Finite Group Databasebeta

← Group #372621

Character table — Group #372621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222444444444444444444444444888888888888888888888888888888888888161616161616
order12222222222244444444444444444444444488888888222244444444444444444444888888888888448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1
χ1711-1-1-1-11111-1-1111-1-1-11-1iiii−i−i−i−i11-1-111-1-1ii−i−i11-1-111-1-1ii−i−iii−i−i1-11-11-11-1ii−i−iii−i−iii−i−ii−i1-11-11-1i−i
χ1811-1-1-1-11111-1-1111-1-1-11-1iiii−i−i−i−i11-1-111-1-1ii−i−i-1-11111-1-1ii−i−i−i−iii1-1-111-1-11−i−iiiii−i−i−i−iiii−i-11-11-11−ii
χ1911-1-1-1-11111-1-1111-1-1-11-1iiii−i−i−i−i11-1-111-1-1−i−iii11-1-1-1-111ii−i−iii−i−i-111-1-111-1−i−iii−i−iiiii−i−i−ii1-1-11-11−ii
χ2011-1-1-1-11111-1-1111-1-1-11-1iiii−i−i−i−i11-1-111-1-1−i−iii-1-111-1-111ii−i−i−i−iii-11-11-11-11ii−i−i−i−iii−i−iii−ii-111-11-1i−i
χ2111-1-1-1-11111-1-1111-1-1-11-1iiii−i−i−i−i-1-111-1-111ii−i−i11-1-1-1-111−i−iii−i−iii1-1-111-1-11ii−i−i−i−iiiii−i−ii−i1-1-111-1−ii
χ2211-1-1-1-11111-1-1111-1-1-11-1iiii−i−i−i−i-1-111-1-111ii−i−i-1-111-1-111−i−iiiii−i−i1-11-11-11-1−i−iii−i−iii−i−iiii−i-111-1-11i−i
χ2311-1-1-1-11111-1-1111-1-1-11-1iiii−i−i−i−i-1-111-1-111−i−iii11-1-111-1-1−i−iii−i−iii-11-11-11-11−i−iiiii−i−iii−i−i−ii1-11-1-11i−i
χ2411-1-1-1-11111-1-1111-1-1-11-1iiii−i−i−i−i-1-111-1-111−i−iii-1-11111-1-1−i−iiiii−i−i-111-1-111-1ii−i−iii−i−i−i−iii−ii-11-111-1−ii
χ2511-1-1-1-11111-1-1111-1-1-11-1−i−i−i−iiiii11-1-111-1-1ii−i−i11-1-1-1-111−i−iii−i−iii-111-1-111-1ii−i−iii−i−i−i−iiii−i1-1-11-11i−i
χ2611-1-1-1-11111-1-1111-1-1-11-1−i−i−i−iiiii11-1-111-1-1ii−i−i-1-111-1-111−i−iiiii−i−i-11-11-11-11−i−iiiii−i−iii−i−ii−i-111-11-1−ii
χ2711-1-1-1-11111-1-1111-1-1-11-1−i−i−i−iiiii11-1-111-1-1−i−iii11-1-111-1-1−i−iii−i−iii1-11-11-11-1−i−iii−i−iii−i−iii−ii1-11-11-1−ii
χ2811-1-1-1-11111-1-1111-1-1-11-1−i−i−i−iiiii11-1-111-1-1−i−iii-1-11111-1-1−i−iiiii−i−i1-1-111-1-11ii−i−i−i−iiiii−i−i−ii-11-11-11i−i
χ2911-1-1-1-11111-1-1111-1-1-11-1−i−i−i−iiiii-1-111-1-111ii−i−i11-1-111-1-1ii−i−iii−i−i-11-11-11-11ii−i−i−i−iii−i−iiii−i1-11-1-11−ii
χ3011-1-1-1-11111-1-1111-1-1-11-1−i−i−i−iiiii-1-111-1-111ii−i−i-1-11111-1-1ii−i−i−i−iii-111-1-111-1−i−iii−i−iiiii−i−ii−i-11-111-1i−i
χ3111-1-1-1-11111-1-1111-1-1-11-1−i−i−i−iiiii-1-111-1-111−i−iii11-1-1-1-111ii−i−iii−i−i1-1-111-1-11−i−iiiii−i−i−i−iii−ii1-1-111-1i−i
χ3211-1-1-1-11111-1-1111-1-1-11-1−i−i−i−iiiii-1-111-1-111−i−iii-1-111-1-111ii−i−i−i−iii1-11-11-11-1ii−i−iii−i−iii−i−i−ii-111-1-11−ii
χ3322222222-2-2-2-222-2-22-2-2222-2-222-2-200000000222200000000000000002200-2-200000000000000-2-200000000
χ3422222222-2-2-2-222-2-22-2-2222-2-222-2-200000000-2-2-2-20000000000000000-2-20022000000000000002200000000
χ3522222222-2-2-2-222-2-22-2-22-2-222-2-2220000000022220000000000000000-2-2002200000000000000-2-200000000
χ3622222222-2-2-2-222-2-22-2-22-2-222-2-22200000000-2-2-2-200000000000000002200-2-2000000000000002200000000
χ3722222222-2-2-2-2-2-222-222-2000000002222-2-2-2-20000222200000000000000-2-2002200000000000000-2-2000000
χ3822222222-2-2-2-2-2-222-222-2000000002222-2-2-2-20000-2-2-2-2000000000000002200-2-20000000000000022000000
χ3922222222-2-2-2-2-2-222-222-200000000-2-2-2-2222200002222000000000000002200-2-200000000000000-2-2000000
χ4022222222-2-2-2-2-2-222-222-200000000-2-2-2-222220000-2-2-2-200000000000000-2-200220000000000000022000000
χ412222-2-2-2-22-22-22-2222-2-2-22-22-22-22-200000000000000002-22-2000000000000000000002-22-200000000000000
χ422222-2-2-2-22-22-22-2222-2-2-22-22-22-22-20000000000000000-22-2200000000000000000000-22-2200000000000000
χ432222-2-2-2-22-22-22-2222-2-2-2-22-22-22-2200000000000000002-22-200000000000000000000-22-2200000000000000
χ442222-2-2-2-22-22-22-2222-2-2-2-22-22-22-220000000000000000-22-22000000000000000000002-22-200000000000000
χ452222-2-2-2-22-22-2-22-2-2-2222000000002i−2i2i−2i2i−2i2i−2i00000000000000002i−2i2i−2i00000000000000002-22-20000000000
χ462222-2-2-2-22-22-2-22-2-2-2222000000002i−2i2i−2i2i−2i2i−2i0000000000000000−2i2i−2i2i0000000000000000-22-220000000000
χ472222-2-2-2-22-22-2-22-2-2-222200000000−2i2i−2i2i−2i2i−2i2i00000000000000002i−2i2i−2i0000000000000000-22-220000000000
χ482222-2-2-2-22-22-2-22-2-2-222200000000−2i2i−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i00000000000000002-22-20000000000
χ492222-2-2-2-2-22-222-2-2-2222-22-2-222-2-222i−2i2i−2i−2i2i−2i2i0000000000002i−2i2i−2i0000000000000000000000000000000000
χ502222-2-2-2-2-22-222-2-2-2222-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i000000000000−2i2i−2i2i0000000000000000000000000000000000
χ512222-2-2-2-2-22-222-2-2-2222-2-222-2-222-22i−2i2i−2i−2i2i−2i2i000000000000−2i2i−2i2i0000000000000000000000000000000000
χ522222-2-2-2-2-22-222-2-2-2222-2-222-2-222-2−2i2i−2i2i2i−2i2i−2i0000000000002i−2i2i−2i0000000000000000000000000000000000
χ5322-2-222-2-22-2-222-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000002-2-22000000000000000000002i−2i−2i2i00000000000000
χ5422-2-222-2-22-2-222-22-2-22-222i−2i2i−2i−2i2i−2i2i0000000000000000-222-200000000000000000000−2i2i2i−2i00000000000000
χ5522-2-222-2-22-2-222-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000002-2-2200000000000000000000−2i2i2i−2i00000000000000
χ5622-2-222-2-22-2-222-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000-222-2000000000000000000002i−2i−2i2i00000000000000
χ5722-2-222-2-22-2-22-22-222-22-2000000002i−2i−2i2i2i−2i−2i2i00000000000000002-2-220000000000000000−2i2i2i−2i0000000000
χ5822-2-222-2-22-2-22-22-222-22-2000000002i−2i−2i2i2i−2i−2i2i0000000000000000-222-200000000000000002i−2i−2i2i0000000000
χ5922-2-222-2-22-2-22-22-222-22-200000000−2i2i2i−2i−2i2i2i−2i00000000000000002-2-2200000000000000002i−2i−2i2i0000000000
χ6022-2-222-2-22-2-22-22-222-22-200000000−2i2i2i−2i−2i2i2i−2i0000000000000000-222-20000000000000000−2i2i2i−2i0000000000
χ6122-2-222-2-2-222-22-2-22-2-2222i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000-222-20000000000000000000000000000000000
χ6222-2-222-2-2-222-22-2-22-2-2222i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000002-2-220000000000000000000000000000000000
χ6322-2-222-2-2-222-22-2-22-2-222−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000002-2-220000000000000000000000000000000000
χ6422-2-222-2-2-222-22-2-22-2-222−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000-222-20000000000000000000000000000000000
χ6522-2-2-2-222-2-22222-22-22-2-22i2i−2i−2i−2i−2i2i2i000000002i2i−2i−2i00000000000000002-200-2200000000000000−2i2i00000000
χ6622-2-2-2-222-2-22222-22-22-2-22i2i−2i−2i−2i−2i2i2i00000000−2i−2i2i2i0000000000000000-22002-2000000000000002i−2i00000000
χ6722-2-2-2-222-2-22222-22-22-2-2−2i−2i2i2i2i2i−2i−2i000000002i2i−2i−2i0000000000000000-22002-200000000000000−2i2i00000000
χ6822-2-2-2-222-2-22222-22-22-2-2−2i−2i2i2i2i2i−2i−2i00000000−2i−2i2i2i00000000000000002-200-22000000000000002i−2i00000000
χ6922-2-2-2-222-2-222-2-22-22-2220000000022-2-2-2-222000022-2-200000000000000-22002-200000000000000-22000000
χ7022-2-2-2-222-2-222-2-22-22-2220000000022-2-2-2-2220000-2-222000000000000002-200-22000000000000002-2000000
χ7122-2-2-2-222-2-222-2-22-22-22200000000-2-22222-2-2000022-2-2000000000000002-200-2200000000000000-22000000
χ7222-2-2-2-222-2-222-2-22-22-22200000000-2-22222-2-20000-2-22200000000000000-22002-2000000000000002-2000000
χ73444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4-44-44-4444-4-4-44000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-4-444-4-444-444-4-4000000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-44444-4-4-4-4-4444-44000000000000000000000000000000000000000000000000000000000000000000
χ774-44-44-44-4000000000000000000000000000022−2222−222i2−2i22i2−2i2000000000000000000002i−2i2i−2i000000000000000000
χ784-44-44-44-4000000000000000000000000000022−2222−22−2i22i2−2i22i200000000000000000000−2i2i−2i2i000000000000000000
χ794-44-44-44-40000000000000000000000000000−2222−22222i2−2i22i2−2i200000000000000000000−2i2i−2i2i000000000000000000
χ804-44-44-44-40000000000000000000000000000−2222−2222−2i22i2−2i22i2000000000000000000002i−2i2i−2i000000000000000000
χ814-4-44-444-400000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-2000000000000000000
χ824-4-44-444-400000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-22000000000000000000
χ834-4-44-444-40000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-22000000000000000000
χ844-4-44-444-40000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-2000000000000000000
χ858-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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