Finite Group Databasebeta

← Group #270976

Character table — Group #270976

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444444444444422444444448888888888888888224444444488888888222444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-11111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ6111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111111-1-11-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1
χ911111111-1-1-1-111-1-1-1-1111111-1-111111-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1-11-1
χ1011111111-1-1-1-111-1-1-1-1111111-1-111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-1-1-1-111-11
χ1111111111-1-1-1-111-1-1-1-1111111-1-111111-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1111-1-111-11
χ1211111111-1-1-1-111-1-1-1-1111111-1-111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111111-1-1-111-1-11-1
χ1311111111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1111-1-111-1-1-11
χ1411111111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-1111-1
χ1511111111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1111-1-1-1-1111-1
χ1611111111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-11
χ1722222222222222-2-2-2-2-2-222-2-2-2-2-2222222-20000000000000000-2-200-2-2002200000000000000000000
χ1822222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-222-2000000000000000022002200-2-200000000000000000000
χ19222222222222-2-2222222-2-222-2-2-20000-2-2-20000000000000000002200220000000000-200-200000000
χ20222222222222-2-2222222-2-222-2-2-20000-2-2-2000000000000000000-2-200-2-20000000000200200000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22220000-2-22000000000000000000000000000000000002-202-2000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22220000-2-2200000000000000000000000000000000000-220-22000000
χ2322222222-2-2-2-2222222-2-222-2-222-22222-2-2-200000000000000002200-2-200-2-200000000000000000000
χ2422222222-2-2-2-2222222-2-222-2-222-2-2-2-2-2-2-2-20000000000000000-2-20022002200000000000000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-220000222000000000000000000000000000000000002-20-22000000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22000022200000000000000000000000000000000000-2202-2000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-22222-2000022-20000000000000000002200-2-20000000000200-200000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-22222-2000022-2000000000000000000-2-200220000000000-200200000000
χ29222-2-2-2-222i2i−2i−2i002i2i−2i−2i2-2002-200000000002222−2−2−2−2i2i2i2i2−i2−i2−i2−i2002-2002i−2i00000000000000002−2i2−i200
χ30222-2-2-2-222i2i−2i−2i002i2i−2i−2i2-2002-200000000002222−2−2−2−2i2i2i2i2−i2−i2−i2−i200-2200−2i2i0000000000000000−22−i2i200
χ31222-2-2-2-222i2i−2i−2i002i2i−2i−2i2-2002-20000000000−2−2−2−22222−i2−i2−i2−i2i2i2i2i2002-2002i−2i0000000000000000−22−i2i200
χ32222-2-2-2-222i2i−2i−2i002i2i−2i−2i2-2002-20000000000−2−2−2−22222−i2−i2−i2−i2i2i2i2i200-2200−2i2i00000000000000002−2i2−i200
χ33222-2-2-2-22−2i−2i2i2i00−2i−2i2i2i2-2002-200000000002222−2−2−2−2−i2−i2−i2−i2i2i2i2i2002-200−2i2i00000000000000002−2−i2i200
χ34222-2-2-2-22−2i−2i2i2i00−2i−2i2i2i2-2002-200000000002222−2−2−2−2−i2−i2−i2−i2i2i2i2i200-22002i−2i0000000000000000−22i2−i200
χ35222-2-2-2-22−2i−2i2i2i00−2i−2i2i2i2-2002-20000000000−2−2−2−22222i2i2i2i2−i2−i2−i2−i2002-200−2i2i0000000000000000−22i2−i200
χ36222-2-2-2-22−2i−2i2i2i00−2i−2i2i2i2-2002-20000000000−2−2−2−22222i2i2i2i2−i2−i2−i2−i200-22002i−2i00000000000000002−2−i2i200
χ3722-22-22-2-22i−2i2i−2i2-20000002-20000022-2-22i−2i0i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000002i−2ii2i2−i2−i222−2−2000000000000
χ3822-22-22-2-22i−2i2i−2i2-20000002-20000022-2-22i−2i0−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000002i−2i−i2−i2i2i2−2−222000000000000
χ3922-22-22-2-22i−2i2i−2i2-20000002-200000-2-2222i−2i0i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000−2i2i−i2−i2i2i2−2−222000000000000
χ4022-22-22-2-22i−2i2i−2i2-20000002-200000-2-2222i−2i0−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000−2i2ii2i2−i2−i222−2−2000000000000
χ4122-22-22-2-2−2i2i−2i2i2-20000002-20000022-2-2−2i2i0i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000−2i2ii2i2−i2−i2−2−222000000000000
χ4222-22-22-2-2−2i2i−2i2i2-20000002-20000022-2-2−2i2i0−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000−2i2i−i2−i2i2i222−2−2000000000000
χ4322-22-22-2-2−2i2i−2i2i2-20000002-200000-2-222−2i2i0i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000002i−2i−i2−i2i2i222−2−2000000000000
χ4422-22-22-2-2−2i2i−2i2i2-20000002-200000-2-222−2i2i0−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000002i−2ii2i2−i2−i2−2−222000000000000
χ452-22-2-222-20000222-22-200-2-2002-202-22-2000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-200000000i2−i2i2−i2i2−i2i2−i2000000000000
χ462-22-2-222-20000222-22-200-2-2002-202-22-2000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-200000000−i2i2−i2i2−i2i2−i2i2000000000000
χ472-22-2-222-20000222-22-200-2-2002-20-22-22000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-2200000000−i2i2−i2i2−i2i2−i2i2000000000000
χ482-22-2-222-20000222-22-200-2-2002-20-22-22000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-2200000000i2−i2i2−i2i2−i2i2−i2000000000000
χ492-22-2-222-2000022-22-2200-2-200-2202-22-2000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2-2200000000i2−i2i2−i2−i2i2−i2i2000000000000
χ502-22-2-222-2000022-22-2200-2-200-2202-22-2000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2-2200000000−i2i2−i2i2i2−i2i2−i2000000000000
χ512-22-2-222-2000022-22-2200-2-200-220-22-22000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i22-200000000−i2i2−i2i2i2−i2i2−i2000000000000
χ522-22-2-222-2000022-22-2200-2-200-220-22-22000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i22-200000000i2−i2i2−i2−i2i2−i2i2000000000000
χ532-2-2-222-2200002-2000022-22-2-20022-2-2200-2000000002i−2i−2i2i2i−2i−2i2i00002-2000000002i−2i−2i2i000000000000
χ542-2-2-222-2200002-2000022-22-2-20022-2-2200-200000000−2i2i2i−2i−2i2i2i−2i00002-200000000−2i2i2i−2i000000000000
χ552-2-2-222-2200002-2000022-22-2-2002-222-200-2000000002i−2i−2i2i2i−2i−2i2i0000-2200000000−2i2i2i−2i000000000000
χ562-2-2-222-2200002-2000022-22-2-2002-222-200-200000000−2i2i2i−2i−2i2i2i−2i0000-22000000002i−2i−2i2i000000000000
χ572-2-2-222-2200002-20000-2-2-222200-22-2-220022-2-222-2-22000000000000-2200002-2-220000000000000000
χ582-2-2-222-2200002-20000-2-2-222200-22-2-22002-222-2-222-2000000000000-220000-222-20000000000000000
χ592-2-2-222-2200002-20000-2-2-222200-2-222-20022-2-222-2-220000000000002-20000-222-20000000000000000
χ602-2-2-222-2200002-20000-2-2-222200-2-222-2002-222-2-222-20000000000002-200002-2-220000000000000000
χ61444-4-4-4-444i4i−4i−4i00−4i−4i4i4i-4400-4400000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44−4i−4i4i4i004i4i−4i−4i-4400-4400000000000000000000000000000000000000000000000000000000
χ6344-44-44-4-44i−4i4i−4i-44000000-44000000000−4i4i00000000000000000000000000000000000000000000000
χ6444-44-44-4-4−4i4i−4i4i-44000000-440000000004i−4i00000000000000000000000000000000000000000000000
χ6544-4-44-44-44-4-4400000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6644-4-44-44-44-4-440000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6744-4-44-44-4-444-400000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6844-4-44-44-4-444-40000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ694-4444-4-4-40000004i−4i−4i4i00000000000000002i−2i2i−2i−2i2i−2i2i-22-222-22-2000000000000000000000000000000
χ704-4444-4-4-40000004i−4i−4i4i0000000000000000−2i2i−2i2i2i−2i2i−2i2-22-2-22-22000000000000000000000000000000
χ714-4444-4-4-4000000−4i4i4i−4i00000000000000002i−2i2i−2i−2i2i−2i2i2-22-2-22-22000000000000000000000000000000
χ724-4444-4-4-4000000−4i4i4i−4i0000000000000000−2i2i−2i2i2i−2i2i−2i-22-222-22-2000000000000000000000000000000
χ734-44-4-444-40000-4-44-44-4004400-44000000000000000000000000000000000000000000000000000000
χ744-44-4-444-40000-4-4-44-440044004-4000000000000000000000000000000000000000000000000000000
χ754-4-44-4-44400000000004-400-4400000000000000000022−22−2222−222222−22000000000000000000000000000000
χ764-4-44-4-44400000000004-400-44000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ774-4-44-4-4440000000000-44004-4000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ784-4-44-4-4440000000000-44004-40000000000−222222−2222−22−222200000000000000000000000000000000000000
χ794-4-4-444-440000-440000444-4-4-400-400000040000000000000000000000000000000000000000000000
χ804-4-4-444-440000-440000-4-44-444004000000-40000000000000000000000000000000000000000000000

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