Finite Group Databasebeta

← Group #72256315

Character table — Group #72256315

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11222222244444488888888888161616161616161616161616161616161616161616161616323232323232323232323232323232323232323232323232646464646464646464646464
order12222222222222222222224444222222444444444444444444224444444444444444444444444444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ4111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ51111111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1
χ61111111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ71111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ911111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ1011111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ1111111111111111111111111111-1-111-1-1-1-111-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111
χ1211111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1
χ1311111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ1411111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-111
χ1511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1111111-1-1-1-1
χ1611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-1-1-11111
χ1722222222222222222-22-2-2-2-2-2-2-222002-222002-200000000000000-2-20000002-2000022-2-20000000000000000
χ1822222222222222222-22-2-2-2-2-2-2-22200-222200-2200000000000000-2-2000000-220000-2-2220000000000000000
χ1922222222222222222-22-2-2-2-2-2-2-2-2-2002-2-2-2002-200000000000000220000002-20000-2-2220000000000000000
χ2022222222222222222-22-2-2-2-2-2-2-2-2-200-22-2-200-220000000000000022000000-22000022-2-20000000000000000
χ2122222222222-2-222-2-22-22-2-22-2-2200222-200222-20000000000000000-2-20000-220000000022-2-2000000000000
χ2222222222222-2-222-2-22-22-2-22-2-220022-220022-220000000000000000-2-200002-200000000-2-222000000000000
χ2322222222222-2-222-2-22-22-2-22-2-2200-2-22-200-2-22-20000000000000000220000-2200000000-2-222000000000000
χ2422222222222-2-222-2-22-22-2-22-2-2200-2-2-2200-2-2-2200000000000000002200002-20000000022-2-2000000000000
χ2522222222222-2-222-2-2-2-2-222-222-200002200002200002222-2-2-2-20000000000-2-222-2-200000000000000000000
χ2622222222222-2-222-2-2-2-2-222-222-20000220000220000-2-2-2-222220000000000-2-2-2-22200000000000000000000
χ2722222222222-2-222-2-2-2-2-222-222-20000-2-20000-2-200002222-2-2-2-2000000000022-2-22200000000000000000000
χ2822222222222-2-222-2-2-2-2-222-222-20000-2-20000-2-20000-2-2-2-2222200000000002222-2-200000000000000000000
χ29222222222-2-222-2-22-2-2-2-2-2-2222200000000000022222i2i−2i−2i2i2i−2i−2i-2-20000000000000000000000000000002i−2i00
χ30222222222-2-222-2-22-2-2-2-2-2-222220000000000002222−2i−2i2i2i−2i−2i2i2i-2-2000000000000000000000000000000−2i2i00
χ31222222222-2-222-2-22-2-2-2-2-2-22222000000000000-2-2-2-22i2i−2i−2i2i2i−2i−2i22000000000000000000000000000000−2i2i00
χ32222222222-2-222-2-22-2-2-2-2-2-22222000000000000-2-2-2-2−2i−2i2i2i−2i−2i2i2i220000000000000000000000000000002i−2i00
χ33222222222-2-2-2-2-2-2-22222-2-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i00000022-2-200000000000000002i−2i00000000
χ34222222222-2-2-2-2-2-2-22222-2-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i000000-2-2220000000000000000−2i2i00000000
χ35222222222-2-2-2-2-2-2-22222-2-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i00000022-2-20000000000000000−2i2i00000000
χ36222222222-2-2-2-2-2-2-22222-2-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i000000-2-22200000000000000002i−2i00000000
χ3722-2-222-2-222222-2-2-2-222-22-222-2-200000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000002-200002i−2i0000
χ3822-2-222-2-222222-2-2-2-222-22-222-2-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000-220000−2i2i0000
χ3922-2-222-2-222222-2-2-2-222-22-222-2-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002-20000−2i2i0000
χ4022-2-222-2-222222-2-2-2-222-22-222-2-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000-2200002i−2i0000
χ4122-2-222-2-2222-2-2-2-222-2-222-2-22-2200000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000002i−2i00002-2
χ4222-2-222-2-2222-2-2-2-222-2-222-2-22-2200000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000−2i2i0000-22
χ4322-2-222-2-2222-2-2-2-222-2-222-2-22-220000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000002i−2i0000-22
χ4422-2-222-2-2222-2-2-2-222-2-222-2-22-220000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000−2i2i00002-2
χ4522-2-222-2-22-2-22222-222-2-22-2-2-222222-200-2-22-200000000000000002-22-20000002-22-200000000000000000000
χ4622-2-222-2-22-2-22222-222-2-22-2-2-22222-2200-2-2-2200000000000000002-2-22000000-22-2200000000000000000000
χ4722-2-222-2-22-2-22222-222-2-22-2-2-222-2-22-200222-20000000000000000-222-2000000-22-2200000000000000000000
χ4822-2-222-2-22-2-22222-222-2-22-2-2-222-2-2-220022-220000000000000000-22-220000002-22-200000000000000000000
χ4922-2-222-2-22-2-22222-22-2-22-2222-2-2220000-2-2000000002-2-222-2-2200-2200000000000000002-22-2000000000000
χ5022-2-222-2-22-2-22222-22-2-22-2222-2-2220000-2-200000000-222-2-222-200-220000000000000000-22-22000000000000
χ5122-2-222-2-22-2-22222-22-2-22-2222-2-2-2-2000022000000002-2-222-2-22002-20000000000000000-22-22000000000000
χ5222-2-222-2-22-2-22222-22-2-22-2222-2-2-2-200002200000000-222-2-222-2002-200000000000000002-22-2000000000000
χ5322-2-222-2-22-2-2-2-2222-222-2-22-22-22002-200002-20000002-2-22-222-20000-2200000000002-22-20000000000000000
χ5422-2-222-2-22-2-2-2-2222-222-2-22-22-22002-200002-2000000-222-22-2-220000-220000000000-22-220000000000000000
χ5522-2-222-2-22-2-2-2-2222-222-2-22-22-2200-220000-220000002-2-22-222-200002-20000000000-22-220000000000000000
χ5622-2-222-2-22-2-2-2-2222-222-2-22-22-2200-220000-22000000-222-22-2-2200002-200000000002-22-20000000000000000
χ5722-2-222-2-22-2-2-2-2222-2-2222-22-22-20000000000000000000000000000000000002-2-222-2-222-2-22000000000000
χ5822-2-222-2-22-2-2-2-2222-2-2222-22-22-20000000000000000000000000000000000002-2-22-222-2-222-2000000000000
χ5922-2-222-2-22-2-2-2-2222-2-2222-22-22-2000000000000000000000000000000000000-222-22-2-22-222-2000000000000
χ6022-2-222-2-22-2-2-2-2222-2-2222-22-22-2000000000000000000000000000000000000-222-2-222-22-2-22000000000000
χ61444444444-4-444-4-44-44-4444-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ62444444444-4-4-4-4-4-4-44-44-4444-4-44000000000000000000000000000000000000000000000000000000000000
χ6344-4-444-4-444444-4-4-4-4-444-44-4-444000000000000000000000000000000000000000000000000000000000000
χ6444-4-444-4-4444-4-4-4-4444-4-4-444-44-4000000000000000000000000000000000000000000000000000000000000
χ6544-4-4-4-44444-4004-40000000000000000400000-422-2-2000000002-200002-22-200000000000000000000000000
χ6644-4-4-4-44444-4004-40000000000000000400000-4-2-22200000000-220000-22-2200000000000000000000000000
χ6744-4-4-4-44444-4004-40000000000000000-400000422-2-2000000002-20000-22-2200000000000000000000000000
χ6844-4-4-4-44444-4004-40000000000000000-4000004-2-22200000000-2200002-22-200000000000000000000000000
χ6944-4-4-4-4444-4400-44000000000000000400000-4022-2-200000000-2200002-2-2200000000000000000000000000
χ7044-4-4-4-4444-4400-44000000000000000400000-40-2-222000000002-20000-222-200000000000000000000000000
χ7144-4-4-4-4444-4400-44000000000000000-4000004022-2-200000000-220000-222-200000000000000000000000000
χ7244-4-4-4-4444-4400-44000000000000000-40000040-2-222000000002-200002-2-2200000000000000000000000000
χ738888-8-8-8-888-800-8800000000000000000000000000000000000000000000000000000000000000000000000
χ748888-8-8-8-88-88008-800000000000000000000000000000000000000000000000000000000000000000000000
χ75888-88-88-8-80000000000000000000440000-4-400000000000000000000000000000000000000000000000000
χ76888-88-88-8-80000000000000000000-4-400004400000000000000000000000000000000000000000000000000
χ77888-8-88-88-8000000000000000004-400004-40000000000000000000000000000000000000000000000000000
χ78888-8-88-88-800000000000000000-440000-440000000000000000000000000000000000000000000000000000
χ7988-888-8-88-800000000000000000004-40000-4400000000000000000000000000000000000000000000000000
χ8088-888-8-88-80000000000000000000-4400004-400000000000000000000000000000000000000000000000000
χ8188-88-888-8-8000000000000000004-40000-440000000000000000000000000000000000000000000000000000
χ8288-88-888-8-800000000000000000-4400004-40000000000000000000000000000000000000000000000000000
χ8316-160000000008-800000000000000000000000004-44-400000000000000000000000000000000000000000000
χ8416-160000000008-80000000000000000000000000-44-4400000000000000000000000000000000000000000000
χ8516-16000000000-8800000000000000000000000004-4-4400000000000000000000000000000000000000000000
χ8616-16000000000-880000000000000000000000000-444-400000000000000000000000000000000000000000000

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