Finite Group Databasebeta

← Group #10858761

Character table — Group #10858761

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order1222222234444666666644888812121212222222444448812121212242424242424242444444444888846612121212121244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11
χ51111111111111111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-11-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-111111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-111-1
χ911111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111111-1-111-1-111-1-1-1-1-11
χ1011111111111111111111-1-1111111111111-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-111-1-111-1-1-111-1-1-1
χ1111111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-111111-1
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1111
χ1311111111111111111111-1-1-1-1-1-11111111111-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11-1-11111-1-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-111-1-1-1-111-1-11-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-1-11111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-2222200-200000022-2-200000000-2-2220000000000000000000-200000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-200-200000022-2-20000000022-2-20000000000000000000200000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222002000000-2-22200000000-2-2-2-20000000000000000000200000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000-2-2220000000022220000000000000000000-200000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-22-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022222-2-2-2-2-1-1-1-111111111000000000000-2-1-1-1-1111100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-22-2-222-2-2-1-1-1-11111111100000000000021111-1-1-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-2-2-2-2-2-2-21111-1-1-1-111110000000000002-1-111-1-11100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-22222-2-21111-1-1-1-11111000000000000-211-1-111-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-2-2222211111111-1-1-1-1000000000000-2-1-11111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-222-2-22211111111-1-1-1-1000000000000211-1-1-1-11100000000
χ2922-222-2-2-2222-2-222-22-2-2-200000022-2-222-2-22-200000000000000000002-2000000000002-20000002-2000000
χ3022-222-2-2-2222-2-222-22-2-2-200000022-2-222-2-2-2200000000000000000002-200000000000-22000000-22000000
χ3122-222-2-2-2222-2-222-22-2-2-200000022-2-2-2-2222-20000000000000000000-22000000000002-2000000-22000000
χ3222-222-2-2-2222-2-222-22-2-2-200000022-2-2-2-222-220000000000000000000-2200000000000-220000002-2000000
χ3322-222-2-2-22-2-22222-22-2-2-2000000-2-22222-2-20002i−2i0000000000000000-22002i2i−2i−2i00000002i−2i000000000000
χ3422-222-2-2-22-2-22222-22-2-2-2000000-2-22222-2-2000−2i2i0000000000000000-2200−2i−2i2i2i0000000−2i2i000000000000
χ3522-222-2-2-22-2-22222-22-2-2-2000000-2-222-2-2220002i−2i00000000000000002-200−2i−2i2i2i00000002i−2i000000000000
χ3622-222-2-2-22-2-22222-22-2-2-2000000-2-222-2-222000−2i2i00000000000000002-2002i2i−2i−2i0000000−2i2i000000000000
χ372-222-2-22-222-22-2-2-2-222-220000002-22-20000000002-20000000000000000002i−2i2i−2i2i2i−2i−2i00000002-200000000
χ382-222-2-22-222-22-2-2-2-222-220000002-22-20000000002-2000000000000000000−2i2i−2i2i−2i−2i2i2i00000002-200000000
χ392-222-2-22-222-22-2-2-2-222-220000002-22-2000000000-220000000000000000002i−2i2i−2i−2i−2i2i2i0000000-2200000000
χ402-222-2-22-222-22-2-2-2-222-220000002-22-2000000000-22000000000000000000−2i2i−2i2i2i2i−2i−2i0000000-2200000000
χ412-22-22-2-22200002-2-2-222-22-2−i2−i2i2i200002-22-20000000−i2i22-200−i2−i2i2i2−i2−i2i2i2002-20000−i2i2−i2i200000000000000−i2i20
χ422-22-22-2-22200002-2-2-222-22-2−i2−i2i2i20000-22-220000000−i2i22-200−i2−i2i2i2−i2−i2i2i200-220000i2−i2i2−i200000000000000i2−i20
χ432-22-22-2-22200002-2-2-222-22-2i2i2−i2−i200002-22-20000000i2−i22-200i2i2−i2−i2i2i2−i2−i2002-20000i2−i2i2−i200000000000000i2−i20
χ442-22-22-2-22200002-2-2-222-22-2i2i2−i2−i20000-22-220000000i2−i22-200i2i2−i2−i2i2i2−i2−i200-220000−i2i2−i2i200000000000000−i2i20
χ452-22-22-2-22200002-2-2-222-2-22−i2−i2i2i200002-22-20000000i2−i2-2200−i2−i2i2i2i2i2−i2−i200-220000−i2i2−i2i200000000000000i2−i20
χ462-22-22-2-22200002-2-2-222-2-22−i2−i2i2i20000-22-220000000i2−i2-2200−i2−i2i2i2i2i2−i2−i2002-20000i2−i2i2−i200000000000000−i2i20
χ472-22-22-2-22200002-2-2-222-2-22i2i2−i2−i200002-22-20000000−i2i2-2200i2i2−i2−i2−i2−i2i2i200-220000i2−i2i2−i200000000000000−i2i20
χ482-22-22-2-22200002-2-2-222-2-22i2i2−i2−i20000-22-220000000−i2i2-2200i2i2−i2−i2−i2−i2i2i2002-20000−i2i2−i2i200000000000000i2−i20
χ492-2-22-22-222-222-2-2-222-22-2002i−2i2i−2i-222-2000000000000000002i−2i2i−2i000000002-2-2200000000000000002i−2i000
χ502-2-22-22-222-222-2-2-222-22-2002i−2i2i−2i-222-2000000000000000002i−2i2i−2i00000000-222-20000000000000000−2i2i000
χ512-2-22-22-222-222-2-2-222-22-200−2i2i−2i2i-222-200000000000000000−2i2i−2i2i000000002-2-220000000000000000−2i2i000
χ522-2-22-22-222-222-2-2-222-22-200−2i2i−2i2i-222-200000000000000000−2i2i−2i2i00000000-222-200000000000000002i−2i000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-24400002222000000-4000000-2-2220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000000400000022-2-20000000000000000000000000000000000000
χ55444-4-44-4-440000-444-44-4-4000000000000000000000000000000000000000000022−22−222200000000000000000
χ56444-4-44-4-440000-444-44-4-40000000000000000000000000000000000000000000−222222−2200000000000000000
χ5744-444-4-4-4-244-4-4-2-22-2222000000-2-22200004-400000000000000000000000000000000-2200000000000000
χ5844-444-4-4-4-244-4-4-2-22-2222000000-2-2220000-44000000000000000000000000000000002-200000000000000
χ5944-444-4-4-4-2-4-444-2-22-222200000022-2-200000004i−4i0000000000000000000000000000000−2i2i000000000000
χ6044-444-4-4-4-2-4-444-2-22-222200000022-2-20000000−4i4i00000000000000000000000000000002i−2i000000000000
χ6144-4-4-4-44440000-44-4-4-4440022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ6244-4-4-4-44440000-44-4-4-44400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ6344-4-4-4-444-200002-2222-2-20022−22−22220000000000000000000−2i32i3−222−2i6−i6i6−i600000000000000000000000000000
χ6444-4-4-4-444-200002-2222-2-20022−22−222200000000000000000002i3−2i3−222−2−i6i6−i6i600000000000000000000000000000
χ6544-4-4-4-444-200002-2222-2-200−222222−220000000000000000000−2i32i32−2−22−i6i6−i6i600000000000000000000000000000
χ6644-4-4-4-444-200002-2222-2-200−222222−2200000000000000000002i3−2i32−2−22i6−i6i6−i600000000000000000000000000000
χ674-444-4-44-44-44-44-4-4-444-44000000-44-44000000000000000000000000000000000000000000000000000000
χ684-444-4-44-4-24-44-4222-2-22-2000000-22-220000000004-4000000000000000000000000000000000-2200000000
χ694-444-4-44-4-24-44-4222-2-22-2000000-22-22000000000-440000000000000000000000000000000002-200000000
χ704-444-4-44-4-2-44-44222-2-22-20000002-22-2000000000000000000000000000000000000000000−2i32i30000000000
χ714-444-4-44-4-2-44-44222-2-22-20000002-22-20000000000000000000000000000000000000000002i3−2i30000000000
χ724-44-44-4-44-20000-2222-2-224-4−2i2−2i22i22i2000000000000000−2i22i2-2200i2i2−i2−i2i2i2−i2−i200000000000000000000000000000
χ734-44-44-4-44-20000-2222-2-224-42i22i2−2i2−2i20000000000000002i2−2i2-2200−i2−i2i2i2−i2−i2i2i200000000000000000000000000000
χ744-44-44-4-44-20000-2222-2-22-44−2i2−2i22i22i20000000000000002i2−2i22-200i2i2−i2−i2−i2−i2i2i200000000000000000000000000000
χ754-44-44-4-44-20000-2222-2-22-442i22i2−2i2−2i2000000000000000−2i22i22-200−i2−i2i2i2i2i2−i2−i200000000000000000000000000000
χ764-4-44-44-4444-4-44-4-444-44-40000004-4-44000000000000000000000000000000000000000000000000000000
χ774-4-44-44-44-24-4-4422-2-22-22000000-222-200000000000000000000023−23−232300000000000000000000000000000
χ784-4-44-44-44-24-4-4422-2-22-22000000-222-2000000000000000000000−232323−2300000000000000000000000000000
χ794-4-44-44-44-2-444-422-2-22-22004i−4i4i−4i2-2-2200000000000000000−2i2i−2i2i000000000000000000000000000000000
χ804-4-44-44-44-2-444-422-2-22-2200−4i4i−4i4i2-2-22000000000000000002i−2i2i−2i000000000000000000000000000000000
χ814-4-4-4444-4400004-44-4-4-4400000000004-4-4400000000000000000000000000000000000000000000000000
χ824-4-4-4444-4400004-44-4-4-440000000000-444-400000000000000000000000000000000000000000000000000
χ83888-8-88-8-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-8888-8-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000

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