Finite Group Databasebeta

← Group #72319822

Character table — Group #72319822

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1122222224444888888888888881616163232323232323232323232323232323232323232323232323232323232323232323232326464646464646464646464
order12222222244442222222244444444424444444444444444444444444448888888844444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-1-1
χ41111111111111111111111111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-11111
χ5111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-111111-1-1-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-111111
χ911111111111111111111111-1-111-1-1-111-1-111-111-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1
χ1011111111111111111111111-1-111-1-1-111-1-111-1-1-111-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-11111-1-111
χ1111111111111111111111111-1-111-1-1-111-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-1-111
χ1211111111111111111111111-1-111-1-1-111-1-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-1111-111-1-1
χ1311111111111111111111111-1-111-1-1-1-1-11111-111-1-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-1-111-1-111-1-1
χ1411111111111111111111111-1-111-1-1-1-1-11111-1-1-111-1-1-111-1-1111111-1-1-1-11111-1-111-111-1-1-1-1-1-111
χ1511111111111111111111111-1-111-1-1-1-1-111-1-1-111-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-11-1-111-11-1-111
χ1611111111111111111111111-1-111-1-1-1-1-111-1-1-1-1-111-111-1-1-1-111-1-1-1-1111111-1-111-1-1111-1-1-1111-1-1
χ17222222222222222-2-222-2-2-2-222-2-2222000000-20000-22222000000000000000000-2-2000000-20000
χ18222222222222222-2-222-2-2-2-222-2-2222000000-20000-2-2-2-2-20000000000000000002200000020000
χ19222222222222222-2-222-2-2-2-2-2-2-2-2-2-2-200000020000222-2-200000000000000000022000000-20000
χ20222222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2000000200002-2-222000000000000000000-2-200000020000
χ212222222222222-2-222-2-222-2-222-2-22-2-2222200-2000020000000000000000-2-200000000000-200000
χ222222222222222-2-222-2-222-2-222-2-22-2-2-2-2-2-200-20000200000000000000002200000000000200000
χ232222222222222-2-222-2-222-2-2-2-2-2-2-22222-2-20020000-200000000000000002200000000000-200000
χ242222222222222-2-222-2-222-2-2-2-2-2-2-222-2-2220020000-20000000000000000-2-200000000000200000
χ252222222222222-2-2-2-2-2-2-2-22222222-2-200002220000-2000000000000000000-2-2-2-20020000000000
χ262222222222222-2-2-2-2-2-2-2-22222222-2-20000-2-220000-2000000000000000000222200-20000000000
χ272222222222222-2-2-2-2-2-2-2-222-2-222-222000022-200002000000000000000000-2-22200-20000000000
χ282222222222222-2-2-2-2-2-2-2-222-2-222-2220000-2-2-20000200000000000000000022-2-20020000000000
χ29222-22-22-2-22-22-22-22-22-22-2-2-2002200000002i−2i00000000000000000022-2-2002i−2i00000002i−2i000000
χ30222-22-22-2-22-22-22-22-22-22-2-2-2002200000002i−2i000000000000000000-2-222002i−2i0000000−2i2i000000
χ31222-22-22-2-22-22-22-22-22-22-2-2-200220000000−2i2i00000000000000000022-2-200−2i2i0000000−2i2i000000
χ32222-22-22-2-22-22-22-22-22-22-2-2-200220000000−2i2i000000000000000000-2-22200−2i2i00000002i−2i000000
χ33222-22-22-2-22-22-2-22-22-22-22-2-2002200000002i−2i0000000000000022-2-2000000−2i2i000002i−2i00000000
χ34222-22-22-2-22-22-2-22-22-22-22-2-2002200000002i−2i00000000000000-2-222000000−2i2i00000−2i2i00000000
χ35222-22-22-2-22-22-2-22-22-22-22-2-200220000000−2i2i0000000000000022-2-20000002i−2i00000−2i2i00000000
χ36222-22-22-2-22-22-2-22-22-22-22-2-200220000000−2i2i00000000000000-2-2220000002i−2i000002i−2i00000000
χ3722-22-222-2-2-222-22-2-2-2-22222-2002-2000002i−2i00000000000000002-22-200002i−2i0000000000000002i−2i
χ3822-22-222-2-2-222-22-2-2-2-22222-2002-2000002i−2i0000000000000000-22-2200002i−2i000000000000000−2i2i
χ3922-22-222-2-2-222-22-2-2-2-22222-2002-200000−2i2i00000000000000002-22-20000−2i2i000000000000000−2i2i
χ4022-22-222-2-2-222-22-2-2-2-22222-2002-200000−2i2i0000000000000000-22-220000−2i2i0000000000000002i−2i
χ4122-22-222-2-2-222-2-22-2-22-222-2200-22000002i−2i000000000000000000002-22-2−2i2i00000000000002i−2i00
χ4222-22-222-2-2-222-2-22-2-22-222-2200-22000002i−2i00000000000000000000-22-22−2i2i0000000000000−2i2i00
χ4322-22-222-2-2-222-2-22-2-22-222-2200-2200000−2i2i000000000000000000002-22-22i−2i0000000000000−2i2i00
χ4422-22-222-2-2-222-2-22-2-22-222-2200-2200000−2i2i00000000000000000000-22-222i−2i00000000000002i−2i00
χ4522-2-2-2-2222-2-222-2-22-222-22-22002-20000000000002-20002-2002-22-2-2200000000002-200000000000
χ4622-2-2-2-2222-2-222-2-22-222-22-22002-20000000000002-2000-22002-2-222-20000000000-2200000000000
χ4722-2-2-2-2222-2-222-2-22-222-22-22002-2000000000000-220002-200-22-222-200000000002-200000000000
χ4822-2-2-2-2222-2-222-2-22-222-22-22002-2000000000000-22000-2200-222-2-220000000000-2200000000000
χ4922-2-2-2-2222-2-222-2-2-22222-22-200-2200000000002-2000002-22-20000002-2-22000000-2200000000000
χ5022-2-2-2-2222-2-222-2-2-22222-22-200-2200000000002-200000-222-2000000-222-20000002-200000000000
χ5122-2-2-2-2222-2-222-2-2-22222-22-200-220000000000-22000002-2-22000000-222-2000000-2200000000000
χ5222-2-2-2-2222-2-222-2-2-22222-22-200-220000000000-2200000-22-220000002-2-220000002-200000000000
χ53444444444-4-4-4-400000000004400-4000000000222200000-2-2-2-2000000000000000000000000000
χ54444444444-4-4-4-400000000004400-4000000000-2-2-2-2000002222000000000000000000000000000
χ55444444444-4-4-4-40000000000-4-400400000000022-2-200000-2-222000000000000000000000000000
χ56444444444-4-4-4-40000000000-4-4004000000000-2-2220000022-2-2000000000000000000000000000
χ57444-44-44-4-44-44-44-4-444-4-444400-4-400000000000000000000000000000000000000000000000000
χ58444-44-44-4-44-44-4-444-4-444-44400-4-400000000000000000000000000000000000000000000000000
χ5944-44-444-4-4-444-44-444-44-4-4-4400-4400000000000000000000000000000000000000000000000000
χ6044-44-444-4-4-444-4-44444-4-4-44-4004-400000000000000000000000000000000000000000000000000
χ6144-4-4-4-444444-4-40000000000000004-400000002-22-200000-22-22000000000000000000000000000
χ6244-4-4-4-444444-4-40000000000000004-40000000-22-22000002-22-2000000000000000000000000000
χ6344-4-4-4-444444-4-4000000000000000-4400000002-2-2200000-222-2000000000000000000000000000
χ6444-4-4-4-444444-4-4000000000000000-440000000-222-2000002-2-22000000000000000000000000000
χ6544-4-4-4-4444-4-444444-4-4-4-444-400-4400000000000000000000000000000000000000000000000000
χ6644-4-4-4-4444-4-44444-44-4-44-4-44004-400000000000000000000000000000000000000000000000000
χ678888-8-8-88-80000000000000000000004-4000000000000000000000000000000000000000000000
χ688888-8-8-88-8000000000000000000000-44000000000000000000000000000000000000000000000
χ69888-88-88-8-8-88-880000000000000000000000000000000000000000000000000000000000000000
χ70888-8-88-8-880000000000000000000000000000000004-4000000000000000000000000000000000
χ71888-8-88-8-88000000000000000000000000000000000-44000000000000000000000000000000000
χ7288-888-8-8-88000000000000008-80000000000000000000000000000000000000000000000000000
χ7388-888-8-8-8800000000000000-880000000000000000000000000000000000000000000000000000
χ7488-88-888-8-88-8-880000000000000000000000000000000000000000000000000000000000000000
χ7588-8-888-88-8000000000000000000000000000000000000000000000000000004i−4i0000000000000
χ7688-8-888-88-800000000000000000000000000000000000000000000000000000−4i4i0000000000000
χ7732-32000000000000000000000000000000000000000000000000000000000000000000000000000

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