1
χ131111111111111-1-1-1-1-1-1111111-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-111-1-1-1-1-1-11
χ141111111111111-1-1-1-1-1-1111111-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-1-1111111-1
χ151111111111111-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111-11111-1-11-111-11-1-1-1-11-1
χ161111111111111-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11111-1-1-11-1-11-11111-11
χ17222222222-1-1-1-1222222-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1000000000000
χ18222222222-1-1-1-1222222-1-1-1-1-1-12-2-2-2-222-1-111111111-1-1-1-1-1-10000-2-2-1-11111000000000000
χ19222222222-1-1-1-12222-2-2-1-1-1-1-1-1-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000-2-2111111000000000000
χ20222222222-1-1-1-12222-2-2-1-1-1-1-1-1-2-2-2-2-2-2-2-1-111111111-1-1111100002211-1-1-1-1000000000000
χ21222222222-1-1-1-1-2-2-2-222-1-1-1-1-1-1222-2-2-2-211-1-1-1-1111111-1-1-1-100002-211-1-111000000000000
χ22222222222-1-1-1-1-2-2-2-222-1-1-1-1-1-12-2-222-2-2111111-1-1-1-111-1-1-1-10000-221111-1-1000000000000
χ23222222222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-222-2-22211-1-1-1-111111111110000-22-1-111-1-1000000000000
χ24222222222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-2-2-22222111111-1-1-1-111111100002-2-1-1-1-111000000000000
χ252222-2-22-2-22-2-2200000022-22-2-20002i−2i000000002i2i−2i−2i0000002i2i−2i−2i0000000000200-2000000
χ262222-2-22-2-22-2-2200000022-22-2-20002i−2i000000002i2i−2i−2i000000−2i−2i2i2i0000000000-2002000000
χ272222-2-22-2-22-2-2200000022-22-2-2000−2i2i00000000−2i−2i2i2i0000002i2i−2i−2i0000000000-2002000000
χ282222-2-22-2-22-2-2200000022-22-2-2000−2i2i00000000−2i−2i2i2i000000−2i−2i2i2i0000000000200-2000000
χ29222-22-2-22-22-2-220000002-22-22-202i−2i0000002i2i−2i−2i00000000002i−2i2i−2i000000000200-20000000
χ30222-22-2-22-22-2-220000002-22-22-202i−2i0000002i2i−2i−2i0000000000−2i2i−2i2i000000000-20020000000
χ31222-22-2-22-22-2-220000002-22-22-20−2i2i000000−2i−2i2i2i00000000002i−2i2i−2i000000000-20020000000
χ32222-22-2-22-22-2-220000002-22-22-20−2i2i000000−2i−2i2i2i0000000000−2i2i−2i2i000000000200-20000000
χ33222-2-22-2-22222222-2-2002-2-2-2-2200000002200000000-2-200002-2-22000000000000002-20000
χ34222-2-22-2-22222222-2-2002-2-2-2-2200000002200000000-2-20000-222-200000000000000-220000
χ35222-2-22-2-222222-2-222002-2-2-2-220000000-2-2000000002200002-2-2200000000000000-220000
χ36222-2-22-2-222222-2-222002-2-2-2-220000000-2-200000000220000-222-2000000000000002-20000
χ3722-222-2-2-222-2-222-22-200-2-2-222200000002-2000000002-20000000000000000200-200002-200
χ3822-222-2-2-222-2-222-22-200-2-2-222200000002-2000000002-20000000000000000-20020000-2200
χ3922-222-2-2-222-2-22-22-2200-2-2-22220000000-2200000000-220000000000000000200-20000-2200
χ4022-222-2-2-222-2-22-22-2200-2-2-22220000000-2200000000-220000000000000000-200200002-200
χ4122-2-2-2-22222-2-222-2-2222-222-2-22-200002-22-200000000-2222-2-20000002-20000000000000000
χ4222-2-2-2-22222-2-222-2-22-2-2-222-2-2220000-222-200000000-22-2-222000000-220000000000000000
χ4322-2-2-2-22222-2-22-222-222-222-2-22-20000-22-22000000002-222-2-2000000-220000000000000000
χ4422-2-2-2-22222-2-22-222-2-2-2-222-2-22200002-2-22000000002-2-2-2220000002-20000000000000000
χ4522-2-2-2-2222-111-12-2-22221-1-111-1-200002-2-113−33−33−33−31-1-1-111000000-113−33−3000000000000
χ4622-2-2-2-2222-111-12-2-22221-1-111-1-200002-2-11−33−33−33−331-1-1-111000000-11−33−33000000000000
χ4722-2-2-2-2222-111-12-2-22-2-21-1-111-120000-22-113−33−33−33−31-111-1-10000001-1−33−33000000000000
χ4822-2-2-2-2222-111-12-2-22-2-21-1-111-120000-22-11−33−33−33−331-111-1-10000001-13−33−3000000000000
χ4922-2-2-2-2222-111-1-222-2221-1-111-1-20000-221-13−33−3−33−33-11-1-1110000001-13−3−33000000000000
χ5022-2-2-2-2222-111-1-222-2221-1-111-1-20000-221-1−33−333−33−3-11-1-1110000001-1−333−3000000000000
χ5122-2-2-2-2222-111-1-222-2-2-21-1-111-1200002-21-13−33−3−33−33-1111-1-1000000-11−333−3000000000000
χ5222-2-2-2-2222-111-1-222-2-2-21-1-111-1200002-21-1−33−333−33−3-1111-1-1000000-113−3−33000000000000
χ534444-4-44-4-4-222-2000000-2-22-2220004i−4i00000000−2i−2i2i2i000000000000000000000000000000
χ544444-4-44-4-4-222-2000000-2-22-222000−4i4i000000002i2i−2i−2i000000000000000000000000000000
χ55444-44-4-44-4-222-2000000-22-22-2204i−4i000000−2i−2i2i2i0000000000000000000000000000000000
χ56444-44-4-44-4-222-2000000-22-22-220−4i4i0000002i2i−2i−2i0000000000000000000000000000000000
χ57444-4-44-4-44-2-2-2-244-4-400-22222-20000000-2-200000000220000000000000000000000000000
χ58444-4-44-4-44-2-2-2-2-4-44400-22222-200000002200000000-2-20000000000000000000000000000
χ5944-444-4-4-44-222-24-44-400222-2-2-20000000-2200000000-220000000000000000000000000000
χ6044-444-4-4-44-222-2-44-4400222-2-2-200000002-2000000002-20000000000000000000000000000
χ6144-44-44-44-44444000000-4-444-4-400000000000000000000000000000000000000000000000
χ6244-44-44-44-4-2-2-2-200000022-2-222000000000−2i32i32i3−2i30000000000000000000000000000000000
χ6344-44-44-44-4-2-2-2-200000022-2-2220000000002i3−2i3−2i32i30000000000000000000000000000000000
χ6444-4-4444-4-44444000000-44-4-44-400000000000000000000000000000000000000000000000
χ6544-4-4444-4-4-2-2-2-20000002-222-220000000000000−2i32i32i3−2i3000000000000000000000000000000
χ6644-4-4444-4-4-2-2-2-20000002-222-2200000000000002i3−2i3−2i32i3000000000000000000000000000000
χ678-80000000800-800004i−4i00000000000000000000000004i−4i00000000000000000000000000
χ688-80000000800-80000−4i4i0000000000000000000000000−4i4i00000000000000000000000000
χ698-80000000-4−4i34i3400004i−4i0000000000000000000000000−2i2i23−23000000000000000000000000
χ708-80000000-4−4i34i340000−4i4i00000000000000000000000002i−2i−2323000000000000000000000000
χ718-80000000-44i3−4i3400004i−4i0000000000000000000000000−2i2i−2323000000000000000000000000
χ728-80000000-44i3−4i340000−4i4i00000000000000000000000002i−2i23−23000000000000000000000000

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