Finite Group Databasebeta

← Group #10868027

Character table — Group #10868027

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order122222223444466666664488881212121244444444444881212121224242424242424244444444488884121212121212121224444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111-1
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
χ4111111111111111111111111111111-1-1-1-11-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-1-1111-1-1-1-11
χ61111111111111111111111-1-1-1-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1111-1-111-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-11111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-111-1-1111
χ911111111111111111111-1-1111111111111-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-11111-111-1-1-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-111-1-11
χ1111111111111111111111-1-111111111-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111111-1-1-1-1111-1-111-1
χ1311111111111111111111-1-1-1-1-1-111111111-11111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1111-1-1-1-111-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-11111-1-11-1-1-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111-1-1-1-11111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-22222-20000000022-2-20000000022-2-200000000000000000-20000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-20000000022-2-200000000-2-2220000000000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222200000000-2-22200000000-2-2-2-20000000000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000-2-22200000000222200000000000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-100002-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000222-2-2-2-2-2-2-1-1-1-1111111110000000000002-1-111-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-100002-2-22222-2-2-1-1-1-111111111000000000000-211-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-222-2-222-2-21111-1-1-1-11111000000000000-21111-1-1-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-222-2-2-2-21111-1-1-1-111110000000000002-1-1-1-1111100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-22222-2-22211111111-1-1-1-1000000000000-211-1-1-1-11100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-10000-2-2-2-2-2222211111111-1-1-1-10000000000002-1-11111-1-100000000
χ29222-22-2-2-22-222-2-2-22-2-2220022-2-22-2-220000000000000000022-2-2000000002i2i−2i−2i000000000000002i−2i00000
χ30222-22-2-2-22-222-2-2-22-2-2220022-2-22-2-220000000000000000022-2-200000000−2i−2i2i2i00000000000000−2i2i00000
χ31222-22-2-2-22-222-2-2-22-2-22200-2-2222-2-2200000000000000000-2-222000000002i2i−2i−2i00000000000000−2i2i00000
χ32222-22-2-2-22-222-2-2-22-2-22200-2-2222-2-2200000000000000000-2-22200000000−2i−2i2i2i000000000000002i−2i00000
χ332-222-2-2-22200002-2-22-22-22i−2i−i2i2−i2i2000022-2-200000002−22i−2i00−i2i2−i2i222−2−22i−2i000000−i2−i2i2i2000000000000002−20
χ342-222-2-2-22200002-2-22-22-22i−2i−i2i2−i2i20000-2-22200000002−22i−2i00−i2i2−i2i222−2−2−2i2i000000i2i2−i2−i200000000000000−220
χ352-222-2-2-22200002-2-22-22-22i−2ii2−i2i2−i2000022-2-20000000−222i−2i00i2−i2i2−i2−2−2222i−2i000000i2i2−i2−i200000000000000−220
χ362-222-2-2-22200002-2-22-22-22i−2ii2−i2i2−i20000-2-2220000000−222i−2i00i2−i2i2−i2−2−222−2i2i000000−i2−i2i2i2000000000000002−20
χ372-222-2-2-22200002-2-22-22-2−2i2i−i2i2−i2i2000022-2-20000000−22−2i2i00−i2i2−i2i2−2−222−2i2i000000−i2−i2i2i200000000000000−220
χ382-222-2-2-22200002-2-22-22-2−2i2i−i2i2−i2i20000-2-2220000000−22−2i2i00−i2i2−i2i2−2−2222i−2i000000i2i2−i2−i2000000000000002−20
χ392-222-2-2-22200002-2-22-22-2−2i2ii2−i2i2−i2000022-2-200000002−2−2i2i00i2−i2i2−i222−2−2−2i2i000000i2i2−i2−i2000000000000002−20
χ402-222-2-2-22200002-2-22-22-2−2i2ii2−i2i2−i20000-2-22200000002−2−2i2i00i2−i2i2−i222−2−22i−2i000000−i2−i2i2i200000000000000−220
χ412-2-222-22-222-22-2-2-2-222-2200000022-2-2000002i−2i00000000000000000000002-22-22i−2i2i−2i000002i−2i0000000000
χ422-2-222-22-222-22-2-2-2-222-2200000022-2-2000002i−2i0000000000000000000000-22-22−2i2i−2i2i000002i−2i0000000000
χ432-2-222-22-222-22-2-2-2-222-2200000022-2-200000−2i2i00000000000000000000002-22-2−2i2i−2i2i00000−2i2i0000000000
χ442-2-222-22-222-22-2-2-2-222-2200000022-2-200000−2i2i0000000000000000000000-22-222i−2i2i−2i00000−2i2i0000000000
χ452-2-2-222-22222-2-222-2-2-2-22000000-22-222i−2i2i−2i0002i−2i0000000000000000002i−2i000000000002i−2i00000002-2000
χ462-2-2-222-22222-2-222-2-2-2-22000000-22-222i−2i2i−2i000−2i2i0000000000000000002i−2i00000000000−2i2i0000000-22000
χ472-2-2-222-22222-2-222-2-2-2-22000000-22-22−2i2i−2i2i0002i−2i000000000000000000−2i2i000000000002i−2i0000000-22000
χ482-2-2-222-22222-2-222-2-2-2-22000000-22-22−2i2i−2i2i000−2i2i000000000000000000−2i2i00000000000−2i2i00000002-2000
χ492-2-2-222-222-2-22222-2-2-2-220000002-22-22i−2i2i−2i000002-20000000000000000−2i2i2i−2i−2i2i000000000002-200000000
χ502-2-2-222-222-2-22222-2-2-2-220000002-22-22i−2i2i−2i00000-220000000000000000−2i2i−2i2i2i−2i00000000000-2200000000
χ512-2-2-222-222-2-22222-2-2-2-220000002-22-2−2i2i−2i2i000002-200000000000000002i−2i−2i2i2i−2i000000000002-200000000
χ522-2-2-222-222-2-22222-2-2-2-220000002-22-2−2i2i−2i2i00000-2200000000000000002i−2i2i−2i−2i2i00000000000-2200000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244000022220000-400000000-2-2220000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400002222000040000000022-2-20000000000000000000000000000000000000
χ55444-44-4-4-444-4-44-4-44-4-444000000-444-4000000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-24-4-4422-222-2-20000002-2-2200000000000000000000023−2323−2300000000000000000000000000000
χ57444-44-4-4-4-24-4-4422-222-2-20000002-2-22000000000000000000000−2323−232300000000000000000000000000000
χ58444-44-4-4-4-2-444-422-222-2-20044-4-4-222-200000000000000000-2-222000000000000000000000000000000000
χ59444-44-4-4-4-2-444-422-222-2-200-4-444-222-20000000000000000022-2-2000000000000000000000000000000000
χ6044-44-44-4-440000-4444-4-4-4000000000000000000000000000000000000000000022−22−222200000000000000000
χ6144-44-44-4-440000-4444-4-4-40000000000000000000000000000000000000000000−222222−2200000000000000000
χ6244-4-4-4-444400004-44-44-4-400000000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6344-4-4-4-444400004-44-44-4-40000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ644-444-4-4-44-20000-222-22-224i−4i−2i22i2−2i22i200000000000000022−22−2i2i00i2−i2i2−i2−2−22200000000000000000000000000000
χ654-444-4-4-44-20000-222-22-224i−4i2i2−2i22i2−2i2000000000000000−2222−2i2i00−i2i2−i2i222−2−200000000000000000000000000000
χ664-444-4-4-44-20000-222-22-22−4i4i−2i22i2−2i22i2000000000000000−22222i−2i00i2−i2i2−i222−2−200000000000000000000000000000
χ674-444-4-4-44-20000-222-22-22−4i4i2i2−2i22i2−2i200000000000000022−222i−2i00−i2i2−i2i2−2−22200000000000000000000000000000
χ684-44-4-444-440000-44-4-444-400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ694-44-4-444-440000-44-4-444-4002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ704-44-4-444-4-200002-222-2-2200−2i22i22i2−2i20000000000000000000−2i32i3i2−i2−i2i26−6−6600000000000000000000000000000
χ714-44-4-444-4-200002-222-2-2200−2i22i22i2−2i200000000000000000002i3−2i3i2−i2−i2i2−666−600000000000000000000000000000
χ724-44-4-444-4-200002-222-2-22002i2−2i2−2i22i20000000000000000000−2i32i3−i2i2i2−i2−666−600000000000000000000000000000
χ734-44-4-444-4-200002-222-2-22002i2−2i2−2i22i200000000000000000002i3−2i3−i2i2i2−i26−6−6600000000000000000000000000000
χ744-4-444-44-44-44-44-4-4-444-44000000-4-444000000000000000000000000000000000000000000000000000000
χ754-4-444-44-4-24-44-4222-2-22-2000000-2-222000004i−4i00000000000000000000000000000000000−2i2i0000000000
χ764-4-444-44-4-24-44-4222-2-22-2000000-2-22200000−4i4i000000000000000000000000000000000002i−2i0000000000
χ774-4-444-44-4-2-44-44222-2-22-200000022-2-200000000000000000000000000000000000000−2i32i300000000000000
χ784-4-444-44-4-2-44-44222-2-22-200000022-2-2000000000000000000000000000000000000002i3−2i300000000000000
χ794-4-4-444-44-244-4-4-2-22222-20000002-22-200000004i−4i0000000000000000000000000000000−2i2i000000000000
χ804-4-4-444-44-244-4-4-2-22222-20000002-22-20000000−4i4i00000000000000000000000000000002i−2i000000000000
χ814-4-4-444-44-2-4-444-2-22222-2000000-22-220000000004-4000000000000000000000000000000000-2200000000
χ824-4-4-444-44-2-4-444-2-22222-2000000-22-22000000000-440000000000000000000000000000000002-200000000
χ8388-88-88-8-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-8-888-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000

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