Finite Group Databasebeta

← Group #10867967

Character table — Group #10867967

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
χ51111111111111111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-1-11-1-111-1-1-1
χ61111111111111111111111-1-1-1-111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-111111-1-1-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-1-1-111-1-1111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-1-11111-1
χ911111111111111111111-1-111111111111111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-11111-1-1-1-1-111-1-1-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-111-1-11
χ1111111111111111111111-1-111111111-1-1-1-111-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-111111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-1-1-1-11111111-1-111-1
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
χ17222222222-2-2-2-22222222220000-2-2-2-2222200-200000022-2-20000000022-2-200000000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-200-200000022-2-200000000-2-2220000000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222002000000-2-22200000000-2-2-2-20000000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000-2-22200000000222200000000000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-22-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
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
χ292222-2-2-2-22-222-2-2-2-2222-20022-2-22-2-220000000000000000022-2-2000000002i2i−2i−2i000000000000002i−2i00000
χ302222-2-2-2-22-222-2-2-2-2222-20022-2-22-2-220000000000000000022-2-200000000−2i−2i2i2i00000000000000−2i2i00000
χ312222-2-2-2-22-222-2-2-2-2222-200-2-2222-2-2200000000000000000-2-222000000002i2i−2i−2i00000000000000−2i2i00000
χ322222-2-2-2-22-222-2-2-2-2222-200-2-2222-2-2200000000000000000-2-22200000000−2i−2i2i2i000000000000002i−2i00000
χ332-22-22-22-22000022-2-2-22-22i−2i2−22−2000022-2-20000000−i2i22i−2i002−22−2−i2−i2i2i22i−2i00000022−2−200000000000000−i2i20
χ342-22-22-22-22000022-2-2-22-22i−2i2−22−20000-2-2220000000−i2i22i−2i002−22−2−i2−i2i2i2−2i2i000000−2−22200000000000000i2−i20
χ352-22-22-22-22000022-2-2-22-22i−2i−22−22000022-2-20000000i2−i22i−2i00−22−22i2i2−i2−i22i−2i000000−2−22200000000000000i2−i20
χ362-22-22-22-22000022-2-2-22-22i−2i−22−220000-2-2220000000i2−i22i−2i00−22−22i2i2−i2−i2−2i2i00000022−2−200000000000000−i2i20
χ372-22-22-22-22000022-2-2-22-2−2i2i2−22−2000022-2-20000000i2−i2−2i2i002−22−2i2i2−i2−i2−2i2i00000022−2−200000000000000i2−i20
χ382-22-22-22-22000022-2-2-22-2−2i2i2−22−20000-2-2220000000i2−i2−2i2i002−22−2i2i2−i2−i22i−2i000000−2−22200000000000000−i2i20
χ392-22-22-22-22000022-2-2-22-2−2i2i−22−22000022-2-20000000−i2i2−2i2i00−22−22−i2−i2i2i2−2i2i000000−2−22200000000000000−i2i20
χ402-22-22-22-22000022-2-2-22-2−2i2i−22−220000-2-2220000000−i2i2−2i2i00−22−22−i2−i2i2i22i−2i00000022−2−200000000000000i2−i20
χ412-2-222-2-22222-2-22-222-2-2-2000000-22-222i−2i2i−2i000002i−2i00000000000000002i−2i00000000000002i−2i000002-2000
χ422-2-222-2-22222-2-22-222-2-2-2000000-22-222i−2i2i−2i00000−2i2i00000000000000002i−2i0000000000000−2i2i00000-22000
χ432-2-222-2-22222-2-22-222-2-2-2000000-22-22−2i2i−2i2i000002i−2i0000000000000000−2i2i00000000000002i−2i00000-22000
χ442-2-222-2-22222-2-22-222-2-2-2000000-22-22−2i2i−2i2i00000−2i2i0000000000000000−2i2i0000000000000−2i2i000002-2000
χ452-2-222-2-222-2-2222-222-2-2-20000002-22-22i−2i2i−2i2-2000000000000000000000−2i2i2i−2i2i−2i000002-200000000000000
χ462-2-222-2-222-2-2222-222-2-2-20000002-22-22i−2i2i−2i-22000000000000000000000−2i2i−2i2i−2i2i00000-2200000000000000
χ472-2-222-2-222-2-2222-222-2-2-20000002-22-2−2i2i−2i2i2-20000000000000000000002i−2i−2i2i−2i2i000002-200000000000000
χ482-2-222-2-222-2-2222-222-2-2-20000002-22-2−2i2i−2i2i-220000000000000000000002i−2i2i−2i2i−2i00000-2200000000000000
χ492-2-22-222-222-22-2-22-22-2-2200000022-2-200000002i−2i000000000000000000002-2-222i−2i2i−2i0002i−2i000000000000
χ502-2-22-222-222-22-2-22-22-2-2200000022-2-200000002i−2i00000000000000000000-222-2−2i2i−2i2i0002i−2i000000000000
χ512-2-22-222-222-22-2-22-22-2-2200000022-2-20000000−2i2i000000000000000000002-2-22−2i2i−2i2i000−2i2i000000000000
χ522-2-22-222-222-22-2-22-22-2-2200000022-2-20000000−2i2i00000000000000000000-222-22i−2i2i−2i000−2i2i000000000000
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
χ554444-4-4-4-444-4-44-4-4-4444-4000000-444-4000000000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-24-4-44222-2-2-220000002-2-2200000000000000000000023−2323−2300000000000000000000000000000
χ574444-4-4-4-4-24-4-44222-2-2-220000002-2-22000000000000000000000−2323−232300000000000000000000000000000
χ584444-4-4-4-4-2-444-4222-2-2-220044-4-4-222-200000000000000000-2-222000000000000000000000000000000000
χ594444-4-4-4-4-2-444-4222-2-2-2200-4-444-222-20000000000000000022-2-2000000000000000000000000000000000
χ6044-4-444-4-4400004-4-4-44-4400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6144-4-444-4-4400004-4-4-44-440000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6244-4-4-4-44440000-444-44-4-40000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ6344-4-4-4-44440000-444-44-4-400000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ644-44-44-44-4-20000-2-2222-224i−4i22−2222−22000000000000000−2i22i2−2i2i00−22−22i2i2−i2−i200000000000000000000000000000
χ654-44-44-44-4-20000-2-2222-224i−4i−2222−22220000000000000002i2−2i2−2i2i002−22−2−i2−i2i2i200000000000000000000000000000
χ664-44-44-44-4-20000-2-2222-22−4i4i22−2222−220000000000000002i2−2i22i−2i00−22−22−i2−i2i2i200000000000000000000000000000
χ674-44-44-44-4-20000-2-2222-22−4i4i−2222−2222000000000000000−2i22i22i−2i002−22−2i2i2−i2−i200000000000000000000000000000
χ684-44-4-44-4440000-4-44-4-4440022−22−222200000000000000000000022−22−2222000000000000000000000000000000000
χ694-44-4-44-4440000-4-44-4-44400−222222−22000000000000000000000−222222−22000000000000000000000000000000000
χ704-44-4-44-44-2000022-222-2-20022−22−22220000000000000000000−2i32i3−222−2i6−i6−i6i600000000000000000000000000000
χ714-44-4-44-44-2000022-222-2-20022−22−222200000000000000000002i3−2i3−222−2−i6i6i6−i600000000000000000000000000000
χ724-44-4-44-44-2000022-222-2-200−222222−220000000000000000000−2i32i32−2−22−i6i6i6−i600000000000000000000000000000
χ734-44-4-44-44-2000022-222-2-200−222222−2200000000000000000002i3−2i32−2−22i6−i6−i6i600000000000000000000000000000
χ744-4-444-4-44-244-4-4-22-2-22220000002-22-20000000004i−4i0000000000000000000000000000000−2i2i0000000000
χ754-4-444-4-44-244-4-4-22-2-22220000002-22-2000000000−4i4i00000000000000000000000000000002i−2i0000000000
χ764-4-444-4-44-2-4-444-22-2-2222000000-22-2200004-400000000000000000000000000000000-2200000000000000
χ774-4-444-4-44-2-4-444-22-2-2222000000-22-220000-44000000000000000000000000000000002-200000000000000
χ784-4-44-444-44-44-44-44-44-4-44000000-4-444000000000000000000000000000000000000000000000000000000
χ794-4-44-444-4-24-44-42-22-222-2000000-2-22200000004i−4i0000000000000000000000000000000−2i2i000000000000
χ804-4-44-444-4-24-44-42-22-222-2000000-2-2220000000−4i4i00000000000000000000000000000002i−2i000000000000
χ814-4-44-444-4-2-44-442-22-222-200000022-2-200000000000000000000000000000000000000000000−2i32i300000000
χ824-4-44-444-4-2-44-442-22-222-200000022-2-2000000000000000000000000000000000000000000002i3−2i300000000
χ8388-8-888-8-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-8-888-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000

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