Finite Group Databasebeta

← Group #10828552

Character table — Group #10828552

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order12222222344446666666224444441212121212121212121212122222444444666666666612121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-11111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-11111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-111-1-1-1-111
χ17222222222-2-2-2-2222222222-2-222-2-2-2-2-2-22222-2-2-2-200002-200002200000000-2-222-2-2000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-222-2-2-2-2-2-2-2-222220000-2200002200000000-2-2-2-222000000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-2-2-2-2-22222-2-2-2-20000-220000-2-20000000022-2-222000000000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-222-2-2-2-2-2-2-2-2222200002-20000-2-2000000002222-2-2000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-111111111-1-1-1-1-1-1111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-11111111122-2-2-2-222-2-2-1-1-1-1-1-11111-1-11111-1-1-1-111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-222-2-2-2-222-1-11111-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-22211-1-1-1-111111111111111-1-1-1-10000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2111111-1-1-1-1111111-1-1-1-111110000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111222222-2-2-2-211-1-1-1-1-1-1-1-111-1-1-1-1111111110000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111-2-2-2-2222222111111111111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-1111100002-20000-1-1−i3−i3i3i3−i3−i3i3i311-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-1-1-1111100002-20000-1-1i3i3−i3−i3i3i3−i3−i311-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22211111111-1-1-1-10000-220000-1-1−i3−i3i3i3i3i3−i3−i31111-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22211111111-1-1-1-10000-220000-1-1i3i3−i3−i3−i3−i3i3i31111-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-111110000-22000011−i3−i3i3i3i3i3−i3−i3-1-111-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-111110000-22000011i3i3−i3−i3−i3−i3i3i3-1-111-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211111111-1-1-1-100002-2000011−i3−i3i3i3−i3−i3i3i3-1-1-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211111111-1-1-1-100002-2000011i3i3−i3−i3i3i3−i3−i3-1-1-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ3722-2-22-2-22222-2-222-2-22-2-200002i−2i2i−2i22-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000002i−2i002-200000000
χ3822-2-22-2-22222-2-222-2-22-2-200002i−2i2i−2i22-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000−2i2i00-2200000000
χ3922-2-22-2-22222-2-222-2-22-2-20000−2i2i−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000002i−2i00-2200000000
χ4022-2-22-2-22222-2-222-2-22-2-20000−2i2i−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000−2i2i002-200000000
χ4122-2-22-2-222-2-22222-2-22-2-200002i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000002i−2i002-20000000000
χ4222-2-22-2-222-2-22222-2-22-2-200002i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000−2i2i00-220000000000
χ4322-2-22-2-222-2-22222-2-22-2-20000−2i2i2i−2i-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000002i−2i00-220000000000
χ4422-2-22-2-222-2-22222-2-22-2-20000−2i2i2i−2i-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000−2i2i002-20000000000
χ452-2-2-2222-222-22-2-2-2-2-22222-22-200002-22-200000000002-200002-22-200002-22-22-2000000002-22-20000000000000000
χ462-2-2-2222-222-22-2-2-2-2-22222-22-200002-22-20000000000-220000-222-20000-22-222-200000000-22-220000000000000000
χ472-2-2-2222-222-22-2-2-2-2-2222-22-2200002-22-200000000002-20000-22-2200002-22-2-2200000000-22-220000000000000000
χ482-2-2-2222-222-22-2-2-2-2-2222-22-2200002-22-20000000000-2200002-2-220000-22-22-22000000002-22-20000000000000000
χ492-2-2-2222-22-22-22-2-2-2-22222-2-220000-22-22000000002-200002-2002-22-22-20000-2200002-22-200000000000000000000
χ502-2-2-2222-22-22-22-2-2-2-22222-2-220000-22-2200000000-220000-22002-2-22-220000-220000-22-2200000000000000000000
χ512-2-2-2222-22-22-22-2-2-2-2222-222-20000-22-22000000002-20000-2200-222-22-200002-20000-22-2200000000000000000000
χ522-2-2-2222-22-22-22-2-2-2-2222-222-20000-22-2200000000-2200002-200-22-22-2200002-200002-22-200000000000000000000
χ532-2-2-2222-2-12-22-21111-1-1-12-22-20000-11-11−i3i3−i3i3−i3i3−i3i3002-200002-2-11−i3i3i3−i3-11-11-11−i3i3−i3i3−i3i3i3−i3-11-110000000000000000
χ542-2-2-2222-2-12-22-21111-1-1-12-22-20000-11-11−i3i3−i3i3−i3i3−i3i300-220000-22-11i3−i3−i3i31-11-1-11−i3i3−i3i3i3−i3−i3i31-11-10000000000000000
χ552-2-2-2222-2-12-22-21111-1-1-12-22-20000-11-11i3−i3i3−i3i3−i3i3−i3002-200002-2-11i3−i3−i3i3-11-11-11i3−i3i3−i3i3−i3−i3i3-11-110000000000000000
χ562-2-2-2222-2-12-22-21111-1-1-12-22-20000-11-11i3−i3i3−i3i3−i3i3−i300-220000-22-11−i3i3i3−i31-11-1-11i3−i3i3−i3−i3i3i3−i31-11-10000000000000000
χ572-2-2-2222-2-12-22-21111-1-1-1-22-220000-11-11−i3i3−i3i3−i3i3−i3i3002-20000-221-1i3−i3−i3i3-11-111-1i3−i3i3−i3−i3i3i3−i31-11-10000000000000000
χ582-2-2-2222-2-12-22-21111-1-1-1-22-220000-11-11−i3i3−i3i3−i3i3−i3i300-2200002-21-1−i3i3i3−i31-11-11-1i3−i3i3−i3i3−i3−i3i3-11-110000000000000000
χ592-2-2-2222-2-12-22-21111-1-1-1-22-220000-11-11i3−i3i3−i3i3−i3i3−i3002-20000-221-1−i3i3i3−i3-11-111-1−i3i3−i3i3i3−i3−i3i31-11-10000000000000000
χ602-2-2-2222-2-12-22-21111-1-1-1-22-220000-11-11i3−i3i3−i3i3−i3i3−i300-2200002-21-1i3−i3−i3i31-11-11-1−i3i3−i3i3−i3i3i3−i3-11-110000000000000000
χ612-2-2-2222-2-1-22-221111-1-1-12-2-2200001-11-1−i3i3−i3i3i3−i3i3−i32-200002-200-11-11-11−i3i3i3−i31-1−i3i3i3−i3-11-11−i3i3i3−i30000000000000000
χ622-2-2-2222-2-1-22-221111-1-1-12-2-2200001-11-1−i3i3−i3i3i3−i3i3−i3-220000-2200-111-11-1i3−i3−i3i31-1−i3i3i3−i31-11-1i3−i3−i3i30000000000000000
χ632-2-2-2222-2-1-22-221111-1-1-12-2-2200001-11-1i3−i3i3−i3−i3i3−i3i32-200002-200-11-11-11i3−i3−i3i31-1i3−i3−i3i3-11-11i3−i3−i3i30000000000000000
χ642-2-2-2222-2-1-22-221111-1-1-12-2-2200001-11-1i3−i3i3−i3−i3i3−i3i3-220000-2200-111-11-1−i3i3i3−i31-1i3−i3−i3i31-11-1−i3i3i3−i30000000000000000
χ652-2-2-2222-2-1-22-221111-1-1-1-222-200001-11-1−i3i3−i3i3i3−i3i3−i32-20000-22001-1-11-11i3−i3−i3i3-11i3−i3−i3i31-11-1−i3i3i3−i30000000000000000
χ662-2-2-2222-2-1-22-221111-1-1-1-222-200001-11-1−i3i3−i3i3i3−i3i3−i3-2200002-2001-11-11-1−i3i3i3−i3-11i3−i3−i3i3-11-11i3−i3−i3i30000000000000000
χ672-2-2-2222-2-1-22-221111-1-1-1-222-200001-11-1i3−i3i3−i3−i3i3−i3i32-20000-22001-1-11-11−i3i3i3−i3-11−i3i3i3−i31-11-1i3−i3−i3i30000000000000000
χ682-2-2-2222-2-1-22-221111-1-1-1-222-200001-11-1i3−i3i3−i3−i3i3−i3i3-2200002-2001-11-11-1i3−i3−i3i3-11−i3i3i3−i3-11-11−i3i3i3−i30000000000000000
χ69444-4-44-4-4400004-44-4-44-4000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ70444-4-44-4-4400004-44-4-44-40000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ7144-44-4-44-4400004-4-44-4-4400000000000000000000000000000000000000000000000000000000000000−2i22i2000000
χ7244-44-4-44-4400004-4-44-4-44000000000000000000000000000000000000000000000000000000000000002i2−2i2000000
χ7344-4-44-4-44-244-4-4-2-222-22200004i−4i4i−4i-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ7444-4-44-4-44-244-4-4-2-222-2220000−4i4i−4i4i-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000
χ7544-4-44-4-44-2-4-444-2-222-22200004i−4i−4i4i22-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000
χ7644-4-44-4-44-2-4-444-2-222-2220000−4i4i4i−4i22-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000
χ774-4444-4-4-444-4-44-4-4444-4-4000000004-4-440000000000000000000000000000000000000000000000000000000000
χ784-4444-4-4-44-444-4-4-4444-4-400000000-444-40000000000000000000000000000000000000000000000000000000000
χ794-4444-4-4-4-24-4-4422-2-2-22200000000-222-223−23−232323−23−232300000000000000000000000000000000000000000000000000
χ804-4444-4-4-4-24-4-4422-2-2-22200000000-222-2−232323−23−232323−2300000000000000000000000000000000000000000000000000
χ814-4444-4-4-4-2-444-422-2-2-222000000002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000000000
χ824-4444-4-4-4-2-444-422-2-2-222000000002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000000000
χ834-44-4-4-44440000-444-4-4-44000000000000000000000000000000000000000000000000000000000000000022−220000
χ844-44-4-4-44440000-444-4-4-440000000000000000000000000000000000000000000000000000000000000000−22220000
χ854-4-44-44-4440000-44-44-44-40000000000000000000000000000000000000000000000000000000000000000000022−22
χ864-4-44-44-4440000-44-44-44-400000000000000000000000000000000000000000000000000000000000000000000−2222
χ87888-8-88-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-88-8-88-8-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8-8-888-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-88-88-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000000000

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