Finite Group Databasebeta

← Group #492174

Character table — Group #492174

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222444444444444444448888888888888888888888816161616163232323232
order1222444488884444488881616161616161616444488888881616161616161616161616164448824448
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11-111
χ511111111111111-1-11-1-111111111111-11111-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-1-1-1
χ611111111111111-1-11-1-111111111111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1111
χ711111111111111-1-11-1-111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-1-111111111-11-1-1-11-1-111
χ811111111111111-1-11-1-111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1-1-1-1-1-1111111111-1111-111-1-1
χ9111111111111-1-1111-1-11111111111-1111-1-111-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111-1
χ10111111111111-1-1111-1-11111111111-11-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-11
χ11111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-1-11111-1-1-1-11111-11-1-1-1-111-11
χ12111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-11111-1-1-1-111111-11111-1-11-1
χ13111111111111-1-1-1-11111111111111-1-111-1-1-1-1111-1-1-1-1-1-1-1-1111111111-1-1-1-11
χ14111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1
χ15111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111-1-1-1-1-11-111-11-11-1
χ16111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-11-11-1-11-11-11
χ1722222222-2-2-2-22222222-2-2000000002200-2-2-2-22-2-20000000000000000000000
χ1822222222-2-2-2-222-2-22-2-2-2-2000000002-200-2-222-2220000000000000000000000
χ1922222222-2-2-2-2-2-2222-2-2-2-200000000-220022-2-2-2220000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2222-2-200000000-2-20022222-2-20000000000000000000000
χ2122222-2-2200002222-222002222−2−2−2−2-2-2000000-20022−2−222−2−222−2−20000000000
χ2222222-2-2200002222-22200−2−2−2−22222-2-2000000-200−2−222−2−222−2−2220000000000
χ2322222-2-22000022-2-2-2-2-2002222−2−2−2−2-2200000020022−2−2−2−222−2−2220000000000
χ2422222-2-22000022-2-2-2-2-200−2−2−2−22222-22000000200−2−22222−2−222−2−20000000000
χ2522222-2-220000-2-222-2-2-2002222−2−2−2−22-2000000200−2−22222−2−2−2−2220000000000
χ2622222-2-220000-2-222-2-2-200−2−2−2−222222-200000020022−2−2−2−22222−2−20000000000
χ2722222-2-220000-2-2-2-2-222002222−2−2−2−222000000-200−2−222−2−22222−2−20000000000
χ2822222-2-220000-2-2-2-2-22200−2−2−2−2222222000000-20022−2−222−2−2−2−2220000000000
χ292222-222-222220000-200-2-222-2-222-2-2002200000000000000000002-2-20000000
χ302222-222-222220000-200-2-222-2-222-2-200-2-20000000000000000000-2220000000
χ312222-222-222220000-200-2-2-2-222-2-22200220000000000000000000-2-220000000
χ322222-222-222220000-200-2-2-2-222-2-22200-2-2000000000000000000022-20000000
χ3322-2-2-200222−2−22i−2i2-202i−2i2−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000i2−i22−20i2−i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ3422-2-2-200222−2−22i−2i2-202i−2i2−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000i2−i22−20i2−i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ3522-2-2-200222−2−22i−2i-220−2i2i2−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000i2−i2−220−i2i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ3622-2-2-200222−2−22i−2i-220−2i2i2−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000i2−i2−220−i2i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ3722-2-2-200222−2−2−2i2i2-20−2i2i2−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000−i2i22−20−i2i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ3822-2-2-200222−2−2−2i2i2-20−2i2i2−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000−i2i22−20−i2i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ3922-2-2-200222−2−2−2i2i-2202i−2i2−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000−i2i2−220i2−i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ4022-2-2-200222−2−2−2i2i-2202i−2i2−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000−i2i2−220i2−i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ4122-2-2-2002−2−2222i−2i2-202i−2i−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000−i2i2−220−i2i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ4222-2-2-2002−2−2222i−2i2-202i−2i−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000−i2i2−220−i2i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ4322-2-2-2002−2−2222i−2i-220−2i2i−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000−i2i22−20i2−i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ4422-2-2-2002−2−2222i−2i-220−2i2i−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000−i2i22−20i2−i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ4522-2-2-2002−2−222−2i2i2-20−2i2i−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000i2−i2−220i2−i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ4622-2-2-2002−2−222−2i2i2-20−2i2i−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000i2−i2−220i2−i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ4722-2-2-2002−2−222−2i2i-2202i−2i−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000i2−i22−20−i2i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ4822-2-2-2002−2−222−2i2i-2202i−2i−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000i2−i22−20−i2i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ494444-444-4-4-4-4-40000-4004400000000000000000000000000000000000000000
χ504444-4-4-4-400000000400002222−22−22−22−222222000000000000000000000000000000000
χ514444-4-4-4-40000000040000−22−2222222222−22−22000000000000000000000000000000000
χ5244-4-4400-42222−22−220000000−22222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000000
χ5344-4-4400-42222−22−220000000−2222−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000000
χ5444-4-4400-4−22−222222000000022−222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000000
χ5544-4-4400-4−22−222222000000022−22−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000000
χ564-4-4404-404-44-400000000000000000004i−4i00000000000000000000000000000
χ574-4-4404-404-44-40000000000000000000−4i4i00000000000000000000000000000
χ584-4-4404-40-44-4400000000000000000000000000000000000000000002i2−2i200000
χ594-4-4404-40-44-440000000000000000000000000000000000000000000−2i22i200000
χ608-88-8000042−42−424200000000000000000000000000000000000000000000000000
χ618-88-80000−424242−4200000000000000000000000000000000000000000000000000
χ628-8-880-880000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.