Finite Group Databasebeta

← Group #276449

Character table — Group #276449

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888822444888888888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ9111111111-1-1-1-11111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ10111111111-1-1-1-11111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ11111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ12111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ13111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ14111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ15111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ16111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ17222222222222222-2-2-2-2222-2-22222-2-2-2-2-2-200000000-2-222-2000000000000000000000000000000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-2-2-222220000000022-2-2-2000000000000000000000000000000
χ19222222222-2-2-2-222-2-2-2-22-2-2222222-2-2-2-2-2-20000000022-2-22000000000000000000000000000000
χ20222222222-2-2-2-222-2-2-2-22-2-222-2-2-2-2-2-2222200000000-2-2222000000000000000000000000000000
χ2122222222-22222-2-22222-2-2-2220000-2-20000222222220000-2-2-2-2-200000000000000000000000000
χ2222222222-22222-2-22222-2-2-2220000-2-20000-2-2-2-2-2-2-2-20000-2222200000000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-2-2-20000220000000000000000200002i2i−2i−2i2i2i−2i−2i000000000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-2-2-2000022000000000000000020000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2522222222-2-2-2-2-2-2-22222-222-2-20000-2-200002222-2-2-2-200002-2-22200000000000000000000000000
χ2622222222-2-2-2-2-2-2-22222-222-2-20000-2-20000-2-2-2-222220000222-2-200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000000000000000-200002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000000000000000-20000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ2922-22-22-2-2-200002-222-2-2200002i2i−2i−2i2-22i2i−2i−2i0000000000000000000000000000022-2-2002i−2i000000
χ3022-22-22-2-2-200002-222-2-2200002i2i−2i−2i2-22i2i−2i−2i00000000000000000000000000000-2-22200−2i2i000000
χ3122-22-22-2-2-200002-222-2-220000−2i−2i2i2i2-2−2i−2i2i2i0000000000000000000000000000022-2-200−2i2i000000
χ3222-22-22-2-2-200002-222-2-220000−2i−2i2i2i2-2−2i−2i2i2i00000000000000000000000000000-2-222002i−2i000000
χ3322-22-22-2-2-200002-2-2-222200002i2i−2i−2i-22−2i−2i2i2i00000000000000000000000002i2i−2i−2i00002-200000000
χ3422-22-22-2-2-200002-2-2-222200002i2i−2i−2i-22−2i−2i2i2i0000000000000000000000000−2i−2i2i2i0000-2200000000
χ3522-22-22-2-2-200002-2-2-22220000−2i−2i2i2i-222i2i−2i−2i00000000000000000000000002i2i−2i−2i0000-2200000000
χ3622-22-22-2-2-200002-2-2-22220000−2i−2i2i2i-222i2i−2i−2i0000000000000000000000000−2i−2i2i2i00002-200000000
χ3722-2-22-2-2222i2i−2i−2i-2-2000022i−2i002-22-200000022−2−2i2i2−i2−i2002i−2i02−2i2−i22−22−2i2−i2i2−i2000000000000000000
χ3822-2-22-2-2222i2i−2i−2i-2-2000022i−2i002-22-2000000−2−222−i2−i2i2i2002i−2i0−22−i2i2−22−22−i2i2−i2i2000000000000000000
χ3922-2-22-2-2222i2i−2i−2i-2-2000022i−2i00-22-2200000022−2−2i2i2−i2−i200−2i2i02−2i2−i2−22−22−i2i2−i2i2000000000000000000
χ4022-2-22-2-2222i2i−2i−2i-2-2000022i−2i00-22-22000000−2−222−i2−i2i2i200−2i2i0−22−i2i22−22−2i2−i2i2−i2000000000000000000
χ4122-2-22-2-222−2i−2i2i2i-2-200002−2i2i002-22-200000022−2−2−i2−i2i2i200−2i2i02−2−i2i22−22−2−i2i2−i2i2000000000000000000
χ4222-2-22-2-222−2i−2i2i2i-2-200002−2i2i002-22-2000000−2−222i2i2−i2−i200−2i2i0−22i2−i2−22−22i2−i2i2−i2000000000000000000
χ4322-2-22-2-222−2i−2i2i2i-2-200002−2i2i00-22-2200000022−2−2−i2−i2i2i2002i−2i02−2−i2i2−22−22i2−i2i2−i2000000000000000000
χ4422-2-22-2-222−2i−2i2i2i-2-200002−2i2i00-22-22000000−2−222i2i2−i2−i2002i−2i0−22i2−i22−22−2−i2i2−i2i2000000000000000000
χ4522-2-22-2-22-22i2i−2i−2i220000-2−2i2i000000002i−2i2i−2i22−2−2i2i2−i2−i22-2000−22−i2i2i2−i2−i2i2−222−2000000000000000000
χ4622-2-22-2-22-22i2i−2i−2i220000-2−2i2i000000002i−2i2i−2i−2−222−i2−i2i2i22-20002−2i2−i2−i2i2i2−i22−2−22000000000000000000
χ4722-2-22-2-22-22i2i−2i−2i220000-2−2i2i00000000−2i2i−2i2i22−2−2i2i2−i2−i2-22000−22−i2i2−i2i2i2−i22−2−22000000000000000000
χ4822-2-22-2-22-22i2i−2i−2i220000-2−2i2i00000000−2i2i−2i2i−2−222−i2−i2i2i2-220002−2i2−i2i2−i2−i2i2−222−2000000000000000000
χ4922-2-22-2-22-2−2i−2i2i2i220000-22i−2i000000002i−2i2i−2i22−2−2−i2−i2i2i2-22000−22i2−i2i2−i2−i2i22−2−22000000000000000000
χ5022-2-22-2-22-2−2i−2i2i2i220000-22i−2i000000002i−2i2i−2i−2−222i2i2−i2−i2-220002−2−i2i2−i2i2i2−i2−222−2000000000000000000
χ5122-2-22-2-22-2−2i−2i2i2i220000-22i−2i00000000−2i2i−2i2i22−2−2−i2−i2i2i22-2000−22i2−i2−i2i2i2−i2−222−2000000000000000000
χ5222-2-22-2-22-2−2i−2i2i2i220000-22i−2i00000000−2i2i−2i2i−2−222i2i2−i2−i22-20002−2−i2i2i2−i2−i2i22−2−22000000000000000000
χ532-222-2-2-2202i−2i2i−2i002-22-20002i−2i00000000002-22-22i−2i2i−2i000000000000000002−22−2i2−i2i2−i200002−2i2−i200
χ542-222-2-2-2202i−2i2i−2i002-22-20002i−2i00000000002-22-22i−2i2i−2i00000000000000000−22−22−i2i2−i2i20000−22−i2i200
χ552-222-2-2-2202i−2i2i−2i002-22-20002i−2i0000000000-22-22−2i2i−2i2i000000000000000002−22−2i2−i2i2−i20000−22−i2i200
χ562-222-2-2-2202i−2i2i−2i002-22-20002i−2i0000000000-22-22−2i2i−2i2i00000000000000000−22−22−i2i2−i2i200002−2i2−i200
χ572-222-2-2-220−2i2i−2i2i002-22-2000−2i2i00000000002-22-2−2i2i−2i2i000000000000000002−22−2−i2i2−i2i200002−2−i2i200
χ582-222-2-2-220−2i2i−2i2i002-22-2000−2i2i00000000002-22-2−2i2i−2i2i00000000000000000−22−22i2−i2i2−i20000−22i2−i200
χ592-222-2-2-220−2i2i−2i2i002-22-2000−2i2i0000000000-22-222i−2i2i−2i000000000000000002−22−2−i2i2−i2i20000−22i2−i200
χ602-222-2-2-220−2i2i−2i2i002-22-2000−2i2i0000000000-22-222i−2i2i−2i00000000000000000−22−22i2−i2i2−i200002−2−i2i200
χ61444-4-4-44-4400004-40000-400000000004-4-440000000000000000000000000000000000000000000
χ62444-4-4-44-4400004-40000-40000000000-444-40000000000000000000000000000000000000000000
χ63444-4-4-44-4-40000-440000400004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-40000-44000040000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ6544-44-44-4-440000-4444-4-4-400000000-4400000000000000000000000000000000000000000000000
χ6644-44-44-4-440000-44-4-444-4000000004-400000000000000000000000000000000000000000000000
χ674-444-4-4-4404i−4i4i−4i00-44-44000−4i4i00000000000000000000000000000000000000000000000000000
χ684-444-4-4-440−4i4i−4i4i00-44-440004i−4i00000000000000000000000000000000000000000000000000000
χ694-4-444-44-400000004-4-44000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ704-4-444-44-400000004-4-4400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ714-4-444-44-40000000-444-400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ724-4-444-44-40000000-444-40000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ734-4-4-4-444404-4-4400000000000000000000022−22−222222−22−222200000000000000000000000000000000000
χ744-4-4-4-444404-4-44000000000000000000000−222222−22−222222−2200000000000000000000000000000000000
χ754-4-4-4-44440-444-400000000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ764-4-4-4-44440-444-4000000000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ778-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000

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