Finite Group Databasebeta

← Group #10826979

Character table — Group #10826979

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order12222222344446666666222244446666121212121212121222222444446666666666661212121212121212121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-111-1-1111111111111-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-111-1-1111111111111-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111-1-111-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-111-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1
χ911111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-111-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-111-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111
χ1111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-111-111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111
χ1211111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-111-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11111-1-11-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11111-1-11-1-111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111
χ17222222222-2-2-2-222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-200000000222-2-20000000000000000-2-2220000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2222222-2-2-2-2-2-2-2-2200000000-2-2-222000000000000000022-2-20000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-2-2-22222200000000-222220000000000000000-2-2-2-20000000000000000
χ20222222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2000000002-2-2-2-2000000000000000022220000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-2-2-2-2-22-1-1-1-11111111111111111-1-1-1-10000000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-22222-2-2-2-2-21111-1-1-1-1-1-1-1-11111111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-22222-2111111111111-1-1-1-1-1-1-1-111110000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-222-2-222-2-2-2-1-111-1-1-1-11111-1-1-1-11111-1-1110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-2-2-222-2-222-2-1-1111111-1-1-1-11111-1-1-1-1-1-1110000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-11111222-2-2-2-222211-1-1-1-1-1-111111111-1-1-1-111-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-111112-2-22222-2-2211-1-11111-1-1-1-1-1-1-1-1111111-1-10000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2000000002-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311-1-10000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2000000002-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311-1-10000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111200000000-211-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-1-1110000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111200000000-211-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-1-1110000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-211111111-1-1-1-1200000000-2-1-1-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i311110000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-211111111-1-1-1-1200000000-2-1-1-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i311110000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-20000000021111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-1-1-1-10000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-20000000021111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-1-1-1-10000000000000000
χ3722-2-2-2-222222-2-222-2-2-2-222-2002-20022-2-222-2-222-2-20000000000000000000000000000000000002-2002-200000000
χ3822-2-2-2-222222-2-222-2-2-2-222-2002-20022-2-222-2-222-2-2000000000000000000000000000000000000-2200-2200000000
χ3922-2-2-2-222222-2-222-2-2-2-22-2200-2200-2-22222-2-2-2-2220000000000000000000000000000000000002-200-2200000000
χ4022-2-2-2-222222-2-222-2-2-2-22-2200-2200-2-22222-2-2-2-222000000000000000000000000000000000000-22002-200000000
χ4122-2-2-2-2222-2-22222-2-2-2-222-200-220022-2-2-2-222-2-22200000000000000000000000000000000002-2002-20000000000
χ4222-2-2-2-2222-2-22222-2-2-2-222-200-220022-2-2-2-222-2-2220000000000000000000000000000000000-2200-220000000000
χ4322-2-2-2-2222-2-22222-2-2-2-22-22002-200-2-222-2-22222-2-200000000000000000000000000000000002-200-220000000000
χ4422-2-2-2-2222-2-22222-2-2-2-22-22002-200-2-222-2-22222-2-20000000000000000000000000000000000-22002-20000000000
χ452-2-2-2222-222-22-2-2-2-2-2222002-2002-200002-22-200000002-2002-202-20000002-22-200002-22-22-2000000000000000000
χ462-2-2-2222-222-22-2-2-2-2-2222002-2002-200002-22-20000000-2200-2202-2000000-22-220000-22-222-2000000000000000000
χ472-2-2-2222-222-22-2-2-2-2-222200-2200-2200002-22-200000002-200-220-220000002-22-20000-22-22-22000000000000000000
χ482-2-2-2222-222-22-2-2-2-2-222200-2200-2200002-22-20000000-22002-20-22000000-22-2200002-22-2-22000000000000000000
χ492-2-2-2222-22-22-22-2-2-2-2222002-200-220000-22-22000002-2002-20002-2002-22-200002-22-20000-22000000000000000000
χ502-2-2-2222-22-22-22-2-2-2-2222002-200-220000-22-2200000-2200-220002-200-22-220000-22-220000-22000000000000000000
χ512-2-2-2222-22-22-22-2-2-2-222200-22002-20000-22-22000002-200-22000-22002-22-20000-22-2200002-2000000000000000000
χ522-2-2-2222-22-22-22-2-2-2-222200-22002-20000-22-2200000-22002-2000-2200-22-2200002-22-200002-2000000000000000000
χ532-2-2-2222-2-12-22-21111-1-1-1002-2002-2−i3i3−i3i3-11-11−i3i3−i3i30002-2002-20-11−i3i3−i3i3i3−i3-11-11−i3i3i3−i3-11-11-11−i3i30000000000000000
χ542-2-2-2222-2-12-22-21111-1-1-1002-2002-2−i3i3−i3i3-11-11−i3i3−i3i3000-2200-220-11−i3i3i3−i3−i3i31-11-1i3−i3−i3i31-11-1-11−i3i30000000000000000
χ552-2-2-2222-2-12-22-21111-1-1-1002-2002-2i3−i3i3−i3-11-11i3−i3i3−i30002-2002-20-11i3−i3i3−i3−i3i3-11-11i3−i3−i3i3-11-11-11i3−i30000000000000000
χ562-2-2-2222-2-12-22-21111-1-1-1002-2002-2i3−i3i3−i3-11-11i3−i3i3−i3000-2200-220-11i3−i3−i3i3i3−i31-11-1−i3i3i3−i31-11-1-11i3−i30000000000000000
χ572-2-2-2222-2-12-22-21111-1-1-100-2200-22−i3i3−i3i3-11-11−i3i3−i3i30002-200-2201-1i3−i3−i3i3i3−i3-11-11i3−i3−i3i31-11-11-1i3−i30000000000000000
χ582-2-2-2222-2-12-22-21111-1-1-100-2200-22−i3i3−i3i3-11-11−i3i3−i3i3000-22002-201-1i3−i3i3−i3−i3i31-11-1−i3i3i3−i3-11-111-1i3−i30000000000000000
χ592-2-2-2222-2-12-22-21111-1-1-100-2200-22i3−i3i3−i3-11-11i3−i3i3−i30002-200-2201-1−i3i3i3−i3−i3i3-11-11−i3i3i3−i31-11-11-1−i3i30000000000000000
χ602-2-2-2222-2-12-22-21111-1-1-100-2200-22i3−i3i3−i3-11-11i3−i3i3−i3000-22002-201-1−i3i3−i3i3i3−i31-11-1i3−i3−i3i3-11-111-1−i3i30000000000000000
χ612-2-2-2222-2-1-22-221111-1-1-1002-200-22−i3i3−i3i31-11-1i3−i3i3−i302-2002-2000-11i3−i3-11-11−i3i3i3−i3-11-11−i3i3i3−i31-1−i3i30000000000000000
χ622-2-2-2222-2-1-22-221111-1-1-1002-200-22−i3i3−i3i31-11-1i3−i3i3−i30-2200-22000-11i3−i31-11-1i3−i3−i3i31-11-1i3−i3−i3i31-1−i3i30000000000000000
χ632-2-2-2222-2-1-22-221111-1-1-1002-200-22i3−i3i3−i31-11-1−i3i3−i3i302-2002-2000-11−i3i3-11-11i3−i3−i3i3-11-11i3−i3−i3i31-1i3−i30000000000000000
χ642-2-2-2222-2-1-22-221111-1-1-1002-200-22i3−i3i3−i31-11-1−i3i3−i3i30-2200-22000-11−i3i31-11-1−i3i3i3−i31-11-1−i3i3i3−i31-1i3−i30000000000000000
χ652-2-2-2222-2-1-22-221111-1-1-100-22002-2−i3i3−i3i31-11-1i3−i3i3−i302-200-220001-1−i3i3-11-11−i3i3i3−i31-11-1i3−i3−i3i3-11i3−i30000000000000000
χ662-2-2-2222-2-1-22-221111-1-1-100-22002-2−i3i3−i3i31-11-1i3−i3i3−i30-22002-20001-1−i3i31-11-1i3−i3−i3i3-11-11−i3i3i3−i3-11i3−i30000000000000000
χ672-2-2-2222-2-1-22-221111-1-1-100-22002-2i3−i3i3−i31-11-1−i3i3−i3i302-200-220001-1i3−i3-11-11i3−i3−i3i31-11-1−i3i3i3−i3-11−i3i30000000000000000
χ682-2-2-2222-2-1-22-221111-1-1-100-22002-2i3−i3i3−i31-11-1−i3i3−i3i30-22002-20001-1i3−i31-11-1−i3i3i3−i3-11-11i3−i3−i3i3-11−i3i30000000000000000
χ69444-44-4-4-4400004-44-44-4-400000000000000000000000000000000000000000000000000000000000000000000−2i22i2
χ70444-44-4-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000000000000000000002i2−2i2
χ7144-44-44-4-4400004-4-44-44-4000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7244-44-44-4-4400004-4-44-44-40000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ7344-4-4-4-444-244-4-4-2-22222-24-4004-400-2-222-2-222-2-22200000000000000000000000000000000000000000000000000
χ7444-4-4-4-444-244-4-4-2-22222-2-4400-440022-2-2-2-22222-2-200000000000000000000000000000000000000000000000000
χ7544-4-4-4-444-2-4-444-2-22222-24-400-4400-2-22222-2-222-2-200000000000000000000000000000000000000000000000000
χ7644-4-4-4-444-2-4-444-2-22222-2-44004-40022-2-222-2-2-2-22200000000000000000000000000000000000000000000000000
χ774-444-4-44-444-4-44-4-444-4-440000000000004-4-44000000000000000000000000000000000000000000000000000000
χ784-444-4-44-44-444-4-4-444-4-44000000000000-444-4000000000000000000000000000000000000000000000000000000
χ794-444-4-44-4-24-4-4422-2-222-200000000−2i32i32i3−2i3-222-2−2i32i32i3−2i300000000000000000000000000000000000000000000000000
χ804-444-4-44-4-24-4-4422-2-222-2000000002i3−2i3−2i32i3-222-22i3−2i3−2i32i300000000000000000000000000000000000000000000000000
χ814-444-4-44-4-2-444-422-2-222-200000000−2i32i32i3−2i32-2-222i3−2i3−2i32i300000000000000000000000000000000000000000000000000
χ824-444-4-44-4-2-444-422-2-222-2000000002i3−2i3−2i32i32-2-22−2i32i32i3−2i300000000000000000000000000000000000000000000000000
χ834-44-4-44-4440000-444-4-44-40000000000000000000000000000000000000000000000000000000000000022−22000000
χ844-44-4-44-4440000-444-4-44-400000000000000000000000000000000000000000000000000000000000000−2222000000
χ854-4-444-4-4440000-44-444-4-4000000000000000000000000000000000000000000000000000000000000000022−220000
χ864-4-444-4-4440000-44-444-4-40000000000000000000000000000000000000000000000000000000000000000−22220000
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).