Finite Group Databasebeta

← Group #10831001

Character table — Group #10831001

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212121212122424242448484848
order12222222344446666666224466668888121212121212121222222244666666666666881212121224242424242424244444888824884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-11-1
χ61111111111111111111111111111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-11
χ71111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-11
χ81111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-11-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-11-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1
χ17222222222-2-2-2-2222222222-2-222220000-2-2-2-2-2-2-2-2000000000000000000000000000000000022-2-200002-2000000
χ18222222222-2-2-2-2222222222-2-222220000-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-2220000-22000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-20000-2-2-22222-2000000000000000000000000000000000022-2-20000-22000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-20000-2-2-22222-20000000000000000000000000000000000-2-22200002-2000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111221111-1-1-1-1-1-1-1-10000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-11111-2-21111111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-2-2-1-1-1-1111111110000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-211112222-1-1-11111-122-2-222-2-2-1-1-1-11111-1-1-1-1-2-21111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-211112222-1-1-11111-1-2-222-2-2221111-1-1-1-11111-2-2-1-1-1-1-1-1-1-111110000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-1-11111-122-2-2-2-222-1-1-1-11111111122-1-1-1-11111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-1-11111-1-2-22222-2-21111-1-1-1-1-1-1-1-12211111111-1-1-1-10000000000000000
χ2922-2-2-2-22222-2-2222-2-2-2-220000000022-2-22-2-200002002-2002-2000022-2-200000022-2-222-2-200000000000000000000
χ3022-2-2-2-22222-2-2222-2-2-2-220000000022-2-22-2-20000200-2200-220000-2-222000000-2-22222-2-200000000000000000000
χ3122-2-2-2-22222-2-2222-2-2-2-2200000000-2-2222-2-200002002-200-22000022-2-2000000-2-222-2-22200000000000000000000
χ3222-2-2-2-22222-2-2222-2-2-2-2200000000-2-2222-2-20000200-22002-20000-2-22200000022-2-2-2-22200000000000000000000
χ3322-2-2-2-222-12-2-22-1-11111-10000−i3−i3i3i322-2-2-111−i3−i3i3i3-1002-2002-2−i3−i3i3i3-1-111−i3−i3i3i300-1-111-1-111−i3−i3i3i30000000000000000
χ3422-2-2-2-222-12-2-22-1-11111-10000−i3−i3i3i322-2-2-111−i3−i3i3i3-100-2200-22i3i3−i3−i311-1-1i3i3−i3−i30011-1-1-1-111−i3−i3i3i30000000000000000
χ3522-2-2-2-222-12-2-22-1-11111-10000−i3−i3i3i3-2-222-111−i3−i3i3i3-1002-200-22−i3−i3i3i3-1-111i3i3−i3−i30011-1-111-1-1i3i3−i3−i30000000000000000
χ3622-2-2-2-222-12-2-22-1-11111-10000−i3−i3i3i3-2-222-111−i3−i3i3i3-100-22002-2i3i3−i3−i311-1-1−i3−i3i3i300-1-11111-1-1i3i3−i3−i30000000000000000
χ3722-2-2-2-222-12-2-22-1-11111-10000i3i3−i3−i322-2-2-111i3i3−i3−i3-1002-2002-2i3i3−i3−i3-1-111i3i3−i3−i300-1-111-1-111i3i3−i3−i30000000000000000
χ3822-2-2-2-222-12-2-22-1-11111-10000i3i3−i3−i322-2-2-111i3i3−i3−i3-100-2200-22−i3−i3i3i311-1-1−i3−i3i3i30011-1-1-1-111i3i3−i3−i30000000000000000
χ3922-2-2-2-222-12-2-22-1-11111-10000i3i3−i3−i3-2-222-111i3i3−i3−i3-1002-200-22i3i3−i3−i3-1-111−i3−i3i3i30011-1-111-1-1−i3−i3i3i30000000000000000
χ4022-2-2-2-222-12-2-22-1-11111-10000i3i3−i3−i3-2-222-111i3i3−i3−i3-100-22002-2−i3−i3i3i311-1-1i3i3−i3−i300-1-11111-1-1−i3−i3i3i30000000000000000
χ412-222-2-22-2222-2-2-2-222-2-222-22-22-22-2000022-22-22-2-2000000000000000000000000000000000000002i2i−2i−2i002i−2i0000
χ422-222-2-22-2222-2-2-2-222-2-222-22-22-22-2000022-22-22-2-200000000000000000000000000000000000000−2i−2i2i2i00−2i2i0000
χ432-222-2-22-2222-2-2-2-222-2-22-22-22-22-22000022-2-22-22-2000000000000000000000000000000000000002i2i−2i−2i00−2i2i0000
χ442-222-2-22-2222-2-2-2-222-2-22-22-22-22-22000022-2-22-22-200000000000000000000000000000000000000−2i−2i2i2i002i−2i0000
χ452-222-2-22-22-2-222-2-222-2-222-2-222-22-22-22-2-2-22-22-222000000000000000000002-200002-22-22-22-20000000000000000
χ462-222-2-22-22-2-222-2-222-2-222-2-222-22-2-22-22-2-22-22-22200000000000000000000-220000-22-22-22-220000000000000000
χ472-222-2-22-22-2-222-2-222-2-22-222-2-22-222-22-2-2-222-22-2200000000000000000000-2200002-22-2-22-220000000000000000
χ482-222-2-22-22-2-222-2-222-2-22-222-2-22-22-22-22-2-222-22-22000000000000000000002-20000-22-222-22-20000000000000000
χ492-222-2-22-2-1-2-22211-1-111-12-2-22-11-112-22-211-11-11-1-100000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i32-2−i3i3−i3i3-11-11-11-110000000000000000
χ502-222-2-22-2-1-2-22211-1-111-12-2-22-11-112-22-211-11-11-1-100000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i32-2i3−i3i3−i3-11-11-11-110000000000000000
χ512-222-2-22-2-1-2-22211-1-111-12-2-22-11-11-22-2211-11-11-1-100000000−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3-22i3−i3i3−i31-11-11-11-10000000000000000
χ522-222-2-22-2-1-2-22211-1-111-12-2-22-11-11-22-2211-11-11-1-100000000i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3-22−i3i3−i3i31-11-11-11-10000000000000000
χ532-222-2-22-2-1-2-22211-1-111-1-222-21-11-12-22-211-1-11-11-100000000−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3-22i3−i3i3−i3-11-111-11-10000000000000000
χ542-222-2-22-2-1-2-22211-1-111-1-222-21-11-12-22-211-1-11-11-100000000i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3-22−i3i3−i3i3-11-111-11-10000000000000000
χ552-222-2-22-2-1-2-22211-1-111-1-222-21-11-1-22-2211-1-11-11-100000000−i3i3−i3i3i3−i3i3−i3i3−i3i3−i32-2−i3i3−i3i31-11-1-11-110000000000000000
χ562-222-2-22-2-1-2-22211-1-111-1-222-21-11-1-22-2211-1-11-11-100000000i3−i3i3−i3−i3i3−i3i3−i3i3−i3i32-2i3−i3i3−i31-11-1-11-110000000000000000
χ572-2-2-2222-22-22-22-2-2-2-2222000000002-2-22-22-2000022-2002-2002-2-2200002-2-220000002-2-2200000000000000000000
χ582-2-2-2222-22-22-22-2-2-2-2222000000002-2-22-22-200002-2200-2200-222-20000-222-20000002-2-2200000000000000000000
χ592-2-2-2222-22-22-22-2-2-2-222200000000-222-2-22-2000022-200-22002-2-220000-222-2000000-222-200000000000000000000
χ602-2-2-2222-22-22-22-2-2-2-222200000000-222-2-22-200002-22002-200-222-200002-2-22000000-222-200000000000000000000
χ612-2-2-2222-2-1-22-221111-1-1-10000−i3i3i3−i32-2-221-11i3−i3−i3i3-12-2002-200-111-1−i3i3i3−i3-111-100−i3i3i3−i3-111-1−i3i3i3−i30000000000000000
χ622-2-2-2222-2-1-22-221111-1-1-10000−i3i3i3−i32-2-221-11i3−i3−i3i3-1-2200-22001-1-11i3−i3−i3i31-1-1100i3−i3−i3i3-111-1−i3i3i3−i30000000000000000
χ632-2-2-2222-2-1-22-221111-1-1-10000−i3i3i3−i3-222-21-11i3−i3−i3i3-12-200-2200-111-1−i3i3i3−i31-1-1100i3−i3−i3i31-1-11i3−i3−i3i30000000000000000
χ642-2-2-2222-2-1-22-221111-1-1-10000−i3i3i3−i3-222-21-11i3−i3−i3i3-1-22002-2001-1-11i3−i3−i3i3-111-100−i3i3i3−i31-1-11i3−i3−i3i30000000000000000
χ652-2-2-2222-2-1-22-221111-1-1-10000i3−i3−i3i32-2-221-11−i3i3i3−i3-12-2002-200-111-1i3−i3−i3i3-111-100i3−i3−i3i3-111-1i3−i3−i3i30000000000000000
χ662-2-2-2222-2-1-22-221111-1-1-10000i3−i3−i3i32-2-221-11−i3i3i3−i3-1-2200-22001-1-11−i3i3i3−i31-1-1100−i3i3i3−i3-111-1i3−i3−i3i30000000000000000
χ672-2-2-2222-2-1-22-221111-1-1-10000i3−i3−i3i3-222-21-11−i3i3i3−i3-12-200-2200-111-1i3−i3−i3i31-1-1100−i3i3i3−i31-1-11−i3i3i3−i30000000000000000
χ682-2-2-2222-2-1-22-221111-1-1-10000i3−i3−i3i3-222-21-11−i3i3i3−i3-1-22002-2001-1-11−i3i3i3−i3-111-100i3−i3−i3i31-1-11−i3i3i3−i30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-200002222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422220000222-2-2-2-2200000000000000000000000000000000000000000000000000
χ71444-44-4-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000000004i−4i000000000000
χ72444-44-4-4-4400004-44-44-4-400000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ7344-44-44-4-4400004-4-44-44-40000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i200000000
χ7444-44-44-4-4400004-4-44-44-400000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i200000000
χ7544-4-4-4-4444-444-444-4-4-4-44000000000000-4440000-400000000000000000000000000000000000000000000000000
χ7644-4-4-4-444-2-444-4-2-22222-20000−2i3−2i32i32i300002-2-22i32i3−2i3−2i3200000000000000000000000000000000000000000000000000
χ7744-4-4-4-444-2-444-4-2-22222-200002i32i3−2i3−2i300002-2-2−2i3−2i32i32i3200000000000000000000000000000000000000000000000000
χ784-444-4-44-4-244-4-422-2-222-24-44-4-22-220000-2-22-22-22200000000000000000000000000000000000000000000000000
χ794-444-4-44-4-244-4-422-2-222-2-44-442-22-20000-2-222-22-2200000000000000000000000000000000000000000000000000
χ804-44-4-44-4440000-444-4-44-40000000000000000000000000000000000000000000000000000004-400000000000000
χ814-44-4-44-4440000-444-4-44-4000000000000000000000000000000000000000000000000000000-4400000000000000
χ824-4-444-4-4440000-44-444-4-4000000000000000000000000000000000000000000000000000000000022−22−222200000000
χ834-4-444-4-4440000-44-444-4-40000000000000000000000000000000000000000000000000000000000−222222−2200000000
χ844-4-4-4444-444-44-4-4-4-4-44440000000000004-440000-400000000000000000000000000000000000000000000000000
χ854-4-4-4444-4-24-44-42222-2-2-20000−2i32i32i3−2i30000-22-2−2i32i32i3−2i3200000000000000000000000000000000000000000000000000
χ864-4-4-4444-4-24-44-42222-2-2-200002i3−2i3−2i32i30000-22-22i3−2i3−2i32i3200000000000000000000000000000000000000000000000000
χ87888-88-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-88-88-8-8-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8-88-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-8-88-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000

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