Finite Group Databasebeta

← Group #10855225

Character table — Group #10855225

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order122222223444466666664488881212121244444444444881212121224242424242424242222444488884121212121212121222444882
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11
χ51111111111111111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-1-1-1111-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-11-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-111-1-111111-1-1-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-1-1111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-111-1-1-11111-1
χ911111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-111-1-11
χ1011111111111111111111-1-1111111111111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1
χ1111111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1111-1-111-1
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ1311111111111111111111-1-1-1-1-1-11111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111-11111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-11111-1-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-111-1-1-1-111-1-11-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111-1-11111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-2222200-200000022-2-200000000000022-2-2000000000000000-200000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-200-200000022-2-2000000000000-2-222000000000000000200000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222002000000-2-222000000000000-2-2-2-2000000000000000200000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000-2-2220000000000002222000000000000000-200000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022222-2-2-2-2-1-1-1-111111111000000000000-2-1-111-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-22-2-222-2-2-1-1-1-111111111000000000000211-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-2-2-2-2-2-2-21111-1-1-1-111110000000000002-1-1-1-1111100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-22222-2-21111-1-1-1-11111000000000000-21111-1-1-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-2-2222211111111-1-1-1-1000000000000-2-1-11111-1-100000000
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
χ292222-2-2-2-22-222-22-22-22-2-20000002-2-220000000002i−2i0000000000000022-2-200002i2i−2i−2i00000002i−2i00000000
χ302222-2-2-2-22-222-22-22-22-2-20000002-2-220000000002i−2i00000000000000-2-2220000−2i−2i2i2i00000002i−2i00000000
χ312222-2-2-2-22-222-22-22-22-2-20000002-2-22000000000−2i2i0000000000000022-2-20000−2i−2i2i2i0000000−2i2i00000000
χ322222-2-2-2-22-222-22-22-22-2-20000002-2-22000000000−2i2i00000000000000-2-22200002i2i−2i−2i0000000−2i2i00000000
χ3322-2-22-2-222000022-22-2-2-22-222−2−200002i2i−2i−2i00000002−22-20022−2−222−2−200002i−2i00−i2i2−i2i200000000000000−i2i20
χ3422-2-22-2-222000022-22-2-2-22-222−2−20000−2i−2i2i2i00000002−22-20022−2−222−2−20000−2i2i00i2−i2i2−i200000000000000i2−i20
χ3522-2-22-2-222000022-22-2-2-22-2−2−22200002i2i−2i−2i0000000−222-200−2−222−2−22200002i−2i00i2−i2i2−i200000000000000i2−i20
χ3622-2-22-2-222000022-22-2-2-22-2−2−2220000−2i−2i2i2i0000000−222-200−2−222−2−2220000−2i2i00−i2i2−i2i200000000000000−i2i20
χ3722-2-22-2-222000022-22-2-2-2-2222−2−200002i2i−2i−2i0000000−22-220022−2−2−2−2220000−2i2i00−i2i2−i2i200000000000000i2−i20
χ3822-2-22-2-222000022-22-2-2-2-2222−2−20000−2i−2i2i2i0000000−22-220022−2−2−2−22200002i−2i00i2−i2i2−i200000000000000−i2i20
χ3922-2-22-2-222000022-22-2-2-2-22−2−22200002i2i−2i−2i00000002−2-2200−2−22222−2−20000−2i2i00i2−i2i2−i200000000000000−i2i20
χ4022-2-22-2-222000022-22-2-2-2-22−2−2220000−2i−2i2i2i00000002−2-2200−2−22222−2−200002i−2i00−i2i2−i2i200000000000000i2−i20
χ412-22-222-2-2222-2-2-222-2-22-2000000-22-222i−2i2i−2i0002i−2i00000000000000002-22-2002i−2i0000000002i−2i0000000000
χ422-22-222-2-2222-2-2-222-2-22-2000000-22-222i−2i2i−2i000−2i2i0000000000000000-22-22002i−2i000000000−2i2i0000000000
χ432-22-222-2-2222-2-2-222-2-22-2000000-22-22−2i2i−2i2i0002i−2i0000000000000000-22-2200−2i2i0000000002i−2i0000000000
χ442-22-222-2-2222-2-2-222-2-22-2000000-22-22−2i2i−2i2i000−2i2i00000000000000002-22-200−2i2i000000000−2i2i0000000000
χ452-22-222-2-22-2-222-222-2-22-20000002-22-22i−2i2i−2i2-20000000000000000000000000−2i2i000002-20000000002i−2i000
χ462-22-222-2-22-2-222-222-2-22-20000002-22-22i−2i2i−2i-220000000000000000000000000−2i2i00000-22000000000−2i2i000
χ472-22-222-2-22-2-222-222-2-22-20000002-22-2−2i2i−2i2i2-200000000000000000000000002i−2i000002-2000000000−2i2i000
χ482-22-222-2-22-2-222-222-2-22-20000002-22-2−2i2i−2i2i-2200000000000000000000000002i−2i00000-220000000002i−2i000
χ492-22-2-2-2222-22-22-2-222-2-22002-22-2-2-222000000000000000002-22-200002-2-22000000000000000002-2000000
χ502-22-2-2-2222-22-22-2-222-2-22002-22-2-2-222000000000000000002-22-20000-222-200000000000000000-22000000
χ512-22-2-2-2222-22-22-2-222-2-2200-22-22-2-22200000000000000000-22-2200002-2-2200000000000000000-22000000
χ522-22-2-2-2222-22-22-2-222-2-2200-22-22-2-22200000000000000000-22-220000-222-2000000000000000002-2000000
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
χ554444-4-4-4-444-4-444-44-44-4-4000000-444-4000000000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-24-4-44-22-22-2220000002-2-220000000000000000000000000000000000000000−2i32i3000000000000
χ574444-4-4-4-4-24-4-44-22-22-2220000002-2-2200000000000000000000000000000000000000002i3−2i3000000000000
χ584444-4-4-4-4-2-444-4-22-22-222000000-222-20000000004i−4i000000000000000000000000000000000−2i2i00000000
χ594444-4-4-4-4-2-444-4-22-22-222000000-222-2000000000−4i4i0000000000000000000000000000000002i−2i00000000
χ6044-4-44-4-44-20000-2-22-22224-42222−22−2200000000000000022−22-2200−2−222−2−22200000000000000000000000000000
χ6144-4-44-4-44-20000-2-22-22224-4−22−222222000000000000000−2222-220022−2−222−2−200000000000000000000000000000
χ6244-4-44-4-44-20000-2-22-2222-442222−22−22000000000000000−22222-200−2−22222−2−200000000000000000000000000000
χ6344-4-44-4-44-20000-2-22-2222-44−22−22222200000000000000022−222-20022−2−2−2−22200000000000000000000000000000
χ6444-4-4-444-4400004-4-4-4-444000000000000000000000000000000000000000000022−22−222200000000000000000
χ6544-4-4-444-4400004-4-4-4-4440000000000000000000000000000000000000000000−222222−2200000000000000000
χ664-44-444-4-4-244-4-42-2-222-220000002-22-200000004i−4i000000000000000000000000000000000−2i2i0000000000
χ674-44-444-4-4-244-4-42-2-222-220000002-22-20000000−4i4i0000000000000000000000000000000002i−2i0000000000
χ684-44-444-4-4-2-4-4442-2-222-22000000-22-2200004-400000000000000000000000000000000-2200000000000000
χ694-44-444-4-4-2-4-4442-2-222-22000000-22-220000-44000000000000000000000000000000002-200000000000000
χ704-44-4-4-44444-44-4-4-444-4-4400000044-4-4000000000000000000000000000000000000000000000000000000
χ714-44-4-4-444-24-44-422-2-222-2000000-2-22200000000000000000000023−2323−2300000000000000000000000000000
χ724-44-4-4-444-24-44-422-2-222-2000000-2-222000000000000000000000−2323−232300000000000000000000000000000
χ734-44-4-4-444-2-44-4422-2-222-2004-44-422-2-200000000000000000-22-22000000000000000000000000000000000
χ744-44-4-4-444-2-44-4422-2-222-200-44-4422-2-2000000000000000002-22-2000000000000000000000000000000000
χ754-4-444-44-440000-44-4-44-4400000000004-4-4400000000000000000000000000000000000000000000000000
χ764-4-444-44-440000-44-4-44-440000000000-444-400000000000000000000000000000000000000000000000000
χ774-4-44-44-4440000-4-4-4444-40022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ784-4-44-44-4440000-4-4-4444-400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ794-4-44-44-44-20000222-2-2-220022−22−2222000000000000000000023−23−222−26−6−6600000000000000000000000000000
χ804-4-44-44-44-20000222-2-2-220022−22−22220000000000000000000−2323−222−2−666−600000000000000000000000000000
χ814-4-44-44-44-20000222-2-2-2200−222222−22000000000000000000023−232−2−22−666−600000000000000000000000000000
χ824-4-44-44-44-20000222-2-2-2200−222222−220000000000000000000−23232−2−226−6−6600000000000000000000000000000
χ8388-8-8-888-8-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-88-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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