Finite Group Databasebeta

← Group #511763

Character table — Group #511763

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112222222224444444444444448888888888888888888888888816161616161632323232
order122224444882222224444448882222222222444444888888161616161616161616162444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1
χ61111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1111111-1-1-1-1-1-111
χ81111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ911111111111-1-111-1-1-1-111-1-11111111-1-111-1-1-1-111-1-1-1-111-1-11111-1-111-1-11-11-1
χ1011111111111-1-111-1-1-1-111-1-11111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-111-11-11
χ1111111111111-1-111-1-1-1-111-1-1111-1-1-1-111-1-11111-1-111-1-111-1-11111-1-111-1-1-11-11
χ1211111111111-1-111-1-1-1-111-1-1111-1-1-1-111-1-11111-1-111-1-111-1-1-1-1-1-111-1-1111-11-1
χ1311111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-111-1
χ1511111111111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-111-111-1
χ1611111111111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11-1-11
χ17222222222-2-2222222222222-2-2-20000000000000000-2-2-2-2-2-200000000000000
χ18222222222-2-222-2-2-2-222-2-2-2-2-2-2-20000000000000000-2-2222200000000000000
χ19222222222-2-2-2-222-2-2-2-222-2-2-2-2-2000000000000000022-2-22200000000000000
χ20222222222-2-2-2-2-2-222-2-2-2-222-2-2-200000000000000002222-2-200000000000000
χ2122222-2-2-2-2002-22-22-22-22-22-2000000000000000000000000022−2−22−22−22−20000
χ2222222-2-2-2-2002-22-22-22-22-22-20000000000000000000000000−2−222−22−22−220000
χ2322222-2-2-2-2002-2-22-222-2-22-22000000000000000000000000022−2−22−2−22−220000
χ2422222-2-2-2-2002-2-22-222-2-22-220000000000000000000000000−2−222−222−22−20000
χ2522222-2-2-2-200-222-2-22-222-2-22000000000000000000000000022−2−2−222−2−220000
χ2622222-2-2-2-200-222-2-22-222-2-220000000000000000000000000−2−2222−2−222−20000
χ2722222-2-2-2-200-22-222-2-22-222-2000000000000000000000000022−2−2−22−222−20000
χ2822222-2-2-2-200-22-222-2-22-222-20000000000000000000000000−2−2222−22−2−220000
χ29222-2-22-2-222200002-20000-222-2-222-2-20000220000-2-200002-200000000000000
χ30222-2-22-2-222200002-20000-222-2-2-2-2220000-2-200002200002-200000000000000
χ31222-2-22-2-22220000-2200002-22-2-222-2-20000-2-20000220000-2200000000000000
χ32222-2-22-2-22220000-2200002-22-2-2-2-2220000220000-2-20000-2200000000000000
χ33222-2-22-2-22-2-200002-20000-22-22200002-22-2002-22-2000000-2200000000000000
χ34222-2-22-2-22-2-200002-20000-22-2220000-22-2200-22-22000000-2200000000000000
χ35222-2-22-2-22-2-20000-2200002-2-22200002-2-22002-2-220000002-200000000000000
χ36222-2-22-2-22-2-20000-2200002-2-2220000-222-200-222-20000002-200000000000000
χ3722-22-2-22-2222002-20000-2200-22-22-22-200220000-2-200002-20000000000000000
χ3822-22-2-22-2222002-20000-2200-22-2-22-2200-2-200002200002-20000000000000000
χ3922-22-2-22-222200-2200002-200-22-22-22-200-2-20000220000-220000000000000000
χ4022-22-2-22-222200-2200002-200-22-2-22-2200220000-2-20000-220000000000000000
χ4122-22-2-22-22-2-2002-20000-22002-2200002-2002-2-22002-200-220000000000000000
χ4222-22-2-22-22-2-2002-20000-22002-220000-2200-222-200-2200-220000000000000000
χ4322-22-2-22-22-2-200-2200002-2002-2200002-200-22-2200-22002-20000000000000000
χ4422-22-2-22-22-2-200-2200002-2002-220000-22002-22-2002-2002-20000000000000000
χ4522-2-22-2-222222-20000-220000-2-222-2-22220000-2-200002-2000000000000000000
χ4622-2-22-2-222222-20000-220000-2-22-222-2-2-200002200002-2000000000000000000
χ4722-2-22-2-22222-2200002-20000-2-222-2-22-2-20000220000-22000000000000000000
χ4822-2-22-2-22222-2200002-20000-2-22-222-2220000-2-20000-22000000000000000000
χ4922-2-22-2-222-2-22-20000-22000022-20000002-22-200-22-22-22000000000000000000
χ5022-2-22-2-222-2-22-20000-22000022-2000000-22-22002-22-2-22000000000000000000
χ5122-2-22-2-222-2-2-2200002-2000022-20000002-2-2200-222-22-2000000000000000000
χ5222-2-22-2-222-2-2-2200002-2000022-2000000-222-2002-2-222-2000000000000000000
χ53444-4-4-444-4000000440000-4-4000000000000000000000000000000000000000
χ54444-4-4-444-4000000-4-4000044000000000000000000000000000000000000000
χ5544-44-44-44-40000440000-4-400000000000000000000000000000000000000000
χ5644-44-44-44-40000-4-400004400000000000000000000000000000000000000000
χ5744-4-4444-4-400440000-4-40000000000000000000000000000000000000000000
χ5844-4-4444-4-400-4-40000440000000000000000000000000000000000000000000
χ598-8000000042−4200000000000000000000000000000000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000
χ608-8000000042−420000000000000000000000000000000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000
χ618-80000000−424200000000000000000000000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000000000
χ628-80000000−42420000000000000000000000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1).