Finite Group Databasebeta

← Group #10826327

Character table — Group #10826327

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order12222222344446666666222222446666121212121212121222224466666666666688881212121224242424242424242244224444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-11-1-111-1-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11-111-1-111-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-111-11-1-1-1-111-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-11-11111-1-11-1
χ911111111111111111111-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ1111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-11111-1-1
χ1211111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-111111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-111111-1-1-1-1-1111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000222200-2-200000000
χ18222222222-2-2-2-22222222000022-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-2-2-2002200000000
χ19222222222-2-2-2-222222220000-2-222-2-2-2-2-2-2-22222-2000000000000000000000000000000000022-2-2002-200000000
χ20222222222-2-2-2-222222220000-2-222-2-2-2-2-2-2-22222-20000000000000000000000000000000000-2-22200-2200000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-11111-2-2-2-21111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-21111-1-1-11111-1-2-222-2-2-1-1-1-11111-1-1-1-122-2-21111-1-1-1-111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-21111-1-1-11111-1-2-2-2-222-1-1-1-111111111-2-222-1-1-1-11111-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2222211111111-1-1-1-1-2-2-2-2-1-1-1-1111111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111122221111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-11111-12222-2-21111-1-1-1-1-1-1-1-1-2-22211111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-11111-122-2-2221111-1-1-1-1111122-2-2-1-1-1-1-1-1-1-111110000000000000000
χ2922-2-22-22-22-222-222-2-2-2-2222-2-2000000002-2-20000200002-222-2-200000000002-222-2-2000022-2-20000000000000000
χ3022-2-22-22-22-222-222-2-2-2-2222-2-2000000002-2-2000020000-2222-2-20000000000-22-2-2220000-2-2220000000000000000
χ3122-2-22-22-22-222-222-2-2-2-22-2-222000000002-2-20000200002-2-2-2220000000000-2222-2-20000-2-2220000000000000000
χ3222-2-22-22-22-222-222-2-2-2-22-2-222000000002-2-2000020000-22-2-22200000000002-2-2-222000022-2-20000000000000000
χ3322-2-22-22-2-1-222-2-1-11111-122-2-20000−i3−i3i3i3-111−i3−i3i3i3-100002-2-1-111−i3−i3i3i3−i3−i3i3i3002-2-1-111−i3−i3i3i3-1-1110000000000000000
χ3422-2-22-22-2-1-222-2-1-11111-122-2-20000−i3−i3i3i3-111−i3−i3i3i3-10000-22-1-111−i3−i3i3i3i3i3−i3−i300-2211-1-1i3i3−i3−i311-1-10000000000000000
χ3522-2-22-22-2-1-222-2-1-11111-122-2-20000i3i3−i3−i3-111i3i3−i3−i3-100002-2-1-111i3i3−i3−i3i3i3−i3−i3002-2-1-111i3i3−i3−i3-1-1110000000000000000
χ3622-2-22-22-2-1-222-2-1-11111-122-2-20000i3i3−i3−i3-111i3i3−i3−i3-10000-22-1-111i3i3−i3−i3−i3−i3i3i300-2211-1-1−i3−i3i3i311-1-10000000000000000
χ3722-2-22-22-2-1-222-2-1-11111-1-2-2220000−i3−i3i3i3-111−i3−i3i3i3-100002-211-1-1i3i3−i3−i3−i3−i3i3i300-22-1-111i3i3−i3−i311-1-10000000000000000
χ3822-2-22-22-2-1-222-2-1-11111-1-2-2220000−i3−i3i3i3-111−i3−i3i3i3-10000-2211-1-1i3i3−i3−i3i3i3−i3−i3002-211-1-1−i3−i3i3i3-1-1110000000000000000
χ3922-2-22-22-2-1-222-2-1-11111-1-2-2220000i3i3−i3−i3-111i3i3−i3−i3-100002-211-1-1−i3−i3i3i3i3i3−i3−i300-22-1-111−i3−i3i3i311-1-10000000000000000
χ4022-2-22-22-2-1-222-2-1-11111-1-2-2220000i3i3−i3−i3-111i3i3−i3−i3-10000-2211-1-1−i3−i3i3i3−i3−i3i3i3002-211-1-1i3i3−i3−i3-1-1110000000000000000
χ412-22-2-222-22-22-22-2-222-2-222-22-200000000-22-200002002-2002-22-200002-22-22-20000002-22-200000000000000000000
χ422-22-2-222-22-22-22-2-222-2-222-22-200000000-22-20000200-22002-22-20000-22-22-22000000-22-2200000000000000000000
χ432-22-2-222-22-22-22-2-222-2-22-22-2200000000-22-200002002-200-22-2200002-22-2-22000000-22-2200000000000000000000
χ442-22-2-222-22-22-22-2-222-2-22-22-2200000000-22-20000200-2200-22-220000-22-222-20000002-22-200000000000000000000
χ452-22-2-222-2-1-22-2211-1-111-12-22-20000−i3i3−i3i31-11−i3i3−i3i3-1002-200-11-11−i3i3−i3i3-11-112-200−i3i3−i3i3-11-11−i3i3−i3i30000000000000000
χ462-22-2-222-2-1-22-2211-1-111-12-22-20000−i3i3−i3i31-11−i3i3−i3i3-100-2200-11-11−i3i3−i3i31-11-1-2200i3−i3i3−i31-11-1i3−i3i3−i30000000000000000
χ472-22-2-222-2-1-22-2211-1-111-12-22-20000i3−i3i3−i31-11i3−i3i3−i3-1002-200-11-11i3−i3i3−i3-11-112-200i3−i3i3−i3-11-11i3−i3i3−i30000000000000000
χ482-22-2-222-2-1-22-2211-1-111-12-22-20000i3−i3i3−i31-11i3−i3i3−i3-100-2200-11-11i3−i3i3−i31-11-1-2200−i3i3−i3i31-11-1−i3i3−i3i30000000000000000
χ492-22-2-222-2-1-22-2211-1-111-1-22-220000−i3i3−i3i31-11−i3i3−i3i3-1002-2001-11-1i3−i3i3−i3-11-11-2200−i3i3−i3i31-11-1i3−i3i3−i30000000000000000
χ502-22-2-222-2-1-22-2211-1-111-1-22-220000−i3i3−i3i31-11−i3i3−i3i3-100-22001-11-1i3−i3i3−i31-11-12-200i3−i3i3−i3-11-11−i3i3−i3i30000000000000000
χ512-22-2-222-2-1-22-2211-1-111-1-22-220000i3−i3i3−i31-11i3−i3i3−i3-1002-2001-11-1−i3i3−i3i3-11-11-2200i3−i3i3−i31-11-1−i3i3−i3i30000000000000000
χ522-22-2-222-2-1-22-2211-1-111-1-22-220000i3−i3i3−i31-11i3−i3i3−i3-100-22001-11-1−i3i3−i3i31-11-12-200−i3i3−i3i3-11-11i3−i3i3−i30000000000000000
χ532-2-22-2-222222-2-2-2-2-2-22222-2-222-22-22-2-22-2-222-2-2222-200002-2-222-2-22000000000000000000000000000000000000
χ542-2-22-2-222222-2-2-2-2-2-22222-2-22-22-22-222-2-2-22-222-22-2200002-2-22-222-2000000000000000000000000000000000000
χ552-2-22-2-222222-2-2-2-2-2-2222-222-22-22-22-2-22-2-222-2-222-220000-222-2-222-2000000000000000000000000000000000000
χ562-2-22-2-222222-2-2-2-2-2-2222-222-2-22-22-222-2-2-22-222-222-20000-222-22-2-22000000000000000000000000000000000000
χ572-2-22-2-2222-2-222-2-2-2-222200002-2-222-2-2222-2-222-2-2000000000000000000000000000000000000002-2002-2000000
χ582-2-22-2-2222-2-222-2-2-2-222200002-2-222-2-2222-2-222-2-200000000000000000000000000000000000000-2200-22000000
χ592-2-22-2-2222-2-222-2-2-2-22220000-222-2-222-222-22-2-22-2000000000000000000000000000000000000002-200-22000000
χ602-2-22-2-2222-2-222-2-2-2-22220000-222-2-222-222-22-2-22-200000000000000000000000000000000000000-22002-2000000
χ612-2-22-2-222-122-2-21111-1-1-12-2-222-22-2-111-111-1-111-1-12-20000-111-1-111-1−i3i3i3−i30000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ622-2-22-2-222-122-2-21111-1-1-12-2-222-22-2-111-111-1-111-1-12-20000-111-1-111-1i3−i3−i3i30000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ632-2-22-2-222-122-2-21111-1-1-12-2-22-22-221-1-1111-11-1-11-1-220000-111-11-1-11−i3i3i3−i30000i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ642-2-22-2-222-122-2-21111-1-1-12-2-22-22-221-1-1111-11-1-11-1-220000-111-11-1-11i3−i3−i3i30000−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ652-2-22-2-222-122-2-21111-1-1-1-222-22-22-2-111-111-1-111-1-1-2200001-1-111-1-11−i3i3i3−i30000−i3i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ662-2-22-2-222-122-2-21111-1-1-1-222-22-22-2-111-111-1-111-1-1-2200001-1-111-1-11i3−i3−i3i30000i3−i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ672-2-22-2-222-122-2-21111-1-1-1-222-2-22-221-1-1111-11-1-11-12-200001-1-11-111-1−i3i3i3−i30000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ682-2-22-2-222-122-2-21111-1-1-1-222-2-22-221-1-1111-11-1-11-12-200001-1-11-111-1i3−i3−i3i30000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-4-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4442222222-2-2-2-2200000000000000000000000000000000000000000000000000
χ714444-4-4-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ724444-4-4-4-4400004-44-44-4-40000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ7344-4-44-44-444-4-4444-4-4-4-44000000000000-4440000-400000000000000000000000000000000000000000000000000
χ7444-4-44-44-4-24-4-44-2-22222-200000000−2i3−2i32i32i32-2-22i32i3−2i3−2i3200000000000000000000000000000000000000000000000000
χ7544-4-44-44-4-24-4-44-2-22222-2000000002i32i3−2i3−2i32-2-2−2i3−2i32i32i3200000000000000000000000000000000000000000000000000
χ7644-4-4-44-44400004-4-44-44-40000000000000000000000000000000000000000000000000000004-400000000000000
χ7744-4-4-44-44400004-4-44-44-4000000000000000000000000000000000000000000000000000000-4400000000000000
χ784-44-44-4-4440000-444-4-44-4000000000000000000000000000000000000000000000000000000004-4000000000000
χ794-44-44-4-4440000-444-4-44-400000000000000000000000000000000000000000000000000000000-44000000000000
χ804-44-4-444-444-44-4-4-444-4-440000000000004-440000-400000000000000000000000000000000000000000000000000
χ814-44-4-444-4-24-44-422-2-222-200000000−2i32i3−2i32i3-22-22i3−2i32i3−2i3200000000000000000000000000000000000000000000000000
χ824-44-4-444-4-24-44-422-2-222-2000000002i3−2i32i3−2i3-22-2−2i32i3−2i32i3200000000000000000000000000000000000000000000000000
χ834-4-4444-4-440000-44-444-4-4000000000000000000000000000000000000000000000000000000000000000022−220000
χ844-4-4444-4-440000-44-444-4-40000000000000000000000000000000000000000000000000000000000000000−22220000
χ854-4-44-4-444-2-4-4442222-2-2-200004-4-44-222-2-2-222-2-22200000000000000000000000000000000000000000000000000
χ864-4-44-4-444-2-4-4442222-2-2-20000-444-42-2-22-2-22-222-2200000000000000000000000000000000000000000000000000
χ878888-8-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-88-88-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-88-8-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8888-8-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000

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