Finite Group Databasebeta

← Group #10858896

Character table — Group #10858896

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order122222223444466666664488881212121244444444444881212121224242424242424242244444488884121212121212121244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11
χ51111111111111111111111-1-1-1-11111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1111-1-11
χ61111111111111111111111-1-1-1-111111111-1-111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-1-11-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-111-1-1-111-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-111-1111
χ911111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-11111-1-1-1-1-1-111-1-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-11
χ1111111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11111-1-111111-1
χ1311111111111111111111-1-1-1-1-1-11111111111-1-111-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-111-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111-1-111-1-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-111-1-111-1-1-1-11-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111111-1-111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-22222000000-20022-2-200000000-2-222000000000000000000000-2000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000-20022-2-20000000022-2-20000000000000000000002000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222000000200-2-22200000000-2-2-2-20000000000000000000002000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2000000200-2-222000000002222000000000000000000000-2000
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
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1000022-2-2-2-22-2-2-1-1-1-111111111000000000000211-1-1-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-222222-2-2-1-1-1-111111111000000000000-2-1-11111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-100002222-2-2-2-2-21111-1-1-1-11111000000000000-2-1-1-1-1111100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-2-222-2-2-21111-1-1-1-1111100000000000021111-1-1-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-222-22211111111-1-1-1-1000000000000-211-1-111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-222-2-2-22211111111-1-1-1-10000000000002-1-111-1-11100000000
χ2922-2-222-2-2222-2-222-2-22-2-200000022-2-222-2-200002-20000000000000002-2000000000000000002-22-2000000
χ3022-2-222-2-2222-2-222-2-22-2-200000022-2-222-2-20000-220000000000000002-200000000000000000-22-22000000
χ3122-2-222-2-2222-2-222-2-22-2-200000022-2-2-2-22200002-2000000000000000-22000000000000000002-2-22000000
χ3222-2-222-2-2222-2-222-2-22-2-200000022-2-2-2-2220000-22000000000000000-2200000000000000000-222-2000000
χ3322-2-222-2-22-2-22222-2-22-2-2000000-2-22222-2-2002i−2i00000000000000000-22002i2i−2i−2i000002i−2i00000000000000
χ3422-2-222-2-22-2-22222-2-22-2-2000000-2-22222-2-200−2i2i00000000000000000-2200−2i−2i2i2i00000−2i2i00000000000000
χ3522-2-222-2-22-2-22222-2-22-2-2000000-2-222-2-222002i−2i000000000000000002-200−2i−2i2i2i000002i−2i00000000000000
χ3622-2-222-2-22-2-22222-2-22-2-2000000-2-222-2-22200−2i2i000000000000000002-2002i2i−2i−2i00000−2i2i00000000000000
χ372-22-22-22-222-22-2-2-2-2-22220000002-22-200002-2000000000000000000000002i−2i2i−2i2i2i−2i−2i0002-2000000000000
χ382-22-22-22-222-22-2-2-2-2-22220000002-22-200002-200000000000000000000000−2i2i−2i2i−2i−2i2i2i0002-2000000000000
χ392-22-22-22-222-22-2-2-2-2-22220000002-22-20000-22000000000000000000000002i−2i2i−2i−2i−2i2i2i000-22000000000000
χ402-22-22-22-222-22-2-2-2-2-22220000002-22-20000-2200000000000000000000000−2i2i−2i2i2i2i−2i−2i000-22000000000000
χ412-2-222-2-222-222-2-2-2222-2-2002i2i−2i−2i-222-2000000000000000002i2i−2i−2i000000002-2-220000000000000002i−2i0000
χ422-2-222-2-222-222-2-2-2222-2-2002i2i−2i−2i-222-2000000000000000002i2i−2i−2i00000000-222-2000000000000000−2i2i0000
χ432-2-222-2-222-222-2-2-2222-2-200−2i−2i2i2i-222-200000000000000000−2i−2i2i2i000000002-2-22000000000000000−2i2i0000
χ442-2-222-2-222-222-2-2-2222-2-200−2i−2i2i2i-222-200000000000000000−2i−2i2i2i00000000-222-20000000000000002i−2i0000
χ452-2-22-222-2200002-2-22-22-22i−2i−i2i2−i2i200002i−2i2i−2i00000002−22i−2i00−i2i2−i2i222−2−2002-200002−22−200000000000000−i2i20
χ462-2-22-222-2200002-2-22-22-22i−2i−i2i2−i2i20000−2i2i−2i2i00000002−22i−2i00−i2i2−i2i222−2−200-220000−22−2200000000000000i2−i20
χ472-2-22-222-2200002-2-22-22-22i−2ii2−i2i2−i200002i−2i2i−2i0000000−222i−2i00i2−i2i2−i2−2−222002-20000−22−2200000000000000i2−i20
χ482-2-22-222-2200002-2-22-22-22i−2ii2−i2i2−i20000−2i2i−2i2i0000000−222i−2i00i2−i2i2−i2−2−22200-2200002−22−200000000000000−i2i20
χ492-2-22-222-2200002-2-22-22-2−2i2i−i2i2−i2i200002i−2i2i−2i0000000−22−2i2i00−i2i2−i2i2−2−22200-2200002−22−200000000000000i2−i20
χ502-2-22-222-2200002-2-22-22-2−2i2i−i2i2−i2i20000−2i2i−2i2i0000000−22−2i2i00−i2i2−i2i2−2−222002-20000−22−2200000000000000−i2i20
χ512-2-22-222-2200002-2-22-22-2−2i2ii2−i2i2−i200002i−2i2i−2i00000002−2−2i2i00i2−i2i2−i222−2−200-220000−22−2200000000000000−i2i20
χ522-2-22-222-2200002-2-22-22-2−2i2ii2−i2i2−i20000−2i2i−2i2i00000002−2−2i2i00i2−i2i2−i222−2−2002-200002−22−200000000000000i2−i20
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
χ554444-4-4-4-440000-44-44-4-440022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ564444-4-4-4-440000-44-44-4-4400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ574444-4-4-4-4-200002-22-222-20022−22−2222000000000000000000023−23−222−26−66−600000000000000000000000000000
χ584444-4-4-4-4-200002-22-222-20022−22−22220000000000000000000−2323−222−2−66−6600000000000000000000000000000
χ594444-4-4-4-4-200002-22-222-200−222222−22000000000000000000023−232−2−22−66−6600000000000000000000000000000
χ604444-4-4-4-4-200002-22-222-200−222222−220000000000000000000−23232−2−226−66−600000000000000000000000000000
χ6144-4-444-4-4-244-4-4-2-222-222000000-2-222000000004-40000000000000000000000000000000000-2200000000
χ6244-4-444-4-4-244-4-4-2-222-222000000-2-22200000000-4400000000000000000000000000000000002-200000000
χ6344-4-444-4-4-2-4-444-2-222-22200000022-2-20000004i−4i000000000000000000000000000000−2i2i00000000000000
χ6444-4-444-4-4-2-4-444-2-222-22200000022-2-2000000−4i4i0000000000000000000000000000002i−2i00000000000000
χ6544-4-4-4-44440000-444-4-44-40000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ6644-4-4-4-44440000-444-4-44-400000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ674-44-44-44-44-44-44-4-4-4-4444000000-44-44000000000000000000000000000000000000000000000000000000
χ684-44-44-44-4-24-44-42222-2-2-2000000-22-2200004-40000000000000000000000000000000000-22000000000000
χ694-44-44-44-4-24-44-42222-2-2-2000000-22-220000-4400000000000000000000000000000000002-2000000000000
χ704-44-44-44-4-2-44-442222-2-2-20000002-22-2000000000000000000000000000000000000000000−2i32i30000000000
χ714-44-44-44-4-2-44-442222-2-2-20000002-22-20000000000000000000000000000000000000000002i3−2i30000000000
χ724-44-4-44-44400004-44-4-4-4400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ734-44-4-44-44400004-44-4-4-440000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ744-4-444-4-4444-4-44-4-4444-4-40000004-4-44000000000000000000000000000000000000000000000000000000
χ754-4-444-4-44-24-4-4422-2-2-222000000-222-200000000000000000000023−23−232300000000000000000000000000000
χ764-4-444-4-44-24-4-4422-2-2-222000000-222-2000000000000000000000−232323−2300000000000000000000000000000
χ774-4-444-4-44-2-444-422-2-2-222004i4i−4i−4i2-2-2200000000000000000−2i−2i2i2i000000000000000000000000000000000
χ784-4-444-4-44-2-444-422-2-2-22200−4i−4i4i4i2-2-22000000000000000002i2i−2i−2i000000000000000000000000000000000
χ794-4-44-444-4-20000-222-22-224i−4i−2i22i2−2i22i200000000000000022−22−2i2i00i2−i2i2−i2−2−22200000000000000000000000000000
χ804-4-44-444-4-20000-222-22-224i−4i2i2−2i22i2−2i2000000000000000−2222−2i2i00−i2i2−i2i222−2−200000000000000000000000000000
χ814-4-44-444-4-20000-222-22-22−4i4i−2i22i2−2i22i2000000000000000−22222i−2i00i2−i2i2−i222−2−200000000000000000000000000000
χ824-4-44-444-4-20000-222-22-22−4i4i2i2−2i22i2−2i200000000000000022−222i−2i00−i2i2−i2i2−2−22200000000000000000000000000000
χ8388-8-8-8-888-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-88-88-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000

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