Finite Group Databasebeta

← Group #195201

Character table — Group #195201

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222222222222444444444444444444222244444444444444444444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ911111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ1111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ1211111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1311111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1411111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ1511111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1611111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1711-1-11-1-1111-11111-1-1-1-1-111-1-1ii−i−iii−i−i1-11-11-11-11-1i−ii−i1-11-1ii−i−iii−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−ii−ii−i
χ1811-1-11-1-1111-11111-1-1-1-1-111-1-1ii−i−iii−i−i1-11-11-11-11-1i−ii−i1-11-1ii−i−iii−i−i-1-111-1-111-1-111-1-111−i−iii−i−iii−ii−ii
χ1911-1-11-1-1111-11111-1-1-1-1-111-1-1ii−i−iii−i−i1-11-11-1-11-11i−ii−i-11-11−i−iii−i−iii11-1-111-1-1-1-111-1-111−i−iii−i−iiii−ii−i
χ2011-1-11-1-1111-11111-1-1-1-1-111-1-1ii−i−iii−i−i1-11-11-1-11-11i−ii−i-11-11−i−iii−i−iii-1-111-1-11111-1-111-1-1ii−i−iii−i−i−ii−ii
χ2111-1-11-1-1111-11111-1-1-1-1-111-1-1−i−iii−i−iii1-11-11-11-11-1−ii−ii1-11-1−i−iii−i−iii11-1-111-1-111-1-111-1-1−i−iii−i−iii−ii−ii
χ2211-1-11-1-1111-11111-1-1-1-1-111-1-1−i−iii−i−iii1-11-11-11-11-1−ii−ii1-11-1−i−iii−i−iii-1-111-1-111-1-111-1-111ii−i−iii−i−ii−ii−i
χ2311-1-11-1-1111-11111-1-1-1-1-111-1-1−i−iii−i−iii1-11-11-1-11-11−ii−ii-11-11ii−i−iii−i−i11-1-111-1-1-1-111-1-111ii−i−iii−i−i−ii−ii
χ2411-1-11-1-1111-11111-1-1-1-1-111-1-1−i−iii−i−iii1-11-11-1-11-11−ii−ii-11-11ii−i−iii−i−i-1-111-1-11111-1-111-1-1−i−iii−i−iiii−ii−i
χ2511-1-11-1-1111-1-1-1-1-11111-1-1-111ii−i−i−i−iii1-1-111-11-1-11i−i−ii1-1-11ii−i−i−i−iii11-1-1-1-11111-1-1-1-111ii−i−i−i−iiii−i−ii
χ2611-1-11-1-1111-1-1-1-1-11111-1-1-111ii−i−i−i−iii1-1-111-11-1-11i−i−ii1-1-11ii−i−i−i−iii-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−iii−i
χ2711-1-11-1-1111-1-1-1-1-11111-1-1-111ii−i−i−i−iii1-1-111-1-111-1i−i−ii-111-1−i−iiiii−i−i11-1-1-1-111-1-11111-1-1−i−iiiii−i−ii−i−ii
χ2811-1-11-1-1111-1-1-1-1-11111-1-1-111ii−i−i−i−iii1-1-111-1-111-1i−i−ii-111-1−i−iiiii−i−i-1-11111-1-111-1-1-1-111ii−i−i−i−iii−iii−i
χ2911-1-11-1-1111-1-1-1-1-11111-1-1-111−i−iiiii−i−i1-1-111-11-1-11−iii−i1-1-11−i−iiiii−i−i11-1-1-1-11111-1-1-1-111−i−iiiii−i−i−iii−i
χ3011-1-11-1-1111-1-1-1-1-11111-1-1-111−i−iiiii−i−i1-1-111-11-1-11−iii−i1-1-11−i−iiiii−i−i-1-11111-1-1-1-11111-1-1ii−i−i−i−iiii−i−ii
χ3111-1-11-1-1111-1-1-1-1-11111-1-1-111−i−iiiii−i−i1-1-111-1-111-1−iii−i-111-1ii−i−i−i−iii11-1-1-1-111-1-11111-1-1ii−i−i−i−iii−iii−i
χ3211-1-11-1-1111-1-1-1-1-11111-1-1-111−i−iiiii−i−i1-1-111-1-111-1−iii−i-111-1ii−i−i−i−iii-1-11111-1-111-1-1-1-111−i−iiiii−i−ii−i−ii
χ3322222222222222222222-2-2-2-222222222-2-2-2-2-2-20000-2-2-2-20000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000022220000000000000000000000000000000000000000
χ3522222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-222-2-20000-2-2220000000000000000000000000000000000000000
χ3622222222222-2-2-2-2-2-2-2-222222-2-2-2-22222-2-222-2-2000022-2-20000000000000000000000000000000000000000
χ3722222222-2-2-222-2-222-2-2-22222000000002-2-2-2-220000000000002-22-22-22-20000000000000000000000000000
χ3822222222-2-2-222-2-222-2-2-22222000000002-2-2-2-22000000000000-22-22-22-220000000000000000000000000000
χ3922222222-2-2-222-2-222-2-2-2-2-2-2-200000000-22222-222-2-20000-2-222000000000000000000000000000000000000
χ4022222222-2-2-222-2-222-2-2-2-2-2-2-200000000-22222-2-2-222000022-2-2000000000000000000000000000000000000
χ4122222222-2-2-2-2-222-2-222-2222200000000-22-2-22-222220000-2-2-2-2000000000000000000000000000000000000
χ4222222222-2-2-2-2-222-2-222-2222200000000-22-2-22-2-2-2-2-200002222000000000000000000000000000000000000
χ4322222222-2-2-2-2-222-2-222-2-2-2-2-2000000002-222-220000000000002-22-2-22-220000000000000000000000000000
χ4422222222-2-2-2-2-222-2-222-2-2-2-2-2000000002-222-22000000000000-22-222-22-20000000000000000000000000000
χ4522-2-22-2-2222-22222-2-2-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i-22-22-220000−2i2i−2i2i0000000000000000000000000000000000000000
χ4622-2-22-2-2222-22222-2-2-2-2-2-2-222−2i−2i2i2i−2i−2i2i2i-22-22-2200002i−2i2i−2i0000000000000000000000000000000000000000
χ4722-2-22-2-2222-2-2-2-2-22222-222-2-22i2i−2i−2i−2i−2i2i2i-222-2-220000−2i2i2i−2i0000000000000000000000000000000000000000
χ4822-2-22-2-2222-2-2-2-2-22222-222-2-2−2i−2i2i2i2i2i−2i−2i-222-2-2200002i−2i−2i2i0000000000000000000000000000000000000000
χ4922-2-22-2-22-2-2222-2-2-2-222222-2-20000000022-22-2-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ5022-2-22-2-22-2-2222-2-2-2-222222-2-20000000022-22-2-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ5122-2-22-2-22-2-2222-2-2-2-2222-2-22200000000-2-22-2222-2-220000-222-2000000000000000000000000000000000000
χ5222-2-22-2-22-2-2222-2-2-2-2222-2-22200000000-2-22-222-222-200002-2-22000000000000000000000000000000000000
χ5322-2-22-2-22-2-22-2-22222-2-2222-2-200000000-2-2-22222-22-20000-22-22000000000000000000000000000000000000
χ5422-2-22-2-22-2-22-2-22222-2-2222-2-200000000-2-2-2222-22-2200002-22-2000000000000000000000000000000000000
χ5522-2-22-2-22-2-22-2-22222-2-22-2-22200000000222-2-2-20000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ5622-2-22-2-22-2-22-2-22222-2-22-2-22200000000222-2-2-2000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ572-2222-2-2-22-2-22-22-22-22-2200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−20000
χ582-2222-2-2-22-2-22-22-22-22-2200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−220000
χ592-2222-2-2-22-2-22-22-22-22-220000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−220000
χ602-2222-2-2-22-2-22-22-22-22-220000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−20000
χ612-2222-2-2-22-2-2-22-22-22-22200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−220000
χ622-2222-2-2-22-2-2-22-22-22-22200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−20000
χ632-2222-2-2-22-2-2-22-22-22-2220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−20000
χ642-2222-2-2-22-2-2-22-22-22-2220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−220000
χ652-2-2-2222-22-222-22-2-22-22-200002-2-222-2-220000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000
χ662-2-2-2222-22-222-22-2-22-22-200002-2-222-2-220000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000
χ672-2-2-2222-22-222-22-2-22-22-20000-222-2-222-20000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000
χ682-2-2-2222-22-222-22-2-22-22-20000-222-2-222-20000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000
χ692-2-2-2222-22-22-22-222-22-2-200002-2-22-222-20000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000
χ702-2-2-2222-22-22-22-222-22-2-200002-2-22-222-20000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000
χ712-2-2-2222-22-22-22-222-22-2-20000-222-22-2-220000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000
χ722-2-2-2222-22-22-22-222-22-2-20000-222-22-2-220000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000
χ734-4444-4-4-4-4444-4-444-4-44-4000000000000000000000000000000000000000000000000000000000000000000
χ744-4444-4-4-4-444-444-4-444-4-4000000000000000000000000000000000000000000000000000000000000000000
χ754-44-4-44-440000000000004-44-400000000000000000000000000000000002-22-22-22-200000000000000000000
χ764-44-4-44-440000000000004-44-40000000000000000000000000000000000-22-22-22-2200000000000000000000
χ774-44-4-44-44000000000000-44-4400000000000000000000000000000000002-22-2-22-2200000000000000000000
χ784-44-4-44-44000000000000-44-440000000000000000000000000000000000-22-222-22-200000000000000000000
χ794-4-44-4-4440000000000004-4-4400000000000000000000000000000000002-2-222-2-2200000000000000000000
χ804-4-44-4-4440000000000004-4-440000000000000000000000000000000000-222-2-222-200000000000000000000
χ814-4-44-4-444000000000000-444-400000000000000000000000000000000002-2-22-222-200000000000000000000
χ824-4-44-4-444000000000000-444-40000000000000000000000000000000000-222-22-2-2200000000000000000000
χ834-4-4-4444-4-44-44-4-44-444-44000000000000000000000000000000000000000000000000000000000000000000
χ844-4-4-4444-4-44-4-444-44-4-444000000000000000000000000000000000000000000000000000000000000000000
χ85888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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