Finite Group Databasebeta

← Group #10868012

Character table — Group #10868012

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order1222222234444666666644888812121212444422444448812121212242424242424242444444444888846612121212121224444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1111-1-111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-1-1-1-111111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-111-1-111-1
χ911111111111111111111-1-111111111111111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-11111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1-1-11111-111-1-1-1-11
χ1111111111111111111111-1-111111111-1-1-1-111-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-1-1-1-111111-1-11111-1
χ1311111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1111-1-1-1-111-1-1-1-1-1111
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111-1
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111-1-1-1-11111111-1-1-1
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-11111-1-11-1-1-1-1-1-11
χ17222222222-2-2-2-22222222220000-2-2-2-2222200-2000000-2-2220000000022-2-200000000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-200-2000000-2-22200000000-2-2220000000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2222200200000022-2-200000000-2-2-2-20000000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-200200000022-2-200000000222200000000000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-22-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000222-2-222-2-2-1-1-1-111111111000000000000-2-1-111-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-2222-2-2-2-2-1-1-1-111111111000000000000211-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-222-2-2-2-21111-1-1-1-11111000000000000-2-1-1-1-1111100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-2-2-222-2-21111-1-1-1-1111100000000000021111-1-1-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-2-2-2-22211111111-1-1-1-10000000000002-1-11111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-222222211111111-1-1-1-1000000000000-211-1-1-1-11100000000
χ2922-22-22-2-2200002-2-2-2-2222-222−2−200002i2i−2i−2i00000002−2002-222−2−222−2−22i−2i000000−i2−i2i2i200000000000000−i2i20
χ3022-22-22-2-2200002-2-2-2-2222-222−2−20000−2i−2i2i2i00000002−2002-222−2−222−2−2−2i2i000000i2i2−i2−i200000000000000i2−i20
χ3122-22-22-2-2200002-2-2-2-2222-2−2−22200002i2i−2i−2i0000000−22002-2−2−222−2−2222i−2i000000i2i2−i2−i200000000000000i2−i20
χ3222-22-22-2-2200002-2-2-2-2222-2−2−2220000−2i−2i2i2i0000000−22002-2−2−222−2−222−2i2i000000−i2−i2i2i200000000000000−i2i20
χ3322-22-22-2-2200002-2-2-2-222-2222−2−200002i2i−2i−2i0000000−2200-2222−2−2−2−222−2i2i000000−i2−i2i2i200000000000000i2−i20
χ3422-22-22-2-2200002-2-2-2-222-2222−2−20000−2i−2i2i2i0000000−2200-2222−2−2−2−2222i−2i000000i2i2−i2−i200000000000000−i2i20
χ3522-22-22-2-2200002-2-2-2-222-22−2−22200002i2i−2i−2i00000002−200-22−2−22222−2−2−2i2i000000i2i2−i2−i200000000000000−i2i20
χ3622-22-22-2-2200002-2-2-2-222-22−2−2220000−2i−2i2i2i00000002−200-22−2−22222−2−22i−2i000000−i2−i2i2i200000000000000i2−i20
χ3722-2-22-2-22222-2-222-22-2-2-20000002-2-222i−2i2i−2i000002i−2i00000000000000002i−2i00000000000002i−2i0002-200000
χ3822-2-22-2-22222-2-222-22-2-2-20000002-2-222i−2i2i−2i00000−2i2i00000000000000002i−2i0000000000000−2i2i000-2200000
χ3922-2-22-2-22222-2-222-22-2-2-20000002-2-22−2i2i−2i2i000002i−2i0000000000000000−2i2i00000000000002i−2i000-2200000
χ4022-2-22-2-22222-2-222-22-2-2-20000002-2-22−2i2i−2i2i00000−2i2i0000000000000000−2i2i0000000000000−2i2i0002-200000
χ4122-2-22-2-222-2-22222-22-2-2-2000000-222-22i−2i2i−2i2-2000000000000000000000−2i2i2i2i−2i−2i000002-200000000000000
χ4222-2-22-2-222-2-22222-22-2-2-2000000-222-22i−2i2i−2i-22000000000000000000000−2i2i−2i−2i2i2i00000-2200000000000000
χ4322-2-22-2-222-2-22222-22-2-2-2000000-222-2−2i2i−2i2i2-20000000000000000000002i−2i−2i−2i2i2i000002-200000000000000
χ4422-2-22-2-222-2-22222-22-2-2-2000000-222-2−2i2i−2i2i-220000000000000000000002i−2i2i2i−2i−2i00000-2200000000000000
χ452-2222-2-2-22-222-2-2-2-2222-2002-22-2-22-22000000000000000002-22-2000000002i−2i2i−2i00000000000000002i−2i000
χ462-2222-2-2-22-222-2-2-2-2222-2002-22-2-22-22000000000000000002-22-200000000−2i2i−2i2i0000000000000000−2i2i000
χ472-2222-2-2-22-222-2-2-2-2222-200-22-22-22-2200000000000000000-22-22000000002i−2i2i−2i0000000000000000−2i2i000
χ482-2222-2-2-22-222-2-2-2-2222-200-22-22-22-2200000000000000000-22-2200000000−2i2i−2i2i00000000000000002i−2i000
χ492-2-2-2222-222-22-2-2-222-2-2200000022-2-200000002i−2i000000000000000000002-2-222i−2i2i−2i0002i−2i000000000000
χ502-2-2-2222-222-22-2-2-222-2-2200000022-2-200000002i−2i00000000000000000000-222-2−2i2i−2i2i0002i−2i000000000000
χ512-2-2-2222-222-22-2-2-222-2-2200000022-2-20000000−2i2i000000000000000000002-2-22−2i2i−2i2i000−2i2i000000000000
χ522-2-2-2222-222-22-2-2-222-2-2200000022-2-20000000−2i2i00000000000000000000-222-22i−2i2i−2i000−2i2i000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-24400002222000000-400000022-2-20000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022220000004000000-2-2220000000000000000000000000000000000000
χ55444-4-4-44-4400004-44-44-4-400000000004-4-4400000000000000000000000000000000000000000000000000
χ56444-4-4-44-4400004-44-44-4-40000000000-444-400000000000000000000000000000000000000000000000000
χ5744-44-44-4-4-20000-22222-2-24-42222−22−2200000000000000022−2200-22−2−222−2−22200000000000000000000000000000
χ5844-44-44-4-4-20000-22222-2-24-4−22−222222000000000000000−222200-2222−2−222−2−200000000000000000000000000000
χ5944-44-44-4-4-20000-22222-2-2-442222−22−22000000000000000−2222002-2−2−22222−2−200000000000000000000000000000
χ6044-44-44-4-4-20000-22222-2-2-44−22−22222200000000000000022−22002-222−2−2−2−22200000000000000000000000000000
χ6144-4-44-4-44-244-4-4-2-22-2222000000-222-20000000004i−4i0000000000000000000000000000000−2i2i0000000000
χ6244-4-44-4-44-244-4-4-2-22-2222000000-222-2000000000−4i4i00000000000000000000000000000002i−2i0000000000
χ6344-4-44-4-44-2-4-444-2-22-22220000002-2-2200004-400000000000000000000000000000000-2200000000000000
χ6444-4-44-4-44-2-4-444-2-22-22220000002-2-220000-44000000000000000000000000000000002-200000000000000
χ654-4444-4-4-444-4-44-4-4-4444-40000004-44-4000000000000000000000000000000000000000000000000000000
χ664-4444-4-4-4-24-4-44222-2-2-22000000-22-2200000000000000000000023−2323−2300000000000000000000000000000
χ674-4444-4-4-4-24-4-44222-2-2-22000000-22-22000000000000000000000−2323−232300000000000000000000000000000
χ684-4444-4-4-4-2-444-4222-2-2-22004-44-42-22-200000000000000000-22-22000000000000000000000000000000000
χ694-4444-4-4-4-2-444-4222-2-2-2200-44-442-22-2000000000000000002-22-2000000000000000000000000000000000
χ704-44-4-44-4440000-44-4-44-44000000000000000000000000000000000000000000022−22−222200000000000000000
χ714-44-4-44-4440000-44-4-44-440000000000000000000000000000000000000000000−222222−2200000000000000000
χ724-4-44-4-44440000-444-4-44-40022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ734-4-44-4-44440000-444-4-44-400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ744-4-44-4-444-200002-2-222-220022−22−22220000000000000000023−2300−222−26−6−6600000000000000000000000000000
χ754-4-44-4-444-200002-2-222-220022−22−222200000000000000000−232300−222−2−666−600000000000000000000000000000
χ764-4-44-4-444-200002-2-222-2200−222222−220000000000000000023−23002−2−22−666−600000000000000000000000000000
χ774-4-44-4-444-200002-2-222-2200−222222−2200000000000000000−2323002−2−226−6−6600000000000000000000000000000
χ784-4-4-4444-44-44-44-4-444-4-44000000-4-444000000000000000000000000000000000000000000000000000000
χ794-4-4-4444-4-24-44-422-2-222-2000000-2-22200000004i−4i0000000000000000000000000000000−2i2i000000000000
χ804-4-4-4444-4-24-44-422-2-222-2000000-2-2220000000−4i4i00000000000000000000000000000002i−2i000000000000
χ814-4-4-4444-4-2-44-4422-2-222-200000022-2-200000000000000000000000000000000000000000000−2i32i300000000
χ824-4-4-4444-4-2-44-4422-2-222-200000022-2-2000000000000000000000000000000000000000000002i3−2i300000000
χ83888-8-8-88-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-88-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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