Finite Group Databasebeta

← Group #72319755

Character table — Group #72319755

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1122222224444888888888888881616161616161616161616161616163232323232323232323232323232323232323232323232323232323232326464646464646464646464
order12222222244442222222244444422444444444888824444444444444444444444488888844444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1111-1-1-1-111-1-111-1-11111111111111111-1-111-1-1-1-1-1-1-1-11-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-111111
χ5111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-1
χ6111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11111
χ7111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111
χ8111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1
χ911111111111111111111111-1-11111111111-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-111-1-1
χ1011111111111111111111111-1-11111111111-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1-111
χ1111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111-1-1111-1-1-111
χ1211111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111111-1-11-111-1-1
χ1311111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-1-11-1-111
χ1411111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-111-1111-1-1
χ1511111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1
χ1611111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ17222222222222222-2-222-2-2-2-222-2-2000022222-2-2000000002-2220000000000000000-2-2000000000-200000
χ18222222222222222-2-222-2-2-2-222-2-20000-2-2-2-22-2-2000000002-2-2-2000000000000000022000000000200000
χ19222222222222222-2-222-2-2-2-2-2-2-2-200002222-22200000000-22-2-20000000000000000-2-2000000000200000
χ20222222222222222-2-222-2-2-2-2-2-2-2-20000-2-2-2-2-22200000000-2222000000000000000022000000000-200000
χ212222222222222-2-222-2-222-2-222-2-22222000022200002200-2-200000000000000000000-2-200000000-20000
χ222222222222222-2-222-2-222-2-222-2-2-2-2-2-200002220000-2-200-2-200000000000000000000220000000020000
χ232222222222222-2-222-2-222-2-2-2-2-2-222220000-2-2-20000-2-2002200000000000000000000-2-20000000020000
χ242222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-20000-2-2-20000220022000000000000000000002200000000-20000
χ252222222222222-2-2-2-2-2-2-2-2222222000000002-2-2222200-2-2-22000000000000000000000022-20000000000
χ262222222222222-2-2-2-2-2-2-2-2222222000000002-2-2-2-2-2-20022-220000000000000000000000-2-220000000000
χ272222222222222-2-2-2-2-2-2-2-222-2-22200000000-222222200-2-22-20000000000000000000000-2-220000000000
χ282222222222222-2-2-2-2-2-2-2-222-2-22200000000-222-2-2-2-200222-2000000000000000000000022-20000000000
χ292222-22-2-2-22-2-222-22-22-22-2-2-20022000000000002i2i−2i−2i002i−2i00000000000000002i2i−2i−2i0000000002-2000000
χ302222-22-2-2-22-2-222-22-22-22-2-2-20022000000000002i2i−2i−2i002i−2i0000000000000000−2i−2i2i2i000000000-22000000
χ312222-22-2-2-22-2-222-22-22-22-2-2-2002200000000000−2i−2i2i2i00−2i2i00000000000000002i2i−2i−2i000000000-22000000
χ322222-22-2-2-22-2-222-22-22-22-2-2-2002200000000000−2i−2i2i2i00−2i2i0000000000000000−2i−2i2i2i0000000002-2000000
χ332222-22-2-2-22-2-22-22-22-22-22-2-20022000000000002i2i−2i−2i00−2i2i0000000000002i2i−2i−2i000000000002-200000000
χ342222-22-2-2-22-2-22-22-22-22-22-2-20022000000000002i2i−2i−2i00−2i2i000000000000−2i−2i2i2i00000000000-2200000000
χ352222-22-2-2-22-2-22-22-22-22-22-2-2002200000000000−2i−2i2i2i002i−2i0000000000002i2i−2i−2i00000000000-2200000000
χ362222-22-2-2-22-2-22-22-22-22-22-2-2002200000000000−2i−2i2i2i002i−2i000000000000−2i−2i2i2i000000000002-200000000
χ3722-2-2222-2-2-2-222222-2-2-2-222-2002-2000022-2-2000000000000000000000002i−2i2i−2i00002-2000000000002i−2i00
χ3822-2-2222-2-2-2-222222-2-2-2-222-2002-2000022-2-200000000000000000000000−2i2i−2i2i00002-200000000000−2i2i00
χ3922-2-2222-2-2-2-222222-2-2-2-222-2002-20000-2-222000000000000000000000002i−2i2i−2i0000-2200000000000−2i2i00
χ4022-2-2222-2-2-2-222222-2-2-2-222-2002-20000-2-22200000000000000000000000−2i2i−2i2i0000-22000000000002i−2i00
χ4122-2-2222-2-2-2-22222-22-2-22-2-2200-22000022-2-20000000000000000000000000002i−2i2i−2i-2200000000000002i−2i
χ4222-2-2222-2-2-2-22222-22-2-22-2-2200-22000022-2-2000000000000000000000000000−2i2i−2i2i-220000000000000−2i2i
χ4322-2-2222-2-2-2-22222-22-2-22-2-2200-220000-2-2220000000000000000000000000002i−2i2i−2i2-20000000000000−2i2i
χ4422-2-2222-2-2-2-22222-22-2-22-2-2200-220000-2-222000000000000000000000000000−2i2i−2i2i2-200000000000002i−2i
χ4522-2-2-22-222-22-222-2-2-2-22222-200-222-22-20000000000000000000000022-2-200002-2-22002-20000000000000
χ4622-2-2-22-222-22-222-2-2-2-22222-200-222-22-200000000000000000000000-2-2220000-222-2002-20000000000000
χ4722-2-2-22-222-22-222-2-2-2-22222-200-22-22-220000000000000000000000022-2-20000-222-200-220000000000000
χ4822-2-2-22-222-22-222-2-2-2-22222-200-22-22-2200000000000000000000000-2-22200002-2-2200-220000000000000
χ4922-2-2-22-222-22-22-22-2-22-222-22002-22-22-2000000000000000000022-2-200002-2-22000000-220000000000000
χ5022-2-2-22-222-22-22-22-2-22-222-22002-22-22-20000000000000000000-2-2220000-222-2000000-220000000000000
χ5122-2-2-22-222-22-22-22-2-22-222-22002-2-22-22000000000000000000022-2-20000-222-20000002-20000000000000
χ5222-2-2-22-222-22-22-22-2-22-222-22002-2-22-220000000000000000000-2-22200002-2-220000002-20000000000000
χ53444444444-4-4-4-40000000000440000000000-4000000000000002-22-22-22-20000000000000000000000000
χ54444444444-4-4-4-40000000000440000000000-400000000000000-22-22-22-220000000000000000000000000
χ55444444444-4-4-4-40000000000-4-400000000004000000000000002-22-2-22-220000000000000000000000000
χ56444444444-4-4-4-40000000000-4-40000000000400000000000000-22-222-22-20000000000000000000000000
χ574444-44-4-4-44-4-444-4-444-4-444400-4-400000000000000000000000000000000000000000000000000000000
χ584444-44-4-4-44-4-44-444-4-444-44400-4-400000000000000000000000000000000000000000000000000000000
χ59444-44-4-44-4000000000000004-4002-2-222i−2i2i−2i0002i−2i2i−2i2-200002i−2i000000000000000000002i−2i00000000000
χ60444-44-4-44-4000000000000004-4002-2-22−2i2i−2i2i000−2i2i−2i2i2-20000−2i2i00000000000000000000−2i2i00000000000
χ61444-44-4-44-4000000000000004-400-222-22i−2i2i−2i000−2i2i−2i2i-2200002i−2i00000000000000000000−2i2i00000000000
χ62444-44-4-44-4000000000000004-400-222-2−2i2i−2i2i0002i−2i2i−2i-220000−2i2i000000000000000000002i−2i00000000000
χ63444-44-4-44-400000000000000-44002-2-222i−2i2i−2i0002i−2i2i−2i-220000−2i2i00000000000000000000−2i2i00000000000
χ64444-44-4-44-400000000000000-44002-2-22−2i2i−2i2i000−2i2i−2i2i-2200002i−2i000000000000000000002i−2i00000000000
χ65444-44-4-44-400000000000000-4400-222-22i−2i2i−2i000−2i2i−2i2i2-20000−2i2i000000000000000000002i−2i00000000000
χ66444-44-4-44-400000000000000-4400-222-2−2i2i−2i2i0002i−2i2i−2i2-200002i−2i00000000000000000000−2i2i00000000000
χ6744-4-4444-4-4-4-444-4-44-444-44-4400-4400000000000000000000000000000000000000000000000000000000
χ6844-4-4444-4-4-4-444-4-4-44444-44-4004-400000000000000000000000000000000000000000000000000000000
χ6944-4-4-44-4444-44-4000000000000000000000004-40000000000002-2-222-2-220000000000000000000000000
χ7044-4-4-44-4444-44-4000000000000000000000004-4000000000000-222-2-222-20000000000000000000000000
χ7144-4-4-44-4444-44-400000000000000000000000-440000000000002-2-22-222-20000000000000000000000000
χ7244-4-4-44-4444-44-400000000000000000000000-44000000000000-222-22-2-220000000000000000000000000
χ7344-4-4-44-444-44-444-444-44-4-4-44004-400000000000000000000000000000000000000000000000000000000
χ7444-4-4-44-444-44-44-44444-4-4-44-400-4400000000000000000000000000000000000000000000000000000000
χ758888-88-8-8-8-888-80000000000000000000000000000000000000000000000000000000000000000000000
χ76888-8-8-88-88000000000000000000000000000004-4-4400000000000000000000000000000000000000000
χ77888-8-8-88-8800000000000000000000000000000-444-400000000000000000000000000000000000000000
χ7888-888-8-8-8800000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ7988-888-8-8-880000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ8088-88-8-888-800000000000000000044-4-40000000000000000000000000000000000000000000000000000
χ8188-88-8-888-8000000000000000000-4-4440000000000000000000000000000000000000000000000000000
χ8288-8-8888-8-888-8-80000000000000000000000000000000000000000000000000000000000000000000000
χ8332-32000000000000000000000000000000000000000000000000000000000000000000000000000000000

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