Finite Group Databasebeta

← Group #290113

Character table — Group #290113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888844444444488888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111111-1-1-1-111111-1-111-1-1111111111111-1-1-1-111-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-111-1-111-1-11-1
χ1011111111111-1-1-1-111111-1-111-1-1111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-11
χ1111111111111-1-1-1-111111-1-111-1-111111111-1-1-1-11111-1-111-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-11
χ1211111111111-1-1-1-111111-1-111-1-111111111-1-1-1-11111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11-1
χ1311111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-11
χ1411111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1111111-1-1111111-1-1-1-1111-1
χ1511111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-111111111-1-111-1-1-1-1-1-111-1-1111-1
χ1611111111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-11111-1-111111111-1-111-1-1-11
χ172222222222-222222-2-2-22-2-2-2-22200000000000000002222-2-2-2-2-200000000000000000000000000
χ182222222222-222222-2-2-22-2-2-2-2220000000000000000-2-2-2-2-2222200000000000000000000000000
χ192222222222-2-2-2-2-22-2-2-2222-2-2-2-2000000000000000022-2-22-2-22200000000000000000000000000
χ202222222222-2-2-2-2-22-2-2-2222-2-2-2-20000000000000000-2-222222-2-200000000000000000000000000
χ2122222222-2-222222-2222-222-2-2-2-200000000222222220000-2000000000000-2-2-2-200000000000000
χ2222222222-2-222222-2222-222-2-2-2-200000000-2-2-2-2-2-2-2-20000-2000000000000222200000000000000
χ2322222222-2-22-2-2-2-2-2222-2-2-2-2-222000000002222-2-2-2-200002000000000000-2-22200000000000000
χ2422222222-2-22-2-2-2-2-2222-2-2-2-2-22200000000-2-2-2-222220000200000000000022-2-200000000000000
χ2522222222-2-2-22222-2-2-2-2-2-2-222-2-22i2i2i2i−2i−2i−2i−2i0000000000002000000002i2i−2i−2i000000000000000000
χ2622222222-2-2-22222-2-2-2-2-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i000000000000200000000−2i−2i2i2i000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222222i2i2i2i−2i−2i−2i−2i000000000000-200000000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222−2i−2i−2i−2i2i2i2i2i000000000000-2000000002i2i−2i−2i000000000000000000
χ292222-2-2-2-200222-2-202-2-202-200000000000022-2-222-2-200000000022−2−20000000022−2−200002−22−200
χ302222-2-2-2-200222-2-202-2-202-200000000000022-2-222-2-2000000000−2−22200000000−2−2220000−22−2200
χ312222-2-2-2-200222-2-202-2-202-2000000000000-2-222-2-22200000000022−2−20000000022−2−20000−22−2200
χ322222-2-2-2-200222-2-202-2-202-2000000000000-2-222-2-222000000000−2−22200000000−2−22200002−22−200
χ332222-2-2-2-2002-2-22202-2-20-2200000000000022-2-2-2-22200000000022−2−200000000−2−22200002−2−2200
χ342222-2-2-2-2002-2-22202-2-20-2200000000000022-2-2-2-222000000000−2−2220000000022−2−20000−222−200
χ352222-2-2-2-2002-2-22202-2-20-22000000000000-2-22222-2-200000000022−2−200000000−2−2220000−222−200
χ362222-2-2-2-2002-2-22202-2-20-22000000000000-2-22222-2-2000000000−2−2220000000022−2−200002−2−2200
χ3722-2-222-2-22202-22-2-2000-200002-222−2−222−2−22−22−22−22−22-22-20000000002−22−22−22−200000000000000
χ3822-2-222-2-22202-22-2-2000-200002-222−2−222−2−2−22−22−22−22-22-220000000002−22−2−22−2200000000000000
χ3922-2-222-2-22202-22-2-2000-200002-2−2−222−2−2222−22−22−22−2-22-22000000000−22−222−22−200000000000000
χ4022-2-222-2-22202-22-2-2000-200002-2−2−222−2−222−22−22−22−222-22-2000000000−22−22−22−2200000000000000
χ4122-2-222-2-2220-22-22-2000-20000-2222−2−222−2−22−22−2−22−222-2-22000000000−22−222−2−2200000000000000
χ4222-2-222-2-2220-22-22-2000-20000-2222−2−222−2−2−22−222−22−2-222-2000000000−22−22−222−200000000000000
χ4322-2-222-2-2220-22-22-2000-20000-22−2−222−2−2222−22−2−22−22-222-20000000002−22−22−2−2200000000000000
χ4422-2-222-2-2220-22-22-2000-20000-22−2−222−2−222−22−222−22−22-2-220000000002−22−2−222−200000000000000
χ4522-2-222-2-2-2-202-22-2200020000-22i2i2−i2−i2−i2−i2i2i22−22−22−22−2000002i−2i2i−2i0000i2−i2−i2i2−22−2200000000000000
χ4622-2-222-2-2-2-202-22-2200020000-22i2i2−i2−i2−i2−i2i2i2−22−22−22−2200000−2i2i−2i2i0000i2−i2−i2i22−22−200000000000000
χ4722-2-222-2-2-2-202-22-2200020000-22−i2−i2i2i2i2i2−i2−i22−22−22−22−200000−2i2i−2i2i0000−i2i2i2−i2−22−2200000000000000
χ4822-2-222-2-2-2-202-22-2200020000-22−i2−i2i2i2i2i2−i2−i2−22−22−22−22000002i−2i2i−2i0000−i2i2i2−i22−22−200000000000000
χ4922-2-222-2-2-2-20-22-222000200002-2i2i2−i2−i2−i2−i2i2i22−22−2−22−22000002i−2i−2i2i0000−i2i2i2−i2−222−200000000000000
χ5022-2-222-2-2-2-20-22-222000200002-2i2i2−i2−i2−i2−i2i2i2−22−222−22−200000−2i2i2i−2i0000−i2i2i2−i22−2−2200000000000000
χ5122-2-222-2-2-2-20-22-222000200002-2−i2−i2i2i2i2i2−i2−i22−22−2−22−2200000−2i2i2i−2i0000i2−i2−i2i2−222−200000000000000
χ5222-2-222-2-2-2-20-22-222000200002-2−i2−i2i2i2i2i2−i2−i2−22−222−22−2000002i−2i−2i2i0000i2−i2−i2i22−2−2200000000000000
χ532-22-22-22-22-2200002-22-2-2002-2002-22-22-22-2000000000000000002-22-20000000000002-200000000
χ542-22-22-22-22-2200002-22-2-2002-2002-22-22-22-200000000000000000-22-22000000000000-2200000000
χ552-22-22-22-22-2200002-22-2-2002-200-22-22-22-22000000000000000002-22-2000000000000-2200000000
χ562-22-22-22-22-2200002-22-2-2002-200-22-22-22-2200000000000000000-22-220000000000002-200000000
χ572-22-22-22-2-22-20000-22-222002-2002i−2i2i−2i−2i2i−2i2i000000000000000000000000000002-22-2002i−2i000000
χ582-22-22-22-2-22-20000-22-222002-2002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000-22-2200−2i2i000000
χ592-22-22-22-2-22-20000-22-222002-200−2i2i−2i2i2i−2i2i−2i000000000000000000000000000002-22-200−2i2i000000
χ602-22-22-22-2-22-20000-22-222002-200−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000-22-22002i−2i000000
χ614444-4-4-4-400-444-4-40-4440-440000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-400-4-4-4440-44404-40000000000000000000000000000000000000000000000000000000
χ6344-4-4-4-4440004-4-44000000000000000000022−22−222222−22−222200000000000000000000000000000000000
χ6444-4-4-4-4440004-4-440000000000000000000−222222−22−222222−2200000000000000000000000000000000000
χ6544-4-4-4-444000-444-4000000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ6644-4-4-4-444000-444-40000000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ674-44-44-44-44-4-4000044-44-400-4400000000000000000000000000000000000000000000000000000
χ684-44-44-44-4-4440000-4-44-4400-4400000000000000000000000000000000000000000000000000000
χ694-44-4-44-4400400000-4-440000000000000000000000000000000022−22−22220000000000000000000000
χ704-44-4-44-4400400000-4-4400000000000000000000000000000000−222222−220000000000000000000000
χ714-44-4-44-4400-40000044-40000000000000000000000000000000000000000000022−22−22220000000000
χ724-44-4-44-4400-40000044-400000000000000000000000000000000000000000000−222222−220000000000
χ734-4-444-4-444-400000-4000400000022−22−222222−22−22220000000000000000000000000000000000000000000
χ744-4-444-4-444-400000-40004000000−222222−22−222222−220000000000000000000000000000000000000000000
χ754-4-444-4-44-44000004000-40000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ764-4-444-4-44-44000004000-4000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ778-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000000

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