Finite Group Databasebeta

← Group #192366

Character table — Group #192366

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
χ311111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ911111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ1111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ1211111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1311111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1411111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ1511111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1611111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ1711-111-1-1-11-1-11111-1-1-1-1111-1-11-11-1ii−i−iii−i−i1-11-11-1i−i1-11-1ii−i−iii−i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-11-11-1
χ1811-111-1-1-11-1-11111-1-1-1-1111-1-11-11-1ii−i−iii−i−i1-11-11-1i−i1-11-1ii−i−iii−i−ii−i−i−iii−i−iii−i−iii−i−iii-1-111-1-111-11-11
χ1911-111-1-1-11-1-11111-1-1-1-1111-1-11-11-1ii−i−iii−i−i1-1-11-11i−i-11-11−i−iii−i−iiii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-1111-11-1
χ2011-111-1-1-11-1-11111-1-1-1-1111-1-11-11-1ii−i−iii−i−i1-1-11-11i−i-11-11−i−iii−i−iiii−i−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1-11-11
χ2111-111-1-1-11-1-11111-1-1-1-1111-1-11-11-1−i−iii−i−iii1-11-11-1−ii1-11-1−i−iii−i−iii−iiii−i−iii−i−iii−i−iii−i−i-1-111-1-111-11-11
χ2211-111-1-1-11-1-11111-1-1-1-1111-1-11-11-1−i−iii−i−iii1-11-11-1−ii1-11-1−i−iii−i−iii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-11-11-1
χ2311-111-1-1-11-1-11111-1-1-1-1111-1-11-11-1−i−iii−i−iii1-1-11-11−ii-11-11ii−i−iii−i−i−iiii−i−iii−i−i−i−iii−i−iii11-1-111-1-1-11-11
χ2411-111-1-1-11-1-11111-1-1-1-1111-1-11-11-1−i−iii−i−iii1-1-11-11−ii-11-11ii−i−iii−i−i−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-1111-11-1
χ2511-111-1-1-11-1-1-1-1-1-111111-1-1111-1-11ii−i−i−i−iii1-11-1-11i−i1-1-11ii−i−i−i−iii−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-1111-1-11
χ2611-111-1-1-11-1-1-1-1-1-111111-1-1111-1-11ii−i−i−i−iii1-11-1-11i−i1-1-11ii−i−i−i−iii−ii−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-111-1
χ2711-111-1-1-11-1-1-1-1-1-111111-1-1111-1-11ii−i−i−i−iii1-1-111-1i−i-111-1−i−iiiii−i−i−iiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-11-1-11
χ2811-111-1-1-11-1-1-1-1-1-111111-1-1111-1-11ii−i−i−i−iii1-1-111-1i−i-111-1−i−iiiii−i−i−ii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111-111-1
χ2911-111-1-1-11-1-1-1-1-1-111111-1-1111-1-11−i−iiiii−i−i1-11-1-11−ii1-1-11−i−iiiii−i−ii−iii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-111-1
χ3011-111-1-1-11-1-1-1-1-1-111111-1-1111-1-11−i−iiiii−i−i1-11-1-11−ii1-1-11−i−iiiii−i−ii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-1111-1-11
χ3111-111-1-1-11-1-1-1-1-1-111111-1-1111-1-11−i−iiiii−i−i1-1-111-1−ii-111-1ii−i−i−i−iiii−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111-111-1
χ3211-111-1-1-11-1-1-1-1-1-111111-1-1111-1-11−i−iiiii−i−i1-1-111-1−ii-111-1ii−i−i−i−iiii−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-11-1-11
χ3322222222222222222222-2-2-2-2-2-2-2-222222222-2-20000-2-2000000000000-2-20000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000022000000000000220000000000000000000000000000
χ3522222222222-2-2-2-2-2-2-2-222222-2-2222222-2-2-2-2-2-20000-2-2000000000000220000000000000000000000000000
χ3622222222222-2-2-2-2-2-2-2-222222-2-222-2-2-2-22222-2-2000022000000000000-2-20000000000000000000000000000
χ3722222222-2-2-222-2-222-2-2-222222-2-2-200000000-22222200-2-2-2-200000000000000000000000000000000000000
χ3822222222-2-2-222-2-222-2-2-222222-2-2-200000000-22-2-2-2-200222200000000000000000000000000000000000000
χ3922222222-2-2-222-2-222-2-2-2-2-2-2-2-2222000000002-200000000002-22-22-22-2000000000000000000000000000000
χ4022222222-2-2-222-2-222-2-2-2-2-2-2-2-2222000000002-20000000000-22-22-22-22000000000000000000000000000000
χ4122222222-2-2-2-2-222-2-222-22222-22-2-2000000002-200000000002-22-2-22-22000000000000000000000000000000
χ4222222222-2-2-2-2-222-2-222-22222-22-2-2000000002-20000000000-22-222-22-2000000000000000000000000000000
χ4322222222-2-2-2-2-222-2-222-2-2-2-2-22-22200000000-2222-2-200-2-22200000000000000000000000000000000000000
χ4422222222-2-2-2-2-222-2-222-2-2-2-2-22-22200000000-22-2-2220022-2-200000000000000000000000000000000000000
χ4522-222-2-2-22-2-22222-2-2-2-22-2-222-22-222i2i−2i−2i2i2i−2i−2i-220000−2i2i000000000000−2i2i0000000000000000000000000000
χ4622-222-2-2-22-2-22222-2-2-2-22-2-222-22-22−2i−2i2i2i−2i−2i2i2i-2200002i−2i0000000000002i−2i0000000000000000000000000000
χ4722-222-2-2-22-2-2-2-2-2-22222222-2-2-222-22i2i−2i−2i−2i−2i2i2i-220000−2i2i0000000000002i−2i0000000000000000000000000000
χ4822-222-2-2-22-2-2-2-2-2-22222222-2-2-222-2−2i−2i2i2i2i2i−2i−2i-2200002i−2i000000000000−2i2i0000000000000000000000000000
χ4922-222-2-2-2-22222-2-2-2-222-222-2-222-2200000000-2-22-22-200-22-2200000000000000000000000000000000000000
χ5022-222-2-2-2-22222-2-2-2-222-222-2-222-2200000000-2-2-22-22002-22-200000000000000000000000000000000000000
χ5122-222-2-2-2-22222-2-2-2-222-2-2-222-2-22-2000000002200000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ5222-222-2-2-2-22222-2-2-2-222-2-2-222-2-22-200000000220000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ5322-222-2-2-2-222-2-22222-2-2-222-2-2-2-2-22000000002200000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ5422-222-2-2-2-222-2-22222-2-2-222-2-2-2-2-2200000000220000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ5522-222-2-2-2-222-2-22222-2-2-2-2-222222-200000000-2-22-2-2200-222-200000000000000000000000000000000000000
χ5622-222-2-2-2-222-2-22222-2-2-2-2-222222-200000000-2-2-222-2002-2-2200000000000000000000000000000000000000
χ572-222-2-2-2222-22-22-22-22-2-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i20000
χ582-222-2-2-2222-22-22-22-22-2-2000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i20000
χ592-222-2-2-2222-22-22-22-22-2-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000
χ602-222-2-2-2222-22-22-22-22-2-200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i20000
χ612-222-2-2-2222-2-22-22-22-22-2000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000
χ622-222-2-2-2222-2-22-22-22-22-2000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000−22−222−22−2−i2i2−i2i2i2−i2i2−i20000
χ632-222-2-2-2222-2-22-22-22-22-200000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000
χ642-222-2-2-2222-2-22-22-22-22-200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000−22−222−22−2i2−i2i2−i2−i2i2−i2i20000
χ652-2-22-222-22-222-22-2-22-22-2000000002-2-222-2-22000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000
χ662-2-22-222-22-222-22-2-22-22-2000000002-2-222-2-22000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000
χ672-2-22-222-22-222-22-2-22-22-200000000-222-2-222-2000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000
χ682-2-22-222-22-222-22-2-22-22-200000000-222-2-222-2000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000
χ692-2-22-222-22-22-22-222-22-2-2000000002-2-22-222-2000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000
χ702-2-22-222-22-22-22-222-22-2-2000000002-2-22-222-2000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000
χ712-2-22-222-22-22-22-222-22-2-200000000-222-22-2-22000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000
χ722-2-22-222-22-22-22-222-22-2-200000000-222-22-2-22000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000
χ734-444-4-4-44-4-444-4-444-4-444000000000000000000000000000000000000000000000000000000000000000000
χ744-444-4-4-44-4-44-444-4-444-44000000000000000000000000000000000000000000000000000000000000000000
χ754-44-444-4-40000000000004-44-400000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ764-44-444-4-40000000000004-44-40000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ774-44-444-4-4000000000000-44-4400000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ784-44-444-4-4000000000000-44-440000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ794-4-44-444-4-44-44-4-44-444-44000000000000000000000000000000000000000000000000000000000000000000
χ804-4-44-444-4-44-4-444-44-4-444000000000000000000000000000000000000000000000000000000000000000000
χ814-4-4-44-4440000000000004-4-4400000000000000000000000000000000002-2-222-2-2200000000000000000000
χ824-4-4-44-4440000000000004-4-440000000000000000000000000000000000-222-2-222-200000000000000000000
χ834-4-4-44-444000000000000-444-400000000000000000000000000000000002-2-22-222-200000000000000000000
χ844-4-4-44-444000000000000-444-40000000000000000000000000000000000-222-22-2-2200000000000000000000
χ85888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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