Finite Group Databasebeta

← Group #285651

Character table — Group #285651

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444444444888888888888888844444444488888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
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
χ911111111-1-1-1-111111111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-11111-1-1-11
χ1211111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1311111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111111111-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ1411111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111111111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ1511111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1111111-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-2-22-22-2-2-2-222000000000000000022-222-2-2-2-200000000000000000000000000
χ1822222222222222-2-2-22-22-2-2-2-2220000000000000000-2-2-2-2-2222200000000000000000000000000
χ19222222222222-2-2222-22-222-2-2-2-2222222220000000000-2000000-2-2-2-20000000000000000000000
χ20222222222222-2-2222-22-222-2-2-2-2-2-2-2-2-2-2-2-20000000000-200000022220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i00200000000002i2i−2i−2i000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i0020000000000−2i−2i2i2i000000000000000000
χ2322222222-2-2-2-222-2-2-22-2222-2-2-2-20000000000000000222-2-222-2-200000000000000000000000000
χ2422222222-2-2-2-222-2-2-22-2222-2-2-2-20000000000000000-2-2222-2-22200000000000000000000000000
χ2522222222-2-2-2-2-2-2222-22-2-2-2-2-2222222-2-2-2-200000000002000000-2-2220000000000000000000000
χ2622222222-2-2-2-2-2-2222-22-2-2-2-2-222-2-2-2-222220000000000200000022-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i00-20000000000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i00-200000000002i2i−2i−2i000000000000000000
χ292222-2-2-2-222-2-20022-20-202-2000022-2-222-2-2000000000000000000000000022−2−222−2−200002−22−200
χ302222-2-2-2-222-2-20022-20-202-2000022-2-222-2-20000000000000000000000000−2−222−2−2220000−22−2200
χ312222-2-2-2-222-2-20022-20-202-20000-2-222-2-222000000000000000000000000022−2−222−2−20000−22−2200
χ322222-2-2-2-222-2-20022-20-202-20000-2-222-2-2220000000000000000000000000−2−222−2−22200002−22−200
χ332222-2-2-2-2-2-2220022-20-20-22000022-2-2-2-222000000000000000000000000022−2−2−2−22200002−2−2200
χ342222-2-2-2-2-2-2220022-20-20-22000022-2-2-2-2220000000000000000000000000−2−22222−2−20000−222−200
χ352222-2-2-2-2-2-2220022-20-20-220000-2-22222-2-2000000000000000000000000022−2−2−2−2220000−222−200
χ362222-2-2-2-2-2-2220022-20-20-220000-2-22222-2-20000000000000000000000000−2−22222−2−200002−2−2200
χ3722-2-2-2-2222-22-222000-20-200002-22−22−22−22−2i2i2−i2−i2i2i2−i2−i22i−2i02i−2i00002−22−2i2−i2i2−i2000000000000000000
χ3822-2-2-2-2222-22-222000-20-200002-22−22−22−22−2−i2−i2i2i2−i2−i2i2i2−2i2i0−2i2i00002−22−2−i2i2−i2i2000000000000000000
χ3922-2-2-2-2222-22-222000-20-200002-2−22−22−22−22i2i2−i2−i2i2i2−i2−i2−2i2i0−2i2i0000−22−22i2−i2i2−i2000000000000000000
χ4022-2-2-2-2222-22-222000-20-200002-2−22−22−22−22−i2−i2i2i2−i2−i2i2i22i−2i02i−2i0000−22−22−i2i2−i2i2000000000000000000
χ4122-2-2-2-2222-22-2-2-20002020000-222−22−22−22−222−2−2−2−222000002-22-2−22−222−2−22000000000000000000
χ4222-2-2-2-2222-22-2-2-20002020000-222−22−22−22−2−2−22222−2−200000-22-22−22−22−222−2000000000000000000
χ4322-2-2-2-2222-22-2-2-20002020000-22−22−22−22−2222−2−2−2−22200000-22-222−22−22−2−22000000000000000000
χ4422-2-2-2-2222-22-2-2-20002020000-22−22−22−22−22−2−22222−2−2000002-22-22−22−2−222−2000000000000000000
χ4522-2-2-2-222-22-2222000-20-20000-222−22−2−22−22i2i2−i2−i2i2i2−i2−i22i−2i0−2i2i00002−2−22−i2i2−i2i2000000000000000000
χ4622-2-2-2-222-22-2222000-20-20000-222−22−2−22−22−i2−i2i2i2−i2−i2i2i2−2i2i02i−2i00002−2−22i2−i2i2−i2000000000000000000
χ4722-2-2-2-222-22-2222000-20-20000-22−22−222−22−2i2i2−i2−i2i2i2−i2−i2−2i2i02i−2i0000−222−2−i2i2−i2i2000000000000000000
χ4822-2-2-2-222-22-2222000-20-20000-22−22−222−22−2−i2−i2i2i2−i2−i2i2i22i−2i0−2i2i0000−222−2i2−i2i2−i2000000000000000000
χ4922-2-2-2-222-22-22-2-200020200002-22−22−2−22−2222−2−2−2−22200000-222-2−222−2−222−2000000000000000000
χ5022-2-2-2-222-22-22-2-200020200002-22−22−2−22−22−2−22222−2−2000002-2-22−222−22−2−22000000000000000000
χ5122-2-2-2-222-22-22-2-200020200002-2−22−222−22−222−2−2−2−222000002-2-222−2−22−222−2000000000000000000
χ5222-2-2-2-222-22-22-2-200020200002-2−22−222−22−2−2−22222−2−200000-222-22−2−222−2−22000000000000000000
χ532-2-22-222-200002-22-22-2-22002-200000000002i−2i2i−2i2i−2i2i−2i0000000000000000000002-22-2002i−2i000000
χ542-2-22-222-200002-22-22-2-22002-200000000002i−2i2i−2i2i−2i2i−2i000000000000000000000-22-2200−2i2i000000
χ552-2-22-222-200002-22-22-2-22002-20000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000002-22-200−2i2i000000
χ562-2-22-222-200002-22-22-2-22002-20000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000-22-22002i−2i000000
χ572-2-22-222-20000-22-22-222-2002-200000000002-22-2-22-22000000000000000002i−2i2i−2i00002i−2i00000000
χ582-2-22-222-20000-22-22-222-2002-200000000002-22-2-22-2200000000000000000−2i2i−2i2i0000−2i2i00000000
χ592-2-22-222-20000-22-22-222-2002-20000000000-22-222-22-2000000000000000002i−2i2i−2i0000−2i2i00000000
χ602-2-22-222-20000-22-22-222-2002-20000000000-22-222-22-200000000000000000−2i2i−2i2i00002i−2i00000000
χ614444-4-4-4-444-4-400-4-44040-440000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-44400-4-440404-40000000000000000000000000000000000000000000000000000000
χ6344-4-444-4-44-4-440000000000000022−22−222222−22−22220000000000000000000000000000000000000000000
χ6444-4-444-4-44-4-4400000000000000−222222−22−222222−220000000000000000000000000000000000000000000
χ6544-4-444-4-4-444-40000000000000022−22−2222−222222−220000000000000000000000000000000000000000000
χ6644-4-444-4-4-444-400000000000000−222222−2222−22−22220000000000000000000000000000000000000000000
χ674-44-44-44-400004-400040-40000000000000022−22−222222−22−222200000000000000000000000000000000000
χ684-44-44-44-400004-400040-400000000000000−222222−22−222222−2200000000000000000000000000000000000
χ694-44-44-44-40000-44000-404000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ704-44-44-44-40000-44000-40400000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ714-4-444-4-440000004-4-4040000000000000000000000000000000000000000000022−22−22220000000000
χ724-4-444-4-440000004-4-40400000000000000000000000000000000000000000000−222222−220000000000
χ734-4-444-4-44000000-4440-400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ744-4-444-4-44000000-4440-40000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ754-4-44-444-400004-4-44-4-44400-4400000000000000000000000000000000000000000000000000000
χ764-4-44-444-40000-444-444-4-400-4400000000000000000000000000000000000000000000000000000
χ778-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000

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