Finite Group Databasebeta

← Group #10826858

Character table — Group #10826858

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order1222222222344446664466666612121212222224446666666612124444444444446881212122424242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111111-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1111-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-111-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111-1-1-11111111-1-11-1-1
χ911111-1-1-1-1111111111-1-111-1-1-1-1111111-1-11-1-111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1111-1-11-1-1-1-111-1
χ1011111-1-1-1-1111111111-1-111-1-1-1-1111111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-11111-1-11
χ1111111-1-1-1-1111111111-1-111-1-1-1-1111111-1-1-111-11111-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-111-111-1-1-1-11
χ1211111-1-1-1-1111111111-1-111-1-1-1-1111111-1-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1111-1-11111-1
χ1311111-1-1-1-1111111111-1-111-1-1-1-11111-1-1111-1-11-1-1-1-11111-1-11111-1-1-1-111111-11-1-11-1-1111-1-1-1-11-11
χ1411111-1-1-1-1111111111-1-111-1-1-1-11111-1-1111-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-11-1-11-1-111-11111-11-1
χ1511111-1-1-1-1111111111-1-111-1-1-1-11111-1-111-111-1-1-1-1-11111-1-11111-1-1-1-11111-11-111-111-1-1-111-1-1-11-1
χ1611111-1-1-1-1111111111-1-111-1-1-1-11111-1-111-111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11-111-111-1-11-1-1111-11
χ1722222222222-2-2-2-2222-2-2222222-2-2-2-20000000000000000-2-222-2-20000000000000000000002-2000
χ1822222222222-2-2-2-2222-2-2222222-2-2-2-20000000000000000-2-2-2-222000000000000000000000-22000
χ192222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000000000000-122-1-1-1-1-1-1-100000000
χ202222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-10000000000001-2-2111111100000000
χ212222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1000000000000-1-2-2-1-1-1111100000000
χ222222222222-12222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1000000000000122111-1-1-1-100000000
χ2322222-2-2-2-222-2-2-2-22222222-2-2-2-2-2-2-2-200000000000000002222-2-2000000000000000000000-22000
χ2422222-2-2-2-222-2-2-2-22222222-2-2-2-2-2-2-2-2000000000000000022-2-2220000000000000000000002-2000
χ2522222-2-2-2-22-12222-1-1-1-2-2-1-11111-1-1-1-122-2-22-2-22-1-1-1-1111111000000000000-12-211-1-1-11100000000
χ2622222-2-2-2-22-12222-1-1-1-2-2-1-11111-1-1-1-122-2-2-222-2-1-1-1-11111110000000000001-22-1-1111-1-100000000
χ2722222-2-2-2-22-12222-1-1-1-2-2-1-11111-1-1-1-1-2-2222-2-221111-1-1-1-111000000000000-1-2211-111-1-100000000
χ2822222-2-2-2-22-12222-1-1-1-2-2-1-11111-1-1-1-1-2-222-222-21111-1-1-1-11100000000000012-2-1-11-1-11100000000
χ292222-222-2-2-2222-2-22222-2-2-222-2-2-2-222000022-2-2000000002-20000000000002002-2-2000000000000
χ302222-222-2-2-2222-2-22222-2-2-222-2-2-2-2220000-2-222000000002-2000000000000-200-222000000000000
χ312222-222-2-2-22-2-222222-22-2-222-2-222-2-20000000000000000-22000000000000000000000022-200-200
χ322222-222-2-2-22-2-222222-22-2-222-2-222-2-20000000000000000-220000000000000000000000-2-2200200
χ332222-222-2-2-2-122-2-2-1-1-12-211-1-11111-1-1000022-2-2−i3−i3i3i3−i3−i3i3i3-11000000000000-100-111−i3i3−i3i300000000
χ342222-222-2-2-2-122-2-2-1-1-12-211-1-11111-1-1000022-2-2i3i3−i3−i3i3i3−i3−i3-11000000000000-100-111i3−i3i3−i300000000
χ352222-222-2-2-2-122-2-2-1-1-12-211-1-11111-1-10000-2-222−i3−i3i3i3−i3−i3i3i3-110000000000001001-1-1i3−i3i3−i300000000
χ362222-222-2-2-2-122-2-2-1-1-12-211-1-11111-1-10000-2-222i3i3−i3−i3i3i3−i3−i3-110000000000001001-1-1−i3i3−i3i300000000
χ372222-2-2-222-2222-2-2222-22-2-2-2-222-2-22200002-22-200000000-22000000000000200-22-2000000000000
χ382222-2-2-222-2222-2-2222-22-2-2-2-222-2-2220000-22-2200000000-22000000000000-2002-22000000000000
χ392222-2-2-222-22-2-2222222-2-2-2-2-22222-2-200000000000000002-200000000000000000000002-2200-200
χ402222-2-2-222-22-2-2222222-2-2-2-2-22222-2-200000000000000002-20000000000000000000000-22-200200
χ412222-2-2-222-2-122-2-2-1-1-1-221111-1-111-1-100002-22-2−i3−i3i3i3i3i3−i3−i31-1000000000000-1001-11−i3i3i3−i300000000
χ422222-2-2-222-2-122-2-2-1-1-1-221111-1-111-1-100002-22-2i3i3−i3−i3−i3−i3i3i31-1000000000000-1001-11i3−i3−i3i300000000
χ432222-2-2-222-2-122-2-2-1-1-1-221111-1-111-1-10000-22-22−i3−i3i3i3i3i3−i3−i31-1000000000000100-11-1i3−i3−i3i300000000
χ442222-2-2-222-2-122-2-2-1-1-1-221111-1-111-1-10000-22-22i3i3−i3−i3−i3−i3i3i31-1000000000000100-11-1−i3i3i3−i300000000
χ452-2-22-20000222-22-2-2-22002-200002-22-2002-2000000002-22-2002-22-2000022-2-2000000000000000000
χ462-2-22-20000222-22-2-2-22002-200002-22-2002-2000000002-22-200-22-220000-2-222000000000000000000
χ472-2-22-20000222-22-2-2-22002-200002-22-200-2200000000-22-22002-22-20000-2-222000000000000000000
χ482-2-22-20000222-22-2-2-22002-200002-22-200-2200000000-22-2200-22-22000022-2-2000000000000000000
χ492-2-22-2000022-22-22-2-22002-20000-22-222-20000002-22-20000002-2-2222-2-20000000000000000000000
χ502-2-22-2000022-22-22-2-22002-20000-22-222-20000002-22-2000000-222-2-2-2220000000000000000000000
χ512-2-22-2000022-22-22-2-22002-20000-22-22-22000000-22-220000002-2-22-2-2220000000000000000000000
χ522-2-22-2000022-22-22-2-22002-20000-22-22-22000000-22-22000000-222-222-2-20000000000000000000000
χ534444444444-2-4-4-4-4-2-2-2-4-4-2-2-2-2-2-22222000000000000000022000000000000000000000000000000
χ5444444-4-4-4-44-2-4-4-4-4-2-2-244-2-2222222220000000000000000-2-2000000000000000000000000000000
χ554444-444-4-4-4-2-4-444-2-2-2-4422-2-222-2-22200000000000000002-2000000000000000000000000000000
χ564444-4-4-444-4-2-4-444-2-2-24-42222-2-2-2-2220000000000000000-22000000000000000000000000000000
χ5744-4-40004-40400004-4-40000004-4000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ5844-4-40004-40400004-4-40000004-400000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ5944-4-4000-440400004-4-4000000-44000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ6044-4-4000-440400004-4-4000000-4400000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ614-44-404-400040000-44-400004-400000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ624-44-404-400040000-44-400004-40000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ634-44-40-4400040000-44-40000-4400000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ644-44-40-4400040000-44-40000-440000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ654-4-4440000-444-4-44-4-4400-440000-444-4000000000000000000000000000000000000000000000000
χ664-4-4440000-44-444-4-4-4400-4400004-4-44000000000000000000000000000000000000000000000000
χ674-4-4440000-4-24-4-4422-2002-200002-2-22000000000000−2i32i32i3−2i300000000000000000000000000000000
χ684-4-4440000-4-24-4-4422-2002-200002-2-220000000000002i3−2i3−2i32i300000000000000000000000000000000
χ694-4-4440000-4-2-444-422-2002-20000-222-200000000−2i32i32i3−2i3000000000000000000000000000000000000
χ704-4-4440000-4-2-444-422-2002-20000-222-2000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ714-4-44-400004-24-44-422-200-220000-22-22004-400000000-22-2200000000000000000000000000000000
χ724-4-44-400004-24-44-422-200-220000-22-2200-44000000002-22-200000000000000000000000000000000
χ734-4-44-400004-2-44-4422-200-2200002-22-24-4000000-22-22000000000000000000000000000000000000
χ744-4-44-400004-2-44-4422-200-2200002-22-2-440000002-22-2000000000000000000000000000000000000
χ7588-8-80008-80-40000-444000000-440000000000000000000000000000000000000000000000000000
χ7688-8-8000-880-40000-4440000004-40000000000000000000000000000000000000000000000000000
χ778-88-808-8000-400004-440000-44000000000000000000000000000000000000000000000000000000
χ788-88-80-88000-400004-4400004-4000000000000000000000000000000000000000000000000000000

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