Finite Group Databasebeta

← Group #349535

Character table — Group #349535

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444422224444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111111111111-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111-1-1-1-1111-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1111111-11111-1-1-1-111-1-1-1-111-11
χ121111111111111-1-1-1-1111-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1111111-1-1-1-1-11111-1-11111-1-11-1
χ131111111111111-1-1-1-1111-1-11-1-1-1-11111-1-11111-1-1-1-11-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111-1-1-1-1111-1-11-1-1-1-11111-1-11111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-111-11111-1-1-1-1-1-111-1-1111-1
χ161111111111111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222-2-22222-2-2222-222220000-2-222220000-20000-2-2-2-200000000-2000000000000000000
χ1822222222222-2-22222-2-2222-2-2-2-2-20000-2-2-2-2-2-20000-20000222200000000-2000000000000000000
χ1922222222222-2-2-2-2-2-2-2-22-2-2-22222000022-2-2-2-20000-20000-2-222000000002000000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-200002222220000-2000022-2-2000000002000000000000000000
χ2122222222-2-2-222222222-2-2-2-2000022222200002222-200000000-2-20000-2-2-2000000000000000000
χ2222222222-2-2-222222222-2-2-2-20000-2-2-2-2220000-2-2-2-2-20000000022000022-2000000000000000000
χ2322222222-2-2-222-2-2-2-222-222-200002222-2-20000-2-2-2-2-200000000-2-20000222000000000000000000
χ2422222222-2-2-222-2-2-2-222-222-20000-2-2-2-2-2-200002222-200000000220000-2-22000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-2200000000-2-200000000222-2-200000022-2-2002000000000000000000
χ2622222222-2-2-2-2-22222-2-2-2-2-2200000000-2-2000000002-2-222000000-2-222002000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222000000002200000000222-2-2000000-2-22200-2000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22220000000022000000002-2-22200000022-2-200-2000000000000000000
χ29222-22-2-2-222-2220000-2-2-200222-2-222-2-20000000000-22-22-22-2002-20000000000000000000000000
χ30222-22-2-2-222-2220000-2-2-200222-2-2-2-2220000000000-2-22-222-200-220000000000000000000000000
χ31222-22-2-2-222-2220000-2-2-2002-2-22222-2-20000000000-2-22-22-22002-20000000000000000000000000
χ32222-22-2-2-222-2220000-2-2-2002-2-222-2-2220000000000-22-22-2-2200-220000000000000000000000000
χ33222-22-2-2-222-2-2-2000022-200-222-2-200000000002i2i−2i−2i20000-2200002i−2i2i−2i2i−2i0000000000000000000
χ34222-22-2-2-222-2-2-2000022-200-222-2-20000000000−2i−2i2i2i20000-220000−2i2i−2i2i−2i2i0000000000000000000
χ35222-22-2-2-222-2-2-2000022-200-2-2-22200000000002i2i−2i−2i200002-20000−2i2i−2i2i2i−2i0000000000000000000
χ36222-22-2-2-222-2-2-2000022-200-2-2-2220000000000−2i−2i2i2i200002-200002i−2i2i−2i−2i2i0000000000000000000
χ37222-22-2-2-2-2-22220000-2-2200-2000022-2-2002i2i−2i−2i000020000002i−2i-222i−2i−2i2i000000000000000000000
χ38222-22-2-2-2-2-22220000-2-2200-2000022-2-200−2i−2i2i2i00002000000−2i2i-22−2i2i2i−2i000000000000000000000
χ39222-22-2-2-2-2-22220000-2-2200-20000-2-222002i2i−2i−2i000020000002i−2i2-2−2i2i2i−2i000000000000000000000
χ40222-22-2-2-2-2-22220000-2-2200-20000-2-22200−2i−2i2i2i00002000000−2i2i2-22i−2i−2i2i000000000000000000000
χ41222-22-2-2-2-2-22-2-2000022200200000000002i2i−2i−2i2i2i−2i−2i-22-2-2200−2i2i000000−2i2i0000000000000000000
χ42222-22-2-2-2-2-22-2-2000022200200000000002i2i−2i−2i−2i−2i2i2i-2-222-200−2i2i0000002i−2i0000000000000000000
χ43222-22-2-2-2-2-22-2-200002220020000000000−2i−2i2i2i2i2i−2i−2i-2-222-2002i−2i000000−2i2i0000000000000000000
χ44222-22-2-2-2-2-22-2-200002220020000000000−2i−2i2i2i−2i−2i2i2i-22-2-22002i−2i0000002i−2i0000000000000000000
χ4522-22-22-2-22-2-20022-2-20022-202i−2i2i−2i0000002i−2i2i−2i0000000000000000000000i2i2−i2−i2i2i2−i2−i22−22−2000000
χ4622-22-22-2-22-2-20022-2-20022-202i−2i2i−2i0000002i−2i2i−2i0000000000000000000000−i2−i2i2i2−i2−i2i2i2−22−22000000
χ4722-22-22-2-22-2-20022-2-20022-20−2i2i−2i2i000000−2i2i−2i2i0000000000000000000000i2i2−i2−i2i2i2−i2−i2−22−22000000
χ4822-22-22-2-22-2-20022-2-20022-20−2i2i−2i2i000000−2i2i−2i2i0000000000000000000000−i2−i2i2i2−i2−i2i2i22−22−2000000
χ4922-22-22-2-22-2-200-2-222002-2202i−2i2i−2i000000−2i2i−2i2i0000000000000000000000i2i2−i2−i2−i2−i2i2i22−2−22000000
χ5022-22-22-2-22-2-200-2-222002-2202i−2i2i−2i000000−2i2i−2i2i0000000000000000000000−i2−i2i2i2i2i2−i2−i2−222−2000000
χ5122-22-22-2-22-2-200-2-222002-220−2i2i−2i2i0000002i−2i2i−2i0000000000000000000000i2i2−i2−i2−i2−i2i2i2−222−2000000
χ5222-22-22-2-22-2-200-2-222002-220−2i2i−2i2i0000002i−2i2i−2i0000000000000000000000−i2−i2i2i2i2i2−i2−i22−2−22000000
χ532-222-2-2-220002-22i−2i2i−2i2-2000000002i−2i2i−2i2i−2i00002-22-2000000000000000000i2−i2i2−i22−22−200002−2i2−i200
χ542-222-2-2-220002-22i−2i2i−2i2-2000000002i−2i2i−2i2i−2i00002-22-2000000000000000000−i2i2−i2i2−22−220000−22−i2i200
χ552-222-2-2-220002-22i−2i2i−2i2-200000000−2i2i−2i2i2i−2i0000-22-22000000000000000000i2−i2i2−i22−22−20000−22−i2i200
χ562-222-2-2-220002-22i−2i2i−2i2-200000000−2i2i−2i2i2i−2i0000-22-22000000000000000000−i2i2−i2i2−22−2200002−2i2−i200
χ572-222-2-2-220002-2−2i2i−2i2i2-2000000002i−2i2i−2i−2i2i0000-22-22000000000000000000i2−i2i2−i2−22−2200002−2−i2i200
χ582-222-2-2-220002-2−2i2i−2i2i2-2000000002i−2i2i−2i−2i2i0000-22-22000000000000000000−i2i2−i2i22−22−20000−22i2−i200
χ592-222-2-2-220002-2−2i2i−2i2i2-200000000−2i2i−2i2i−2i2i00002-22-2000000000000000000i2−i2i2−i2−22−220000−22i2−i200
χ602-222-2-2-220002-2−2i2i−2i2i2-200000000−2i2i−2i2i−2i2i00002-22-2000000000000000000−i2i2−i2i22−22−200002−2−i2i200
χ6144-44-44-4-4-4440044-4-400-4-440000000000000000000000000000000000000000000000000000000
χ6244-44-44-4-4-44400-4-44400-44-40000000000000000000000000000000000000000000000000000000
χ6344-4-4-4-4444-4400000000-40004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-4400000000-4000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6544-4-4-4-444-44-400000000400000000000004-4-440000000000000000000000000000000000000000
χ6644-4-4-4-444-44-40000000040000000000000-444-40000000000000000000000000000000000000000
χ674-444-4-4-44000-444i−4i4i−4i-44000000000000−4i4i00000000000000000000000000000000000000000000
χ684-444-4-4-44000-44−4i4i−4i4i-440000000000004i−4i00000000000000000000000000000000000000000000
χ694-44-4-444-40004-40000-44000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ704-44-4-444-40004-40000-4400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ714-44-4-444-4000-4400004-40000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ724-44-4-444-4000-4400004-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ734-4-444-44-4000004i−4i−4i4i0000000000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ744-4-444-44-4000004i−4i−4i4i000000000000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ754-4-444-44-400000−4i4i4i−4i0000000000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ764-4-444-44-400000−4i4i4i−4i000000000000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ778-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000

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