Finite Group Databasebeta

← Group #10868055

Character table — Group #10868055

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order122222223444466666664488881212121244444444444881212121224242424242424244444444488884121212121212121224444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111-1
χ3111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-111-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-11111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-111-1-1111
χ911111111111111111111-1-1111111111111-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-111-1-1-1-111-111-1-1-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-11111-1-1-1-1-111-1-11
χ1111111111111111111111-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-1-11111-1-1111-1-111-1
χ1311111111111111111111-1-1-1-1-1-111111111-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1-1111111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11-1-111-1-111-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111111111-111-1-111-1-11-1-1-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-111-1-11111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-22222-20000000022-2-20000000022-2-200000000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-20000000022-2-200000000-2-2220000000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222200000000-2-22200000000-2-2-2-20000000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000-2-22200000000222200000000000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-100002-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000222-2-2-2-2-2-2-1-1-1-1111111110000000000002-1-1-1-1111100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-100002-2-22222-2-2-1-1-1-111111111000000000000-21111-1-1-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-22222-2-2-2-21111-1-1-1-11111000000000000-2-1-11111-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-2-2-222-2-21111-1-1-1-11111000000000000211-1-1-1-11100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-222-2-2222211111111-1-1-1-1000000000000-2-1-111-1-11100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-222-2-22211111111-1-1-1-1000000000000211-1-111-1-100000000
χ2922-222-2-2-22-22-22-222-2-2-220000002-22-2000002i−2i00000000000000000000002i2i−2i−2i22-2-202i−2i00000000000000
χ3022-222-2-2-22-22-22-222-2-2-220000002-22-2000002i−2i0000000000000000000000−2i−2i2i2i-2-22202i−2i00000000000000
χ3122-222-2-2-22-22-22-222-2-2-220000002-22-200000−2i2i00000000000000000000002i2i−2i−2i-2-2220−2i2i00000000000000
χ3222-222-2-2-22-22-22-222-2-2-220000002-22-200000−2i2i0000000000000000000000−2i−2i2i2i22-2-20−2i2i00000000000000
χ3322-2-2-22-2220000-22-222-2-22i−2i22−2−2000022-2-20000000−i2i22i−2i0022−2−2−i2−i2i2i22i−2i0000002−22−200000000000000−i2i20
χ3422-2-2-22-2220000-22-222-2-22i−2i22−2−20000-2-2220000000−i2i22i−2i0022−2−2−i2−i2i2i2−2i2i000000−22−2200000000000000i2−i20
χ3522-2-2-22-2220000-22-222-2-22i−2i−2−222000022-2-20000000i2−i22i−2i00−2−222i2i2−i2−i22i−2i000000−22−2200000000000000i2−i20
χ3622-2-2-22-2220000-22-222-2-22i−2i−2−2220000-2-2220000000i2−i22i−2i00−2−222i2i2−i2−i2−2i2i0000002−22−200000000000000−i2i20
χ3722-2-2-22-2220000-22-222-2-2−2i2i22−2−2000022-2-20000000i2−i2−2i2i0022−2−2i2i2−i2−i2−2i2i0000002−22−200000000000000i2−i20
χ3822-2-2-22-2220000-22-222-2-2−2i2i22−2−20000-2-2220000000i2−i2−2i2i0022−2−2i2i2−i2−i22i−2i000000−22−2200000000000000−i2i20
χ3922-2-2-22-2220000-22-222-2-2−2i2i−2−222000022-2-20000000−i2i2−2i2i00−2−222−i2−i2i2i2−2i2i000000−22−2200000000000000−i2i20
χ4022-2-2-22-2220000-22-222-2-2−2i2i−2−2220000-2-2220000000−i2i2−2i2i00−2−222−i2−i2i2i22i−2i0000002−22−200000000000000i2−i20
χ412-222-22-2-222-2-22-2-2-22-22200000022-2-22i−2i2i−2i000002i−2i00000000000000002i−2i00000000000002i−2i000002-2000
χ422-222-22-2-222-2-22-2-2-22-22200000022-2-22i−2i2i−2i00000−2i2i00000000000000002i−2i0000000000000−2i2i00000-22000
χ432-222-22-2-222-2-22-2-2-22-22200000022-2-2−2i2i−2i2i000002i−2i0000000000000000−2i2i00000000000002i−2i00000-22000
χ442-222-22-2-222-2-22-2-2-22-22200000022-2-2−2i2i−2i2i00000−2i2i0000000000000000−2i2i0000000000000−2i2i000002-2000
χ452-222-22-2-22-222-2-2-2-22-222000000-2-2222i−2i2i−2i0002-2000000000000000000−2i2i2i−2i2i−2i000000000002-200000000
χ462-222-22-2-22-222-2-2-2-22-222000000-2-2222i−2i2i−2i000-22000000000000000000−2i2i−2i2i−2i2i00000000000-2200000000
χ472-222-22-2-22-222-2-2-2-22-222000000-2-222−2i2i−2i2i0002-20000000000000000002i−2i−2i2i−2i2i000000000002-200000000
χ482-222-22-2-22-222-2-2-2-22-222000000-2-222−2i2i−2i2i000-220000000000000000002i−2i2i−2i2i−2i00000000000-2200000000
χ492-2-22-2-222222-2-22-2-2-22-22002i−2i2i−2i-222-2000000000000000002i−2i2i−2i000000002-2-22000000000000002i−2i00000
χ502-2-22-2-222222-2-22-2-2-22-22002i−2i2i−2i-222-2000000000000000002i−2i2i−2i00000000-222-200000000000000−2i2i00000
χ512-2-22-2-222222-2-22-2-2-22-2200−2i2i−2i2i-222-200000000000000000−2i2i−2i2i000000002-2-2200000000000000−2i2i00000
χ522-2-22-2-222222-2-22-2-2-22-2200−2i2i−2i2i-222-200000000000000000−2i2i−2i2i00000000-222-2000000000000002i−2i00000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022220000-400000000-2-2220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000040000000022-2-20000000000000000000000000000000000000
χ55444-4-4-44-44000044-4-4-44-4000000000000000000000000000000000000000000022−22−222200000000000000000
χ56444-4-4-44-44000044-4-4-44-40000000000000000000000000000000000000000000−222222−2200000000000000000
χ5744-444-4-4-444-44-4-444-4-4-44000000-44-44000000000000000000000000000000000000000000000000000000
χ5844-444-4-4-4-24-44-42-2-2222-20000002-22-2000000000000000000000000000000000000000023−23000000000000
χ5944-444-4-4-4-24-44-42-2-2222-20000002-22-20000000000000000000000000000000000000000−2323000000000000
χ6044-444-4-4-4-2-44-442-2-2222-2000000-22-22000004i−4i0000000000000000000000000000000−2i2i00000000000000
χ6144-444-4-4-4-2-44-442-2-2222-2000000-22-2200000−4i4i00000000000000000000000000000002i−2i00000000000000
χ6244-4-4-44-44-200002-22-2-2224i−4i2222−22−22000000000000000−2i22i2−2i2i00−2−222i2i2−i2−i200000000000000000000000000000
χ6344-4-4-44-44-200002-22-2-2224i−4i−22−2222220000000000000002i2−2i2−2i2i0022−2−2−i2−i2i2i200000000000000000000000000000
χ6444-4-4-44-44-200002-22-2-222−4i4i2222−22−220000000000000002i2−2i22i−2i00−2−222−i2−i2i2i200000000000000000000000000000
χ6544-4-4-44-44-200002-22-2-222−4i4i−22−222222000000000000000−2i22i22i−2i0022−2−2i2i2−i2−i200000000000000000000000000000
χ664-444-44-4-4-24-4-44222-22-2-2000000-2-2220000000004i−4i0000000000000000000000000000000−2i2i0000000000
χ674-444-44-4-4-24-4-44222-22-2-2000000-2-222000000000−4i4i00000000000000000000000000000002i−2i0000000000
χ684-444-44-4-4-2-444-4222-22-2-200000022-2-200000004-400000000000000000000000000000000000-2200000000
χ694-444-44-4-4-2-444-4222-22-2-200000022-2-20000000-44000000000000000000000000000000000002-200000000
χ704-44-44-4-4440000-4-44-444-400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ714-44-44-4-4440000-4-44-444-4002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ724-44-44-4-44-2000022-22-2-2200−2i22i22i2−2i2000000000000000000023−23i2−i2−i2i2i6−i6i6−i600000000000000000000000000000
χ734-44-44-4-44-2000022-22-2-2200−2i22i22i2−2i20000000000000000000−2323i2−i2−i2i2−i6i6−i6i600000000000000000000000000000
χ744-44-44-4-44-2000022-22-2-22002i2−2i2−2i22i2000000000000000000023−23−i2i2i2−i2−i6i6−i6i600000000000000000000000000000
χ754-44-44-4-44-2000022-22-2-22002i2−2i2−2i22i20000000000000000000−2323−i2i2i2−i2i6−i6i6−i600000000000000000000000000000
χ764-4-44-4-4444-4-4444-4-4-44-440000004-4-44000000000000000000000000000000000000000000000000000000
χ774-4-44-4-444-244-4-4-2222-22-2004i−4i4i−4i2-2-2200000000000000000−2i2i−2i2i000000000000000000000000000000000
χ784-4-44-4-444-244-4-4-2222-22-200−4i4i−4i4i2-2-22000000000000000002i−2i2i−2i000000000000000000000000000000000
χ794-4-44-4-444-2-4-444-2222-22-2000000-222-200000000000000000000023−23−232300000000000000000000000000000
χ804-4-44-4-444-2-4-444-2222-22-2000000-222-2000000000000000000000−232323−2300000000000000000000000000000
χ814-4-4-4444-4400004-444-4-4-400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ824-4-4-4444-4400004-444-4-4-40000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ83888-8-8-88-8-40000-4-4444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-8888-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000

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