Finite Group Databasebeta

← Group #295521

Character table — Group #295521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444444444444444444444448888888888888888224444444488888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-111111-1-11-1
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111-1-1-1-1-111-11
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1111-1-111-11
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111111-1-1-111-1-11-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-11-1-111-1-1-11
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11-111-1-1111-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-111-11-1-1-1-1111-1
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11-11111-1-1-11
χ172222222222-2-22222-2-2-2-222-2-2-2-2222222-2-20000000000000000-2-222-2-2000000000000000000000000
χ182222222222-2-22222-2-2-2-222-2-2-2-222-2-2-2-2-2-2000000000000000022-2-222000000000000000000000000
χ192222222222-2-2-2-2-2-2222222-2-222-2-22222-2-2000000000000000022-2-2-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2222222-2-222-2-2-2-2-2-2-2-20000000000000000-2-22222000000000000000000000000
χ2122222222-2-22222222222-2-222-2-2-2-20000-2-2000000000000000000000022220000000000-2-200000000
χ2222222222-2-22222222222-2-222-2-2-2-20000-2-20000000000000000000000-2-2-2-200000000002200000000
χ2322222222-2-222-2-2-2-2-2-2-2-2-2-22222220000-2-2000000000000000000000022-2-200000000002-200000000
χ2422222222-2-222-2-2-2-2-2-2-2-2-2-22222220000-2-20000000000000000000000-2-2220000000000-2200000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-200002200000000000000000000000000000000002-2002-2000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-20000220000000000000000000000000000000000-2200-22000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22200002200000000000000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2220000220000000000000000000000000000000000-22002-2000000
χ29222-22-2-2-2-2-22-200000000222-200002i2i−2i−2i2-2000000002i2i2i2i−2i−2i−2i−2i00002i−2i0000000022-2-2000000000000
χ30222-22-2-2-2-2-22-200000000222-200002i2i−2i−2i2-200000000−2i−2i−2i−2i2i2i2i2i00002i−2i00000000-2-222000000000000
χ31222-22-2-2-2-2-22-200000000222-20000−2i−2i2i2i2-2000000002i2i2i2i−2i−2i−2i−2i0000−2i2i00000000-2-222000000000000
χ32222-22-2-2-2-2-22-200000000222-20000−2i−2i2i2i2-200000000−2i−2i−2i−2i2i2i2i2i0000−2i2i0000000022-2-2000000000000
χ33222-22-2-2-2-2-2-220000000022-2200002i2i−2i−2i-222i2i2i2i−2i−2i−2i−2i000000000000−2i2i000022-2-20000000000000000
χ34222-22-2-2-2-2-2-220000000022-2200002i2i−2i−2i-22−2i−2i−2i−2i2i2i2i2i000000000000−2i2i0000-2-2220000000000000000
χ35222-22-2-2-2-2-2-220000000022-220000−2i−2i2i2i-222i2i2i2i−2i−2i−2i−2i0000000000002i−2i0000-2-2220000000000000000
χ36222-22-2-2-2-2-2-220000000022-220000−2i−2i2i2i-22−2i−2i−2i−2i2i2i2i2i0000000000002i−2i000022-2-20000000000000000
χ3722-22-2-2-222-2002i2i−2i−2i00002-200002i−2i2-22-20022−2−222−2−2i2i2−i2−i2i2i2−i2−i2002i−2i0000002−22−2i2−i2i2−i2000000000000
χ3822-22-2-2-222-2002i2i−2i−2i00002-200002i−2i2-22-200−2−222−2−222−i2−i2i2i2−i2−i2i2i2002i−2i000000−22−22−i2i2−i2i2000000000000
χ3922-22-2-2-222-2002i2i−2i−2i00002-200002i−2i-22-220022−2−222−2−2i2i2−i2−i2i2i2−i2−i200−2i2i000000−22−22−i2i2−i2i2000000000000
χ4022-22-2-2-222-2002i2i−2i−2i00002-200002i−2i-22-2200−2−222−2−222−i2−i2i2i2−i2−i2i2i200−2i2i0000002−22−2i2−i2i2−i2000000000000
χ4122-22-2-2-222-200−2i−2i2i2i00002-20000−2i2i2-22-20022−2−222−2−2−i2−i2i2i2−i2−i2i2i200−2i2i0000002−22−2−i2i2−i2i2000000000000
χ4222-22-2-2-222-200−2i−2i2i2i00002-20000−2i2i2-22-200−2−222−2−222i2i2−i2−i2i2i2−i2−i200−2i2i000000−22−22i2−i2i2−i2000000000000
χ4322-22-2-2-222-200−2i−2i2i2i00002-20000−2i2i-22-220022−2−222−2−2−i2−i2i2i2−i2−i2i2i2002i−2i000000−22−22i2−i2i2−i2000000000000
χ4422-22-2-2-222-200−2i−2i2i2i00002-20000−2i2i-22-2200−2−222−2−222i2i2−i2−i2i2i2−i2−i2002i−2i0000002−22−2−i2i2−i2i2000000000000
χ4522-2-2-222-2-220000002i2i−2i−2i2-2002i−2i002i−2i−2i2i00i2i2−i2−i2−i2−i2i2i222−2−2−2−2222-2000000002−2−22−i2i2i2−i2000000000000
χ4622-2-2-222-2-220000002i2i−2i−2i2-2002i−2i002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2−2−22222−2−22-200000000−222−2i2−i2−i2i2000000000000
χ4722-2-2-222-2-220000002i2i−2i−2i2-2002i−2i00−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i222−2−2−2−222-2200000000−222−2i2−i2−i2i2000000000000
χ4822-2-2-222-2-220000002i2i−2i−2i2-2002i−2i00−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i2−2−22222−2−2-22000000002−2−22−i2i2i2−i2000000000000
χ4922-2-2-222-2-22000000−2i−2i2i2i2-200−2i2i002i−2i−2i2i00i2i2−i2−i2−i2−i2i2i2−2−22222−2−2-22000000002−2−22i2−i2−i2i2000000000000
χ5022-2-2-222-2-22000000−2i−2i2i2i2-200−2i2i002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i222−2−2−2−222-2200000000−222−2−i2i2i2−i2000000000000
χ5122-2-2-222-2-22000000−2i−2i2i2i2-200−2i2i00−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2−2−22222−2−22-200000000−222−2−i2i2i2−i2000000000000
χ5222-2-2-222-2-22000000−2i−2i2i2i2-200−2i2i00−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i222−2−2−2−2222-2000000002−2−22i2−i2−i2i2000000000000
χ532-222-2-22-2002-22i−2i2i−2i2i−2i2i−2i00-220000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−20000002-22i−2i00000000000000i2−i22−200
χ542-222-2-22-2002-22i−2i2i−2i2i−2i2i−2i00-220000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000-22−2i2i00000000000000−i2i2−2200
χ552-222-2-22-2002-22i−2i2i−2i2i−2i2i−2i00-220000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−220000002-22i−2i00000000000000−i2i2−2200
χ562-222-2-22-2002-22i−2i2i−2i2i−2i2i−2i00-220000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000-22−2i2i00000000000000i2−i22−200
χ572-222-2-22-2002-2−2i2i−2i2i−2i2i−2i2i00-220000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−220000002-2−2i2i00000000000000i2−i2−2200
χ582-222-2-22-2002-2−2i2i−2i2i−2i2i−2i2i00-220000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000-222i−2i00000000000000−i2i22−200
χ592-222-2-22-2002-2−2i2i−2i2i−2i2i−2i2i00-220000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−20000002-2−2i2i00000000000000−i2i22−200
χ602-222-2-22-2002-2−2i2i−2i2i−2i2i−2i2i00-220000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000-222i−2i00000000000000i2−i2−2200
χ61444-44-4-4-4444-400000000-4-44-400000000-440000000000000000000000000000000000000000000000
χ62444-44-4-4-444-4400000000-4-4-44000000004-40000000000000000000000000000000000000000000000
χ6344-44-4-4-44-44004i4i−4i−4i0000-440000−4i4i0000000000000000000000000000000000000000000000000000
χ6444-44-4-4-44-4400−4i−4i4i4i0000-4400004i−4i0000000000000000000000000000000000000000000000000000
χ6544-4-4-444-44-40000004i4i−4i−4i-4400−4i4i000000000000000000000000000000000000000000000000000000
χ6644-4-4-444-44-4000000−4i−4i4i4i-44004i−4i000000000000000000000000000000000000000000000000000000
χ674-444-4-44-400-444i−4i4i−4i−4i4i−4i4i004-400000000000000000000000000000000000000000000000000000000
χ684-444-4-44-400-44−4i4i−4i4i4i−4i4i−4i004-400000000000000000000000000000000000000000000000000000000
χ694-44-4-44-4400440000000000-4-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ704-44-4-44-4400440000000000-4-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ714-44-4-44-4400-4-4000000000044000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ724-44-4-44-4400-4-40000000000440000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ734-4-4444-4-400004-4-440000000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ744-4-4444-4-400004-4-44000000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ754-4-4444-4-40000-444-40000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ764-4-4444-4-40000-444-4000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ774-4-4-44-444000000004-4-44000000000000002-2-22-222-22-2-22-222-2000000000000000000000000000000
χ784-4-4-44-444000000004-4-4400000000000000-222-22-2-22-222-22-2-22000000000000000000000000000000
χ794-4-4-44-44400000000-444-4000000000000002-2-22-222-2-222-22-2-22000000000000000000000000000000
χ804-4-4-44-44400000000-444-400000000000000-222-22-2-222-2-22-222-2000000000000000000000000000000

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