Finite Group Databasebeta

← Group #10896471

Character table — Group #10896471

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444466666666888888888888888888888888121212121616161616161616242424242424242424242424
order122222223444466666664444121212124444444444444444888812121212242424242424242444441212121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-111
χ1111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1
χ1311111111111111111111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-111
χ1411111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-111-1-1
χ1611111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-111-1-1-1-111
χ17222222222-2-2-2-2222222222-2-2-2-2-2-22222-2-2-2-2000000000000-2-2220000000022-2-200000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-22222000000000000-2-22200000000-2-22200000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-22222222200000000000022-2-200000000-2-2-2-200000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2-2-2-2-200000000000022-2-200000000222200000000000000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000222222222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1000000002222-2-2-2-2-2-2-2-2-1-1-1-11111111100001111-1-1-1-1000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-22222-2-2-2-2-1-1-1-1111111110000-1-1-1-11111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1000011111111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000000022-2-222-2-222-2-21111-1-1-1-11111000011-1-1-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000000022-2-2-2-222-2-22211111111-1-1-1-10000-1-111-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-22222-2-2-2-22211111111-1-1-1-1000011-1-111-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-100000000-2-222-2-22222-2-21111-1-1-1-111110000-1-11111-1-1000000000000
χ29222-2-2-22-2222-2-22-22-22-2-2000022-2-222-2-200000000002-20000000000000000002-22-2000000002-200000000
χ30222-2-2-22-2222-2-22-22-22-2-2000022-2-222-2-20000000000-220000000000000000002-2-2200000000-2200000000
χ31222-2-2-22-2222-2-22-22-22-2-2000022-2-2-2-22200000000002-2000000000000000000-222-200000000-2200000000
χ32222-2-2-22-2222-2-22-22-22-2-2000022-2-2-2-2220000000000-22000000000000000000-22-22000000002-200000000
χ33222-2-2-22-22-2-2222-22-22-2-20000-2-22222-2-2000000002i−2i00000000000000000000-22002i−2i00002i−2i0000000000
χ34222-2-2-22-22-2-2222-22-22-2-20000-2-22222-2-200000000−2i2i00000000000000000000-2200−2i2i0000−2i2i0000000000
χ35222-2-2-22-22-2-2222-22-22-2-20000-2-222-2-222000000002i−2i000000000000000000002-2002i−2i0000−2i2i0000000000
χ36222-2-2-22-22-2-2222-22-22-2-20000-2-222-2-22200000000−2i2i000000000000000000002-200−2i2i00002i−2i0000000000
χ3722-2-2-22-2222-22-2-2-222-22-200002-22-200002i2i−2i−2i002i−2i000000000000000000002i−2i000000002i−2i00002-2000000
χ3822-2-2-22-2222-22-2-2-222-22-200002-22-200002i2i−2i−2i00−2i2i000000000000000000002i−2i00000000−2i2i0000-22000000
χ3922-2-2-22-2222-22-2-2-222-22-200002-22-20000−2i−2i2i2i002i−2i00000000000000000000−2i2i000000002i−2i0000-22000000
χ4022-2-2-22-2222-22-2-2-222-22-200002-22-20000−2i−2i2i2i00−2i2i00000000000000000000−2i2i00000000−2i2i00002-2000000
χ4122-2-2-22-222-22-22-2-222-22-20000-22-2200002i2i−2i−2i2i−2i0000000000000000000000−2i2i0000002i−2i000000002-20000
χ4222-2-2-22-222-22-22-2-222-22-20000-22-2200002i2i−2i−2i−2i2i0000000000000000000000−2i2i000000−2i2i00000000-220000
χ4322-2-2-22-222-22-22-2-222-22-20000-22-220000−2i−2i2i2i2i−2i00000000000000000000002i−2i0000002i−2i00000000-220000
χ4422-2-2-22-222-22-22-2-222-22-20000-22-220000−2i−2i2i2i−2i2i00000000000000000000002i−2i000000−2i2i000000002-20000
χ452-22-22-2-22200002-2-22-2-22002-200002-22-22-22-200000000−i2i2−i2i22-200−i2−i2i2i2−i2−i2i2i200000000000000000000−i2i2−i2i2
χ462-22-22-2-22200002-2-22-2-22002-200002-22-22-22-200000000i2−i2i2−i22-200i2i2−i2−i2i2i2−i2−i200000000000000000000i2−i2i2−i2
χ472-22-22-2-22200002-2-22-2-22002-20000-22-22-22-2200000000−i2i2−i2i22-200−i2−i2i2i2−i2−i2i2i200000000000000000000i2−i2i2−i2
χ482-22-22-2-22200002-2-22-2-22002-20000-22-22-22-2200000000i2−i2i2−i22-200i2i2−i2−i2i2i2−i2−i200000000000000000000−i2i2−i2i2
χ492-22-22-2-22200002-2-22-2-2200-2200002-22-2-22-2200000000−i2i2i2−i2-2200−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i2
χ502-22-22-2-22200002-2-22-2-2200-2200002-22-2-22-2200000000i2−i2−i2i2-2200i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i2
χ512-22-22-2-22200002-2-22-2-2200-220000-22-222-22-200000000−i2i2i2−i2-2200−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i2
χ522-22-22-2-22200002-2-22-2-2200-220000-22-222-22-200000000i2−i2−i2i2-2200i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i2
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-422220000000000000000000022-2-200000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222200000000000000000000-2-22200000000000000000000000000000000
χ55444-4-4-44-4-244-4-4-22-22-2220000-2-222000000000000004-400000000000000000000-22000000000000000000
χ56444-4-4-44-4-244-4-4-22-22-2220000-2-22200000000000000-44000000000000000000002-2000000000000000000
χ57444-4-4-44-4-2-4-444-22-22-222000022-2-20000000000004i−4i000000000000000000000000−2i2i0000000000000000
χ58444-4-4-44-4-2-4-444-22-22-222000022-2-2000000000000−4i4i0000000000000000000000002i−2i0000000000000000
χ5944-444-4-4-444-4-44-444-4-4-4400004-4-4400000000000000000000000000000000000000000000000000000000
χ6044-444-4-4-44-444-4-444-4-4-440000-444-400000000000000000000000000000000000000000000000000000000
χ6144-444-4-4-4-24-4-442-2-2222-20000-222-200000000000000000000000023−2323−230000000000000000000000000000
χ6244-444-4-4-4-24-4-442-2-2222-20000-222-2000000000000000000000000−2323−23230000000000000000000000000000
χ6344-444-4-4-4-2-444-42-2-2222-200002-2-22000000000000000000000000000023−2323−23000000000000000000000000
χ6444-444-4-4-4-2-444-42-2-2222-200002-2-220000000000000000000000000000−2323−2323000000000000000000000000
χ6544-4-4-44-44-24-44-422-2-22-220000-22-2200000000004i−4i000000000000000000000000000000−2i2i000000000000
χ6644-4-4-44-44-24-44-422-2-22-220000-22-220000000000−4i4i0000000000000000000000000000002i−2i000000000000
χ6744-4-4-44-44-2-44-4422-2-22-2200002-22-2000000004i−4i000000000000000000000000000000−2i2i00000000000000
χ6844-4-4-44-44-2-44-4422-2-22-2200002-22-200000000−4i4i0000000000000000000000000000002i−2i00000000000000
χ694-444-44-4-44000044-4-4-44-4000000004-4-440000000000000000000000000000000000000000000000000000
χ704-444-44-4-44000044-4-4-44-400000000-444-40000000000000000000000000000000000000000000000000000
χ714-44-44-4-44-20000-222-222-2004-400000000000000000000−2i22i2−2i22i2-2200i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ724-44-44-4-44-20000-222-222-2004-4000000000000000000002i2−2i22i2−2i2-2200−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ734-44-44-4-44-20000-222-222-200-4400000000000000000000−2i22i22i2−2i22-200i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ744-44-44-4-44-20000-222-222-200-44000000000000000000002i2−2i2−2i22i22-200−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ754-4-44-4-44440000-44-444-4-40000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ764-4-44-4-44440000-44-444-4-4000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ774-4-4-4444-440000-4-4-4-44444-400000000000000000000000000004-400000000000000000000000000000000
χ784-4-4-4444-440000-4-4-4-4444-440000000000000000000000000000-4400000000000000000000000000000000
χ794-4-4-4444-4-200002222-2-2-24-40000000000000000000000000000-22i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ804-4-4-4444-4-200002222-2-2-24-40000000000000000000000000000-22−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ814-4-4-4444-4-200002222-2-2-2-4400000000000000000000000000002-2i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ824-4-4-4444-4-200002222-2-2-2-4400000000000000000000000000002-2−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ838-888-88-8-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-8-888-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000

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