Finite Group Databasebeta

← Group #10826291

Character table — Group #10826291

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order122222223444466666664488881212121244442222224881212121224242424242424242244444488884666666121224444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111111-1-111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-11111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-111111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111-111-1-111-1
χ911111111111111111111-1-111111111111111-1-111-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-111-1-111-1-1-1-1-111-1-1-1
χ1011111111111111111111-1-1111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-1-111-1-111-111-1-1-1-11
χ1111111111111111111111-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-1111-1-1111
χ1211111111111111111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11-1-111-1-1111-1-11111-1
χ1311111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111-1-1-1-111-1-1-1-1-1111
χ1411111111111111111111-1-1-1-1-1-111111111-1-11111-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111-1
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111111-1-1-1-11111111-1-1-1
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-11111-1-11-1-1-1-1-1-11
χ17222222222-2-2-2-22222222220000-2-2-2-22222000000-20022-2-200000000-2-22200000000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000-20022-2-20000000022-2-20000000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222000000200-2-22200000000-2-2-2-20000000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2000000200-2-22200000000222200000000000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-2-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-100002222-2-22-2-2-1-1-1-111111111000000000000-2-1-1-1-1111100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-2-2-2222-2-2-1-1-1-11111111100000000000021111-1-1-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-2-222-2-2-21111-1-1-1-11111000000000000-2-1-111-1-11100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-222-2-2-2-2-21111-1-1-1-11111000000000000211-1-111-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-2-2-2-22211111111-1-1-1-10000000000002-1-11111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-22222-22211111111-1-1-1-1000000000000-211-1-1-1-11100000000
χ2922-222-2-2-2200002-2-22-2-222-222−2−200002i2i−2i−2i00000002−22-20022−2−222−2−2002i−2i0000−i2−i2i2i200000000000000−i2i20
χ3022-222-2-2-2200002-2-22-2-222-222−2−20000−2i−2i2i2i00000002−22-20022−2−222−2−200−2i2i0000i2i2−i2−i200000000000000i2−i20
χ3122-222-2-2-2200002-2-22-2-222-2−2−22200002i2i−2i−2i0000000−222-200−2−222−2−222002i−2i0000i2i2−i2−i200000000000000i2−i20
χ3222-222-2-2-2200002-2-22-2-222-2−2−2220000−2i−2i2i2i0000000−222-200−2−222−2−22200−2i2i0000−i2−i2i2i200000000000000−i2i20
χ3322-222-2-2-2200002-2-22-2-22-2222−2−200002i2i−2i−2i0000000−22-220022−2−2−2−22200−2i2i0000−i2−i2i2i200000000000000i2−i20
χ3422-222-2-2-2200002-2-22-2-22-2222−2−20000−2i−2i2i2i0000000−22-220022−2−2−2−222002i−2i0000i2i2−i2−i200000000000000−i2i20
χ3522-222-2-2-2200002-2-22-2-22-22−2−22200002i2i−2i−2i00000002−2-2200−2−22222−2−200−2i2i0000i2i2−i2−i200000000000000−i2i20
χ3622-222-2-2-2200002-2-22-2-22-22−2−2220000−2i−2i2i2i00000002−2-2200−2−22222−2−2002i−2i0000−i2−i2i2i200000000000000i2−i20
χ3722-2-2-22-222-22-2222-2-22-2-2000000-2-222000000002-2000000000000000000022-2-22-22-2000002-20000000000
χ3822-2-2-22-222-22-2222-2-22-2-2000000-2-222000000002-20000000000000000000-2-222-22-22000002-20000000000
χ3922-2-2-22-222-22-2222-2-22-2-2000000-2-22200000000-22000000000000000000022-2-2-22-2200000-220000000000
χ4022-2-2-22-222-22-2222-2-22-2-2000000-2-22200000000-220000000000000000000-2-2222-22-200000-220000000000
χ412-22-22-2-222-2-222-2-22-22-22002-22-22-22-2000000000000000002-22-2000000002-22-200000000000000002-2000
χ422-22-22-2-222-2-222-2-22-22-22002-22-22-22-2000000000000000002-22-200000000-22-220000000000000000-22000
χ432-22-22-2-222-2-222-2-22-22-2200-22-222-22-200000000000000000-22-22000000002-22-20000000000000000-22000
χ442-22-22-2-222-2-222-2-22-22-2200-22-222-22-200000000000000000-22-2200000000-22-2200000000000000002-2000
χ452-2-22-2-22222-2-22-2-2-2222-2000000-222-22-22-22-200000000000000000002-2002-2-22000002-200000000000000
χ462-2-22-2-22222-2-22-2-2-2222-2000000-222-22-22-2-2200000000000000000002-200-222-200000-2200000000000000
χ472-2-22-2-22222-2-22-2-2-2222-2000000-222-2-22-222-20000000000000000000-2200-222-2000002-200000000000000
χ482-2-22-2-22222-2-22-2-2-2222-2000000-222-2-22-22-220000000000000000000-22002-2-2200000-2200000000000000
χ492-2-22-2-2222-222-2-2-2-2222-20000002-2-222-22-2002-200000000000000000-2200000000000002-2000002-200000
χ502-2-22-2-2222-222-2-2-2-2222-20000002-2-222-22-200-2200000000000000000-220000000000000-2200000-2200000
χ512-2-22-2-2222-222-2-2-2-2222-20000002-2-22-22-22002-2000000000000000002-200000000000002-200000-2200000
χ522-2-22-2-2222-222-2-2-2-2222-20000002-2-22-22-2200-22000000000000000002-20000000000000-22000002-200000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022220000000000-400-2-2220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000000000040022-2-20000000000000000000000000000000000000
χ55444-4-4-44-4400004-44-4-44-40000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ56444-4-4-44-4400004-44-4-44-400000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ5744-444-4-4-4-20000-222-222-24-42222−22−2200000000000000022−22-2200−2−222−2−22200000000000000000000000000000
χ5844-444-4-4-4-20000-222-222-24-4−22−222222000000000000000−2222-220022−2−222−2−200000000000000000000000000000
χ5944-444-4-4-4-20000-222-222-2-442222−22−22000000000000000−22222-200−2−22222−2−200000000000000000000000000000
χ6044-444-4-4-4-20000-222-222-2-44−22−22222200000000000000022−222-20022−2−2−2−22200000000000000000000000000000
χ6144-4-4-44-4444-44-444-4-44-4-400000044-4-4000000000000000000000000000000000000000000000000000000
χ6244-4-4-44-44-24-44-4-2-222-222000000-2-2220000000000000000000000000000000000000000000023−2300000000
χ6344-4-4-44-44-24-44-4-2-222-222000000-2-22200000000000000000000000000000000000000000000−232300000000
χ6444-4-4-44-44-2-44-44-2-222-22200000022-2-2000000004-400000000000000000000000000000000-220000000000
χ6544-4-4-44-44-2-44-44-2-222-22200000022-2-200000000-44000000000000000000000000000000002-20000000000
χ664-444-44-4-440000-4444-4-4-400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ674-444-44-4-440000-4444-4-4-40000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ684-44-44-4-44444-4-4-4-44-44-44000000-44-44000000000000000000000000000000000000000000000000000000
χ694-44-44-4-44-244-4-422-22-22-20000002-22-2000000000000000000000−2i32i3−2i32i300000000000000000000000000000
χ704-44-44-4-44-244-4-422-22-22-20000002-22-20000000000000000000002i3−2i32i3−2i300000000000000000000000000000
χ714-44-44-4-44-2-4-44422-22-22-2004-44-4-22-2200000000000000000-22-22000000000000000000000000000000000
χ724-44-44-4-44-2-4-44422-22-22-200-44-44-22-22000000000000000002-22-2000000000000000000000000000000000
χ734-4-44-4-444-24-4-44222-2-2-220000002-2-2200004-400000000000000000000000000000000-2200000000000000
χ744-4-44-4-444-24-4-44222-2-2-220000002-2-220000-44000000000000000000000000000000002-200000000000000
χ754-4-44-4-444-2-444-4222-2-2-22000000-222-20000004-400000000000000000000000000000000-22000000000000
χ764-4-44-4-444-2-444-4222-2-2-22000000-222-2000000-44000000000000000000000000000000002-2000000000000
χ774-4-4-4444-440000-44-4-4-4440022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ784-4-4-4444-440000-44-4-4-44400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ794-4-4-4444-4-200002-2222-2-20022−22−22220000000000000000000−2i32i3−222−2i6−i6−i6i600000000000000000000000000000
χ804-4-4-4444-4-200002-2222-2-20022−22−222200000000000000000002i3−2i3−222−2−i6i6i6−i600000000000000000000000000000
χ814-4-4-4444-4-200002-2222-2-200−222222−220000000000000000000−2i32i32−2−22−i6i6i6−i600000000000000000000000000000
χ824-4-4-4444-4-200002-2222-2-200−222222−2200000000000000000002i3−2i32−2−22i6−i6−i6i600000000000000000000000000000
χ83888-8-8-88-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000

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