Finite Group Databasebeta

← Group #349546

Character table — Group #349546

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222244444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-11-1-11-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-11-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11-1-11-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11-1-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ911111111111-1-1-1-1111111111-1-11-1-1-1-11111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111111-1-1-1-1111111111-1-11-1-1-1-11111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ1211111111111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ1311111111111-1-1-1-111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11
χ1411111111111-1-1-1-111111-1-1-1-1-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1111-1
χ1511111111111-1-1-1-111111-1-1-1-1-1-111111-1-1-1-1-1-111111-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111111-1-1-1-111111-1-1-1-1-1-111111-1-1-1-1-1-111111-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ17222222222222222-2-2-2-22222222-222220000-2-20000-200-200-2-20000-2-20000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-222-2-2-2-2-20000-2-20000-200-200220000220000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-20000220000-200200-2-20000220000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-222220000220000-200200220000-2-20000000000000000000000
χ2122222222-2-2-222222222-20000-2-2-200002222222222-2-2-2-2-2-2000000000000000000000000000000
χ2222222222-2-2-222222222-20000-2-2-20000-2-2-2-222-2-2-2-2-222-222000000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-20000-2-2200000000-2-200002002000022-2-20022-2-2000000000000000000
χ2422222222-2-2-22222-2-2-2-2-20000-2-2200000000-2-2000020020000-2-22200-2-222000000000000000000
χ2522222222-2-2-2-2-2-2-22222-2000022-200002222-2-2-2-2-2-2-2-2-2222000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-22222-2000022-20000-2-2-2-2-2-22222-2222-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000022200000000220000200-2000022-2-200-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000022200000000220000200-20000-2-2220022-2-2000000000000000000
χ292222-2-2-2-222-222-2-20000-222-2-22-2022-2-2000000000000000000000000000022−2−222−2−22−22−2000000
χ302222-2-2-2-222-222-2-20000-222-2-22-2022-2-20000000000000000000000000000−2−222−2−222−22−22000000
χ312222-2-2-2-222-222-2-20000-2-2-2222-20-2-222000000000000000000000000000022−2−222−2−2−22−22000000
χ322222-2-2-2-222-222-2-20000-2-2-2222-20-2-2220000000000000000000000000000−2−222−2−2222−22−2000000
χ332222-2-2-2-222-2-2-2220000-222-2-2-220-2-222000000000000000000000000000022−2−2−2−2222−2−22000000
χ342222-2-2-2-222-2-2-2220000-222-2-2-220-2-2220000000000000000000000000000−2−22222−2−2−222−2000000
χ352222-2-2-2-222-2-2-2220000-2-2-222-22022-2-2000000000000000000000000000022−2−2−2−222−222−2000000
χ362222-2-2-2-222-2-2-2220000-2-2-222-22022-2-20000000000000000000000000000−2−22222−2−22−2−22000000
χ3722-2-22-22-22-22000022-2-2-22-22-2002000022-2-2000000-22-20002-22-22-2000000000000000000000000
χ3822-2-22-22-22-22000022-2-2-22-22-20020000-2-222000000-2-220002-2-22-22000000000000000000000000
χ3922-2-22-22-22-22000022-2-2-2-22-22002000022-2-2000000-22-2000-22-22-22000000000000000000000000
χ4022-2-22-22-22-22000022-2-2-2-22-220020000-2-222000000-2-22000-222-22-2000000000000000000000000
χ4122-2-22-22-22-220000-2-222-22-22-200-200000000002i2i−2i−2i20002i−2i-220000002i−2i2i−2i000000000000000000
χ4222-2-22-22-22-220000-2-222-22-22-200-20000000000−2i−2i2i2i2000−2i2i-22000000−2i2i−2i2i000000000000000000
χ4322-2-22-22-22-220000-2-222-2-22-2200-200000000002i2i−2i−2i20002i−2i2-2000000−2i2i−2i2i000000000000000000
χ4422-2-22-22-22-220000-2-222-2-22-2200-20000000000−2i−2i2i2i2000−2i2i2-20000002i−2i2i−2i000000000000000000
χ4522-2-22-22-2-22-2000022-2-22000000-22i−2i2i−2i22-2-20000002-220000000002i−2i2i−2i−2i2i000000000000000000
χ4622-2-22-22-2-22-2000022-2-22000000-22i−2i2i−2i-2-22200000022-20000000002i−2i−2i2i2i−2i000000000000000000
χ4722-2-22-22-2-22-2000022-2-22000000-2−2i2i−2i2i22-2-20000002-22000000000−2i2i−2i2i2i−2i000000000000000000
χ4822-2-22-22-2-22-2000022-2-22000000-2−2i2i−2i2i-2-22200000022-2000000000−2i2i2i−2i−2i2i000000000000000000
χ4922-2-22-22-2-22-20000-2-222200000022i−2i2i−2i0000002i2i−2i−2i-2000−2i2i002-2-22−2i2i0000000000000000000000
χ5022-2-22-22-2-22-20000-2-222200000022i−2i2i−2i000000−2i−2i2i2i-20002i−2i00-222-2−2i2i0000000000000000000000
χ5122-2-22-22-2-22-20000-2-22220000002−2i2i−2i2i0000002i2i−2i−2i-2000−2i2i00-222-22i−2i0000000000000000000000
χ5222-2-22-22-2-22-20000-2-22220000002−2i2i−2i2i000000−2i−2i2i2i-20002i−2i002-2-222i−2i0000000000000000000000
χ532-22-2-222-20002i−2i2i−2i2-22-20000000000002-22-22i−2i2i−2i2i−2i0000000000000000002−22−2i2−i2i2−i200002−2i2−i200
χ542-22-2-222-20002i−2i2i−2i2-22-20000000000002-22-22i−2i2i−2i2i−2i000000000000000000−22−22−i2i2−i2i20000−22−i2i200
χ552-22-2-222-20002i−2i2i−2i2-22-2000000000000-22-222i−2i−2i2i−2i2i0000000000000000002−22−2i2−i2i2−i20000−22−i2i200
χ562-22-2-222-20002i−2i2i−2i2-22-2000000000000-22-222i−2i−2i2i−2i2i000000000000000000−22−22−i2i2−i2i200002−2i2−i200
χ572-22-2-222-2000−2i2i−2i2i2-22-20000000000002-22-2−2i2i−2i2i−2i2i0000000000000000002−22−2−i2i2−i2i200002−2−i2i200
χ582-22-2-222-2000−2i2i−2i2i2-22-20000000000002-22-2−2i2i−2i2i−2i2i000000000000000000−22−22i2−i2i2−i20000−22i2−i200
χ592-22-2-222-2000−2i2i−2i2i2-22-2000000000000-22-22−2i2i2i−2i2i−2i0000000000000000002−22−2−i2i2−i2i20000−22i2−i200
χ602-22-2-222-2000−2i2i−2i2i2-22-2000000000000-22-22−2i2i2i−2i2i−2i000000000000000000−22−22i2−i2i2−i200002−2−i2i200
χ614444-4-4-4-4-4-4444-4-4000040000-44000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-44-4-4440000400004-4000000000000000000000000000000000000000000000000000
χ6344-4-4-44-444-4-40000000044-4-4400000000000000000000000000000000000000000000000000000
χ6444-4-4-44-444-4-4000000004-444-400000000000000000000000000000000000000000000000000000
χ6544-4-4-44-44-44400000000-400000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6644-4-4-44-44-44400000000-40000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ674-44-44-4-440004i−4i−4i4i000000000000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ684-44-44-4-440004i−4i−4i4i00000000000000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ694-44-44-4-44000−4i4i4i−4i000000000000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ704-44-44-4-44000−4i4i4i−4i00000000000000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ714-44-4-444-40004i−4i4i−4i-44-440000000000000000−4i4i0000000000000000000000000000000000000000
χ724-44-4-444-4000−4i4i−4i4i-44-4400000000000000004i−4i0000000000000000000000000000000000000000
χ734-4-44-4-44400000004-4-440000000000004-4-44000000000000000000000000000000000000000000
χ744-4-44-4-44400000004-4-44000000000000-444-4000000000000000000000000000000000000000000
χ754-4-44-4-4440000000-444-40000000000000000004-4-44000000000000000000000000000000000000
χ764-4-44-4-4440000000-444-4000000000000000000-444-4000000000000000000000000000000000000
χ778-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000000000

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