Finite Group Databasebeta

← Group #251513

Character table — Group #251513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222222244444444444444448888888888888888224444444444244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-111111111-1-1-1-1
χ911111111-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-11-111-1-11111-1-1-1-111
χ1111111111-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-1111-1-111-1-11111-1-1
χ1311111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111
χ1411111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-1-1-1-1-11111-1-111-1-1
χ1611111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-11-111111-1-111-1-1-1-111
χ1722222222222222-2-222-2-2-2-2-222-2-2-20000000000000000000000002222-200-200000000000000
χ1822222222222222-2-222-2-2-2-2-222-2-2-2000000000000000000000000-2-2-2-2200200000000000000
χ19222222222222-2-222-2-222-2-2-2-2-222-200000000000000002222000000000-2-2000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-222-20000000000000000-2-2-2-200000000022000000000000000
χ21222222222222-2-2-2-2-2-2-2-2222-2-2-2-220000000000000000000022-2-2000000002-2000000000000
χ22222222222222-2-2-2-2-2-2-2-2222-2-2-2-2200000000000000000000-2-22200000000-22000000000000
χ2322222222-2-2-2-222-2-222-2-2-222-2-222-200000000000000000000000022-2-2200-200000000000000
χ2422222222-2-2-2-222-2-222-2-2-222-2-222-2000000000000000000000000-2-222-200200000000000000
χ2522222222-2-2-2-2-2-222-2-222-22222-2-2-2000000000000000022-2-20000000002-2000000000000000
χ2622222222-2-2-2-2-2-222-2-222-22222-2-2-20000000000000000-2-222000000000-22000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22-2-2222220000000000000000000022-2-200000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22-2-22222200000000000000000000-2-222000000002-2000000000000
χ292-22-222-2-222-2-2-2-20022000002-20002222−2−2−2−22222−2−2−2−2000000002i−2i2i−2i00000000000000i2−i2i2−i2
χ302-22-222-2-222-2-2-2-20022000002-20002222−2−2−2−22222−2−2−2−200000000−2i2i−2i2i00000000000000−i2i2−i2i2
χ312-22-222-2-222-2-2-2-20022000002-2000−2−2−2−22222−2−2−2−22222000000002i−2i2i−2i00000000000000−i2i2−i2i2
χ322-22-222-2-222-2-2-2-20022000002-2000−2−2−2−22222−2−2−2−2222200000000−2i2i−2i2i00000000000000i2−i2i2−i2
χ332-22-222-2-2-2-222-2-2002200000-220002222−2−2−2−2−2−2−2−22222000000002i−2i−2i2i00000000000000i2−i2−i2i2
χ342-22-222-2-2-2-222-2-2002200000-220002222−2−2−2−2−2−2−2−2222200000000−2i2i2i−2i00000000000000−i2i2i2−i2
χ352-22-222-2-2-2-222-2-2002200000-22000−2−2−2−222222222−2−2−2−2000000002i−2i−2i2i00000000000000−i2i2i2−i2
χ362-22-222-2-2-2-222-2-2002200000-22000−2−2−2−222222222−2−2−2−200000000−2i2i2i−2i00000000000000i2−i2−i2i2
χ372-2-222-2-2200002-22-22-22-22000000-2000000002i2i−2i−2i2i2i−2i−2i00002i−2i2i−2i0000000000002-200000000
χ382-2-222-2-2200002-22-22-22-22000000-2000000002i2i−2i−2i2i2i−2i−2i0000−2i2i−2i2i000000000000-2200000000
χ392-2-222-2-2200002-22-22-22-22000000-200000000−2i−2i2i2i−2i−2i2i2i00002i−2i2i−2i000000000000-2200000000
χ402-2-222-2-2200002-22-22-22-22000000-200000000−2i−2i2i2i−2i−2i2i2i0000−2i2i−2i2i0000000000002-200000000
χ412-2-222-2-220000-22-22-22-222000000-22i2i−2i−2i2i2i−2i−2i0000000000002i−2i−2i2i00000000002-20000000000
χ422-2-222-2-220000-22-22-22-222000000-22i2i−2i−2i2i2i−2i−2i000000000000−2i2i2i−2i0000000000-220000000000
χ432-2-222-2-220000-22-22-22-222000000-2−2i−2i2i2i−2i−2i2i2i0000000000002i−2i−2i2i0000000000-220000000000
χ442-2-222-2-220000-22-22-22-222000000-2−2i−2i2i2i−2i−2i2i2i000000000000−2i2i2i−2i00000000002-20000000000
χ452-2-2-2-22222-22-200-2-20022000002-202−22−22−22−22−22−22−22−22-22-20000000000000000002−22−20000
χ462-2-2-2-22222-22-200-2-20022000002-202−22−22−22−22−22−22−22−2-22-22000000000000000000−22−220000
χ472-2-2-2-22222-22-200-2-20022000002-20−22−22−22−22−22−22−22−222-22-2000000000000000000−22−220000
χ482-2-2-2-22222-22-200-2-20022000002-20−22−22−22−22−22−22−22−22-22-220000000000000000002−22−20000
χ492-2-2-2-2222-22-2200-2-2002200000-2202−22−22−22−2−22−22−22−222-2-220000000000000000002−2−220000
χ502-2-2-2-2222-22-2200-2-2002200000-2202−22−22−22−2−22−22−22−22-222-2000000000000000000−222−20000
χ512-2-2-2-2222-22-2200-2-2002200000-220−22−22−22−222−22−22−22−22-2-22000000000000000000−222−20000
χ522-2-2-2-2222-22-2200-2-2002200000-220−22−22−22−222−22−22−22−2-222-20000000000000000002−2−220000
χ53444-4-4-4-440000004-400-44000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ54444-4-4-4-440000004-400-4400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ55444-4-4-4-44000000-44004-400000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ56444-4-4-4-44000000-44004-40000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ5744-44-44-4-44-4-4400000000000000002-22-2-22-222-22-2-22-22000000000000000000000000000000
χ5844-44-44-4-44-4-440000000000000000-22-222-22-2-22-222-22-2000000000000000000000000000000
χ5944-44-44-4-4-444-400000000000000002-22-2-22-22-22-222-22-2000000000000000000000000000000
χ6044-44-44-4-4-444-40000000000000000-22-222-22-22-22-2-22-22000000000000000000000000000000
χ6144-4-44-44-400004-400-4400000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ6244-4-44-44-400004-400-440000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ6344-4-44-44-40000-44004-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000
χ6444-4-44-44-40000-44004-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000
χ654-444-4-44-400000000000004-4000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ664-444-4-44-400000000000004-400000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ674-444-4-44-40000000000000-44000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ684-444-4-44-40000000000000-4400000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ694-44-444-4-444-4-44400-4-400000-440000000000000000000000000000000000000000000000000
χ704-44-444-4-4-4-4444400-4-4000004-40000000000000000000000000000000000000000000000000
χ714-4-444-4-4400004-4-444-4-44-400000040000000000000000000000000000000000000000000000
χ724-4-444-4-440000-444-4-444-4-400000040000000000000000000000000000000000000000000000
χ734-4-4-4-44444-44-4004400-4-400000-4400000000000000000000000000000000000000000000000
χ744-4-4-4-4444-44-44004400-4-4000004-400000000000000000000000000000000000000000000000

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