Finite Group Databasebeta

← Group #10826269

Character table — Group #10826269

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444466668888888888888888888881212121212121212121212121616161616161616162424242424242448
order1222222234444666666644888812121212222222444448812121212242424242424242422444444888846612121212121222444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1
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
χ4111111111111111111111111111111-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111-1-11-1-11
χ61111111111111111111111-1-1-1-111111111-1-111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-111-111-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1111
χ911111111111111111111-1-111111111111111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-111-1-111-1-111-1-1-1-1-1-1
χ1011111111111111111111-1-1111111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-111-1-111-1-111-1-1-11
χ1111111111111111111111-1-111111111-1-1-1-111-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111
χ1211111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-1-111-1-11111-1-1111-1
χ1311111111111111111111-1-1-1-1-1-11111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-111-1
χ1411111111111111111111-1-1-1-1-1-111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11-1-11111-1-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1111111-1-111111111-111-1-1-1-111-1-1-1-11-1-11
χ1611111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-11111-1-111111-1-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-2222200-200000022-2-20000000022-2-2000000000000000000000-2000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-200-200000022-2-200000000-2-2220000000000000000000002000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-22222002000000-2-22200000000-2-2-2-20000000000000000000002000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2002000000-2-222000000002222000000000000000000000-2000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-10000-2-22-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000222-2-2-2-2-2-2-1-1-1-1111111110000000000002-1-1-1-1111100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-10000-2-222222-2-2-1-1-1-111111111000000000000-21111-1-1-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-1000022-222-2-2-2-21111-1-1-1-11111000000000000-2-1-111-1-11100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-1-1-1-10000-2-2-2-2-222-2-21111-1-1-1-11111000000000000211-1-111-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1000022-2-2-2222211111111-1-1-1-1000000000000-2-1-11111-1-100000000
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
χ2922-2-22-2-222-2-2222-2-2-2-2220022-2-22-22-20000000000000000022-2-20000000022-2-200000000000002-2000000
χ3022-2-22-2-222-2-2222-2-2-2-2220022-2-22-22-20000000000000000022-2-200000000-2-2220000000000000-22000000
χ3122-2-22-2-222-2-2222-2-2-2-22200-2-2222-22-200000000000000000-2-2220000000022-2-20000000000000-22000000
χ3222-2-22-2-222-2-2222-2-2-2-22200-2-2222-22-200000000000000000-2-22200000000-2-22200000000000002-2000000
χ332-22-2-22-222-22-22-222-2-2-22000000-2-22200002-2000000000000000000000002-22-222-2-202-200000000000000
χ342-22-2-22-222-22-22-222-2-2-22000000-2-22200002-200000000000000000000000-22-22-2-22202-200000000000000
χ352-22-2-22-222-22-22-222-2-2-22000000-2-2220000-22000000000000000000000002-22-2-2-2220-2200000000000000
χ362-22-2-22-222-22-22-222-2-2-22000000-2-2220000-2200000000000000000000000-22-2222-2-20-2200000000000000
χ372-2-2222-2-220000-22-22-22-22-2−i2i2−i2i2000022-2-20000000−i2i22-200−i2i2−i2i2−i2−i2i2i22-2000000−i2i2−i2i200000000000000−i2i20
χ382-2-2222-2-220000-22-22-22-22-2−i2i2−i2i20000-2-2220000000−i2i22-200−i2i2−i2i2−i2−i2i2i2-22000000i2−i2i2−i200000000000000i2−i20
χ392-2-2222-2-220000-22-22-22-22-2i2−i2i2−i2000022-2-20000000i2−i22-200i2−i2i2−i2i2i2−i2−i22-2000000i2−i2i2−i200000000000000i2−i20
χ402-2-2222-2-220000-22-22-22-22-2i2−i2i2−i20000-2-2220000000i2−i22-200i2−i2i2−i2i2i2−i2−i2-22000000−i2i2−i2i200000000000000−i2i20
χ412-2-2222-2-220000-22-22-22-2-22−i2i2−i2i2000022-2-20000000i2−i2-2200−i2i2−i2i2i2i2−i2−i2-22000000−i2i2−i2i200000000000000i2−i20
χ422-2-2222-2-220000-22-22-22-2-22−i2i2−i2i20000-2-2220000000i2−i2-2200−i2i2−i2i2i2i2−i2−i22-2000000i2−i2i2−i200000000000000−i2i20
χ432-2-2222-2-220000-22-22-22-2-22i2−i2i2−i2000022-2-20000000−i2i2-2200i2−i2i2−i2−i2−i2i2i2-22000000i2−i2i2−i200000000000000−i2i20
χ442-2-2222-2-220000-22-22-22-2-22i2−i2i2−i20000-2-2220000000−i2i2-2200i2−i2i2−i2−i2−i2i2i22-2000000−i2i2−i2i200000000000000i2−i20
χ452-2-22-2-22222-2-22-2-2-222-22000000-222-22-22-20002-20000000000000000002-22-2-220000000002-20000000000
χ462-2-22-2-22222-2-22-2-2-222-22000000-222-22-22-2000-220000000000000000002-2-222-2000000000-220000000000
χ472-2-22-2-22222-2-22-2-2-222-22000000-222-2-22-220002-2000000000000000000-22-222-20000000002-20000000000
χ482-2-22-2-22222-2-22-2-2-222-22000000-222-2-22-22000-22000000000000000000-222-2-22000000000-220000000000
χ492-2-22-2-2222-222-2-2-2-222-220000002-2-222-22-2000002-20000000000000000-220000000000000002-2002-20000
χ502-2-22-2-2222-222-2-2-2-222-220000002-2-222-22-200000-220000000000000000-22000000000000000-2200-220000
χ512-2-22-2-2222-222-2-2-2-222-220000002-2-22-22-22000002-200000000000000002-20000000000000002-200-220000
χ522-2-22-2-2222-222-2-2-2-222-220000002-2-22-22-2200000-2200000000000000002-2000000000000000-22002-20000
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
χ554444-4-4-4-4400004-444-4-4-400000000004-4-4400000000000000000000000000000000000000000000000000
χ564444-4-4-4-4400004-444-4-4-40000000000-444-400000000000000000000000000000000000000000000000000
χ5744-4-44-4-44444-4-44-4-4-4-444000000-44-44000000000000000000000000000000000000000000000000000000
χ5844-4-44-4-44-244-4-4-22222-2-20000002-22-2000000000000000000000−2i32i3−2i32i300000000000000000000000000000
χ5944-4-44-4-44-244-4-4-22222-2-20000002-22-20000000000000000000002i3−2i32i3−2i300000000000000000000000000000
χ6044-4-44-4-44-2-4-444-22222-2-20044-4-4-22-2200000000000000000-2-222000000000000000000000000000000000
χ6144-4-44-4-44-2-4-444-22222-2-200-4-444-22-220000000000000000022-2-2000000000000000000000000000000000
χ6244-4-4-444-44000044-4-44-4-40000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ6344-4-4-444-44000044-4-44-4-400000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ644-44-44-44-440000-4-44-444-400−2i22i22i2−2i2000000000000000000000−2i22i22i2−2i2000000000000000000000000000000000
χ654-44-44-44-440000-4-44-444-4002i2−2i2−2i22i20000000000000000000002i2−2i2−2i22i2000000000000000000000000000000000
χ664-44-44-44-4-2000022-22-2-2200−2i22i22i2−2i20000000000000000000−2i32i3i2−i2−i2i26−6−6600000000000000000000000000000
χ674-44-44-44-4-2000022-22-2-2200−2i22i22i2−2i200000000000000000002i3−2i3i2−i2−i2i2−666−600000000000000000000000000000
χ684-44-44-44-4-2000022-22-2-22002i2−2i2−2i22i20000000000000000000−2i32i3−i2i2i2−i2−666−600000000000000000000000000000
χ694-44-44-44-4-2000022-22-2-22002i2−2i2−2i22i200000000000000000002i3−2i3−i2i2i2−i26−6−6600000000000000000000000000000
χ704-44-4-44-4444-44-4-444-4-4-4400000044-4-4000000000000000000000000000000000000000000000000000000
χ714-44-4-44-44-24-44-42-2-2222-2000000-2-222000000000000000000000000000000000000000023−23000000000000
χ724-44-4-44-44-24-44-42-2-2222-2000000-2-2220000000000000000000000000000000000000000−2323000000000000
χ734-44-4-44-44-2-44-442-2-2222-200000022-2-200004-400000000000000000000000000000000-2200000000000000
χ744-44-4-44-44-2-44-442-2-2222-200000022-2-20000-44000000000000000000000000000000002-200000000000000
χ754-4-4444-4-4-200002-22-22-224-4−2i22i2−2i22i2000000000000000−2i22i2-2200i2−i2i2−i2i2i2−i2−i200000000000000000000000000000
χ764-4-4444-4-4-200002-22-22-224-42i2−2i22i2−2i20000000000000002i2−2i2-2200−i2i2−i2i2−i2−i2i2i200000000000000000000000000000
χ774-4-4444-4-4-200002-22-22-22-44−2i22i2−2i22i20000000000000002i2−2i22-200i2−i2i2−i2−i2−i2i2i200000000000000000000000000000
χ784-4-4444-4-4-200002-22-22-22-442i2−2i22i2−2i2000000000000000−2i22i22-200−i2i2−i2i2i2i2−i2−i200000000000000000000000000000
χ794-4-44-4-444-24-4-44222-2-22-20000002-2-2200000004-4000000000000000000000000000000000-220000000000
χ804-4-44-4-444-24-4-44222-2-22-20000002-2-220000000-440000000000000000000000000000000002-20000000000
χ814-4-44-4-444-2-444-4222-2-22-2000000-222-20000000004-4000000000000000000000000000000000-2200000000
χ824-4-44-4-444-2-444-4222-2-22-2000000-222-2000000000-440000000000000000000000000000000002-200000000
χ838888-8-8-8-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-888-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000

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