Finite Group Databasebeta

← Group #270991

Character table — Group #270991

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444444444444422222244448888888888888888444444444488888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1
χ911111111-1-1-1-11111-1-1-1-11111-1-111111-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-111-1-11-1
χ1011111111-1-1-1-11111-1-1-1-11111-1-111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1-111-1-111-11
χ1111111111-1-1-1-11111-1-1-1-11111-1-111111-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-11
χ1211111111-1-1-1-11111-1-1-1-11111-1-111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111111-1-1-11111-1-11-1
χ1311111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-11-1-11111-1-1-11
χ1411111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-111-1-1-1-1111-1
χ1511111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-11-1-111-1-1111-1
χ1611111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-11-111-1-111-1-1-11
χ1722222222222222-2-2222222-2-2-2-20000-2-2-2-20000000000000000002200002200000000-2-20000000000
χ1822222222222222-2-2222222-2-2-2-20000-2-2-2-2000000000000000000-2-20000-2-200000000220000000000
χ19222222222222-2-222-2-2-2-2-2-222-2-22222-222-200000000000000002200-2-2-2-20000000000000000000000
χ20222222222222-2-222-2-2-2-2-2-222-2-2-2-2-2-2-222-20000000000000000-2-20022220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22200002-2-220000000000000000000000000000000000002-22-2000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22200002-2-22000000000000000000000000000000000000-22-22000000
χ2322222222-2-2-2-222-2-2-2-2-2-222-2-2220000-222-2000000000000000000220000-2-2000000002-20000000000
χ2422222222-2-2-2-222-2-2-2-2-2-222-2-2220000-222-2000000000000000000-2-200002200000000-220000000000
χ2522222222-2-2-2-2-2-2222222-2-222222222-2-2-2-20000000000000000-2-200-2-2220000000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-20000000000000000220022-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000022220000000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-200002222000000000000000000000000000000000000-222-2000000
χ2922-22-2-2-222i2i−2i−2i002-20000002-20022-2-202i−2i0i2i2i2i2−i2−i2−i2−i22222−2−2−2−22i−2i00000000i2i2−i2−i222−2−2000000000000
χ3022-22-2-2-222i2i−2i−2i002-20000002-20022-2-202i−2i0−i2−i2−i2−i2i2i2i2i2−2−2−2−222222i−2i00000000−i2−i2i2i2−2−222000000000000
χ3122-22-2-2-222i2i−2i−2i002-20000002-200-2-22202i−2i0i2i2i2i2−i2−i2−i2−i22222−2−2−2−2−2i2i00000000−i2−i2i2i2−2−222000000000000
χ3222-22-2-2-222i2i−2i−2i002-20000002-200-2-22202i−2i0−i2−i2−i2−i2i2i2i2i2−2−2−2−22222−2i2i00000000i2i2−i2−i222−2−2000000000000
χ3322-22-2-2-22−2i−2i2i2i002-20000002-20022-2-20−2i2i0i2i2i2i2−i2−i2−i2−i2−2−2−2−22222−2i2i00000000i2i2−i2−i2−2−222000000000000
χ3422-22-2-2-22−2i−2i2i2i002-20000002-20022-2-20−2i2i0−i2−i2−i2−i2i2i2i2i22222−2−2−2−2−2i2i00000000−i2−i2i2i222−2−2000000000000
χ3522-22-2-2-22−2i−2i2i2i002-20000002-200-2-2220−2i2i0i2i2i2i2−i2−i2−i2−i2−2−2−2−222222i−2i00000000−i2−i2i2i222−2−2000000000000
χ3622-22-2-2-22−2i−2i2i2i002-20000002-200-2-2220−2i2i0−i2−i2−i2−i2i2i2i2i22222−2−2−2−22i−2i00000000i2i2−i2−i2−2−222000000000000
χ3722-2-2-222-22i−2i2i−2i2-2002i2i−2i−2i2-2000000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2002-200002i−2i00000000000000i2−i22−200
χ3822-2-2-222-22i−2i2i−2i2-2002i2i−2i−2i2-2000000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−200-220000−2i2i00000000000000−i2i2−2200
χ3922-2-2-222-22i−2i2i−2i2-2002i2i−2i−2i2-2000000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222002-200002i−2i00000000000000−i2i2−2200
χ4022-2-2-222-22i−2i2i−2i2-2002i2i−2i−2i2-2000000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200-220000−2i2i00000000000000i2−i22−200
χ4122-2-2-222-2−2i2i−2i2i2-200−2i−2i2i2i2-2000000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222002-20000−2i2i00000000000000i2−i2−2200
χ4222-2-2-222-2−2i2i−2i2i2-200−2i−2i2i2i2-2000000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200-2200002i−2i00000000000000−i2i22−200
χ4322-2-2-222-2−2i2i−2i2i2-200−2i−2i2i2i2-2000000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2002-20000−2i2i00000000000000−i2i22−200
χ4422-2-2-222-2−2i2i−2i2i2-200−2i−2i2i2i2-2000000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−200-2200002i−2i00000000000000i2−i2−2200
χ452-22-2-22-22000000222-22-200-2-22-22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000002-200i2−i2i2−i2i2−i2i2−i2000000000000
χ462-22-2-22-22000000222-22-200-2-22-22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000002-200−i2i2−i2i2−i2i2−i2i2000000000000
χ472-22-2-22-22000000222-22-200-2-22-2-22-220000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000-2200−i2i2−i2i2−i2i2−i2i2000000000000
χ482-22-2-22-22000000222-22-200-2-22-2-22-220000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000-2200i2−i2i2−i2i2−i2i2−i2000000000000
χ492-22-2-22-2200000022-22-2200-2-2-222-22-20000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000-2200i2−i2i2−i2−i2i2−i2i2000000000000
χ502-22-2-22-2200000022-22-2200-2-2-222-22-20000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000-2200−i2i2−i2i2i2−i2i2−i2000000000000
χ512-22-2-22-2200000022-22-2200-2-2-22-22-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000002-200−i2i2−i2i2i2−i2i2−i2000000000000
χ522-22-2-22-2200000022-22-2200-2-2-22-22-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000002-200i2−i2i2−i2−i2i2−i2i2000000000000
χ532-2-2-22-2220000222-20000-2-2-22002-2-22200-2000000002i−2i2i−2i−2i2i−2i2i00002-2000000002i−2i−2i2i000000000000
χ542-2-2-22-2220000222-20000-2-2-22002-2-22200-200000000−2i2i−2i2i2i−2i2i−2i00002-200000000−2i2i2i−2i000000000000
χ552-2-2-22-2220000222-20000-2-2-2200-222-2200-2000000002i−2i2i−2i−2i2i−2i2i0000-2200000000−2i2i2i−2i000000000000
χ562-2-2-22-2220000222-20000-2-2-2200-222-2200-200000000−2i2i−2i2i2i−2i2i−2i0000-22000000002i−2i−2i2i000000000000
χ572-2-2-22-2220000-2-22-2000022-22002-2-22-20022-22-2-22-22000000000000-2200002-2-220000000000000000
χ582-2-2-22-2220000-2-22-2000022-22002-2-22-2002-22-222-22-2000000000000-220000-222-20000000000000000
χ592-2-2-22-2220000-2-22-2000022-2200-222-2-20022-22-2-22-220000000000002-20000-222-20000000000000000
χ602-2-2-22-2220000-2-22-2000022-2200-222-2-2002-22-222-22-20000000000002-200002-2-220000000000000000
χ61444-44-4-4-44-4-44000000000000000000000022-2-2-2-22222-2-2-2-222000000000000000000000000000000
χ62444-44-4-4-44-4-440000000000000000000000-2-22222-2-2-2-22222-2-2000000000000000000000000000000
χ63444-44-4-4-4-444-4000000000000000000000022-2-2-2-222-2-22222-2-2000000000000000000000000000000
χ64444-44-4-4-4-444-40000000000000000000000-2-22222-2-222-2-2-2-222000000000000000000000000000000
χ6544-44-4-4-444i4i−4i−4i00-44000000-440000000−4i4i00000000000000000000000000000000000000000000000
χ6644-44-4-4-44−4i−4i4i4i00-44000000-4400000004i−4i00000000000000000000000000000000000000000000000
χ6744-4-4-444-44i−4i4i−4i-4400−4i−4i4i4i-440000000000000000000000000000000000000000000000000000000000
χ6844-4-4-444-4−4i4i−4i4i-44004i4i−4i−4i-440000000000000000000000000000000000000000000000000000000000
χ694-444-4-44-400004-4000000-44000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ704-444-4-44-400004-4000000-4400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ714-444-4-44-40000-440000004-40000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ724-444-4-44-40000-440000004-4000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ734-44-4-44-44000000-4-44-44-40044-44000000000000000000000000000000000000000000000000000000
χ744-44-4-44-44000000-4-4-44-4400444-4000000000000000000000000000000000000000000000000000000
χ754-4-4444-4-4000000004i−4i−4i4i000000000000002-2-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ764-4-4444-4-4000000004i−4i−4i4i00000000000000-222-2-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ774-4-4444-4-400000000−4i4i4i−4i000000000000002-2-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ784-4-4444-4-400000000−4i4i4i−4i00000000000000-222-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ794-4-4-44-444000044-440000-4-44-4000000-40040000000000000000000000000000000000000000000000
χ804-4-4-44-4440000-4-4-440000444-4000000400-40000000000000000000000000000000000000000000000

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