Finite Group Databasebeta

← Group #10897636

Character table — Group #10897636

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order12442223444444461212446668888121212121212122424242424242424224466668888881212121212122424242424242424242424242244444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1
χ611111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-11
χ811111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1
χ911111111-1-1-1-1111111-1-1111111111-1-1-1-11111111111-11-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-11
χ1011111111-1-1-1-1111111-1-1111111111-1-1-1-11111111111-11-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ1111111111-1-1-1-1111111-1-1111111111-1-1-1-1111111111-11-11-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-1
χ1211111111-1-1-1-1111111-1-1111111111-1-1-1-1111111111-11-11-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11
χ1311111111-1-1-1-1111111-1-1111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ1411111111-1-1-1-1111111-1-1111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1511111111-1-1-1-1111111-1-1111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111
χ1611111111-1-1-1-1111111-1-1111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-11111-1-11111-1-1
χ172222222-12222222-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222-12222222-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2221111-1-111111111-1-1-1-10000000000000000
χ192222222-12222222-1-1-122-1-1-1-2-2-2-2-1-1-1-1-1-1-1111111112-22-2-1-11122-2-2-2-2-1-111-1-1-1-1-1-1111111110000000000000000
χ202222222-12222222-1-1-122-1-1-1-2-2-2-2-1-1-1-1-1-1-111111111-22-2211-1-1-2-222-2-211-1-1-1-11111-1-1-1-111110000000000000000
χ212222222-1-2-2-2-2222-1-1-1-2-2-1-1-12222-1-11111-1-1-1-1-1-1-1-1-12-22-2-1-111-2-222-2-2-1-111111111-1-1-1-111110000000000000000
χ222222222-1-2-2-2-2222-1-1-1-2-2-1-1-12222-1-11111-1-1-1-1-1-1-1-1-1-22-2211-1-122-2-2-2-211-1-111-1-1-1-1111111110000000000000000
χ232222222-1-2-2-2-2222-1-1-1-2-2-1-1-1-2-2-2-2-1-11111-1111111112222-1-1-1-1-2-2-2-222-1-1-1-11111111111-1-1-1-10000000000000000
χ242222222-1-2-2-2-2222-1-1-1-2-2-1-1-1-2-2-2-2-1-11111-111111111-2-2-2-21111222222111111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ252222-2-2222222-2-22222-2-2-2-2222-2-2-2-2222222222-2-2-2-20000000000002-20000-2-20000000022-2-20000000000000000
χ262222-2-2222222-2-22222-2-2-2-22-2-222-2-222222-2-2-2-22222000000000000-220000-2-200000000-2-2220000000000000000
χ272222-2-222-2-2-2-2-2-2222222-2-2222-2-2-2-2-2-2-2-222222-2-2-2-2000000000000-2200002200000000-2-2220000000000000000
χ282222-2-222-2-2-2-2-2-2222222-2-22-2-222-2-2-2-2-2-22-2-2-2-222220000000000002-20000220000000022-2-20000000000000000
χ292222-2-22-12222-2-22-1-1-1-2-211-122-2-211-1-1-1-1-1-1-1-1-111110000−i3i3−i3i300002-2−i3i3−i3i311−i3−i3i3i3−i3−i3i3i3-1-1110000000000000000
χ302222-2-22-12222-2-22-1-1-1-2-211-122-2-211-1-1-1-1-1-1-1-1-111110000i3−i3i3−i300002-2i3−i3i3−i311i3i3−i3−i3i3i3−i3−i3-1-1110000000000000000
χ312222-2-22-12222-2-22-1-1-1-2-211-1-2-22211-1-1-1-1-11111-1-1-1-10000−i3i3i3−i30000-22−i3i3i3−i311−i3−i3i3i3i3i3−i3−i311-1-10000000000000000
χ322222-2-22-12222-2-22-1-1-1-2-211-1-2-22211-1-1-1-1-11111-1-1-1-10000i3−i3−i3i30000-22i3−i3−i3i311i3i3−i3−i3−i3−i3i3i311-1-10000000000000000
χ332222-2-22-1-2-2-2-2-2-22-1-1-12211-122-2-2111111-1-1-1-1-111110000−i3i3i3−i30000-22−i3i3i3−i3-1-1i3i3−i3−i3−i3−i3i3i311-1-10000000000000000
χ342222-2-22-1-2-2-2-2-2-22-1-1-12211-122-2-2111111-1-1-1-1-111110000i3−i3−i3i30000-22i3−i3−i3i3-1-1−i3−i3i3i3i3i3−i3−i311-1-10000000000000000
χ352222-2-22-1-2-2-2-2-2-22-1-1-12211-1-2-222111111-11111-1-1-1-10000−i3i3−i3i300002-2−i3i3−i3i3-1-1i3i3−i3−i3i3i3−i3−i3-1-1110000000000000000
χ362222-2-22-1-2-2-2-2-2-22-1-1-12211-1-2-222111111-11111-1-1-1-10000i3−i3i3−i300002-2i3−i3i3−i3-1-1−i3−i3i3i3−i3−i3i3i3-1-1110000000000000000
χ3722-2-222220000-2-2-22-2-2002222i−2i2i−2i-2-20000-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000022-2-20000002i−2i0000
χ3822-2-222220000-2-2-22-2-2002222i−2i2i−2i-2-20000-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000-2-222000000−2i2i0000
χ3922-2-222220000-2-2-22-2-200222−2i2i−2i2i-2-20000-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000022-2-2000000−2i2i0000
χ4022-2-222220000-2-2-22-2-200222−2i2i−2i2i-2-20000-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000-2-2220000002i−2i0000
χ4122-2-22-2-222i2i−2i−2i2-222-2-22i−2i2-2-200002-22i2i−2i−2i200000000020-20022002i−2i0000-2-22i−2i00002i−2i2i−2i00000000000000000000
χ4222-2-22-2-222i2i−2i−2i2-222-2-22i−2i2-2-200002-22i2i−2i−2i2000000000-20200-2-200−2i2i0000222i−2i0000−2i2i−2i2i00000000000000000000
χ4322-2-22-2-22−2i−2i2i2i2-222-2-2−2i2i2-2-200002-2−2i−2i2i2i200000000020-2002200−2i2i0000-2-2−2i2i0000−2i2i−2i2i00000000000000000000
χ4422-2-22-2-22−2i−2i2i2i2-222-2-2−2i2i2-2-200002-2−2i−2i2i2i2000000000-20200-2-2002i−2i000022−2i2i00002i−2i2i−2i00000000000000000000
χ4522-2-22-2-2-12i2i−2i−2i2-22-1112i−2i-1110000-11−i−iii-13−33−33−33−3020-2−i3i3-1-1002i−2i00i3−i311−ii3−33−3−ii−ii−i3i3−i3i30000000000000000
χ4622-2-22-2-2-12i2i−2i−2i2-22-1112i−2i-1110000-11−i−iii-13−33−33−33−30-202i3−i31100−2i2i00−i3i3-1-1−ii−33−33i−ii−i−i3i3−i3i30000000000000000
χ4722-2-22-2-2-12i2i−2i−2i2-22-1112i−2i-1110000-11−i−iii-1−33−33−33−33020-2i3−i3-1-1002i−2i00−i3i311−ii−33−33−ii−iii3−i3i3−i30000000000000000
χ4822-2-22-2-2-12i2i−2i−2i2-22-1112i−2i-1110000-11−i−iii-1−33−33−33−330-202−i3i31100−2i2i00i3−i3-1-1−ii3−33−3i−ii−ii3−i3i3−i30000000000000000
χ4922-2-22-2-2-1−2i−2i2i2i2-22-111−2i2i-1110000-11ii−i−i-13−33−33−33−3020-2i3−i3-1-100−2i2i00−i3i311i−i3−33−3i−ii−ii3−i3i3−i30000000000000000
χ5022-2-22-2-2-1−2i−2i2i2i2-22-111−2i2i-1110000-11ii−i−i-13−33−33−33−30-202−i3i311002i−2i00i3−i3-1-1i−i−33−33−ii−iii3−i3i3−i30000000000000000
χ5122-2-22-2-2-1−2i−2i2i2i2-22-111−2i2i-1110000-11ii−i−i-1−33−33−33−33020-2−i3i3-1-100−2i2i00i3−i311i−i−33−33i−ii−i−i3i3−i3i30000000000000000
χ5222-2-22-2-2-1−2i−2i2i2i2-22-111−2i2i-1110000-11ii−i−i-1−33−33−33−330-202i3−i311002i−2i00−i3i3-1-1i−i3−33−3−ii−ii−i3i3−i3i30000000000000000
χ5322-2-2-22-222i2i−2i−2i-2222-2-2−2i2i-22-20000-222i2i−2i−2i20000000020-2022002i−2i0000-2-200−2i2i2i−2i−2i2i000000000000000000000000
χ5422-2-2-22-222i2i−2i−2i-2222-2-2−2i2i-22-20000-222i2i−2i−2i200000000-2020-2-200−2i2i00002200−2i2i−2i2i2i−2i000000000000000000000000
χ5522-2-2-22-22−2i−2i2i2i-2222-2-22i−2i-22-20000-22−2i−2i2i2i20000000020-202200−2i2i0000-2-2002i−2i−2i2i2i−2i000000000000000000000000
χ5622-2-2-22-22−2i−2i2i2i-2222-2-22i−2i-22-20000-22−2i−2i2i2i200000000-2020-2-2002i−2i000022002i−2i2i−2i−2i2i000000000000000000000000
χ5722-2-2-22-2-12i2i−2i−2i-222-111−2i2i1-1100001-1−i−iii-13−33−3−33−3320-20-1-1−i3i32i−2i000011i3−i3i−i−iii−i3−3−33−i3i3i3−i30000000000000000
χ5822-2-2-22-2-12i2i−2i−2i-222-111−2i2i1-1100001-1−i−iii-13−33−3−33−33-202011i3−i3−2i2i0000-1-1−i3i3i−ii−i−ii−333−3−i3i3i3−i30000000000000000
χ5922-2-2-22-2-12i2i−2i−2i-222-111−2i2i1-1100001-1−i−iii-1−33−333−33−320-20-1-1i3−i32i−2i000011−i3i3i−i−iii−i−333−3i3−i3−i3i30000000000000000
χ6022-2-2-22-2-12i2i−2i−2i-222-111−2i2i1-1100001-1−i−iii-1−33−333−33−3-202011−i3i3−2i2i0000-1-1i3−i3i−ii−i−ii3−3−33i3−i3−i3i30000000000000000
χ6122-2-2-22-2-1−2i−2i2i2i-222-1112i−2i1-1100001-1ii−i−i-13−33−3−33−3320-20-1-1i3−i3−2i2i000011−i3i3−iii−i−ii3−3−33i3−i3−i3i30000000000000000
χ6222-2-2-22-2-1−2i−2i2i2i-222-1112i−2i1-1100001-1ii−i−i-13−33−3−33−33-202011−i3i32i−2i0000-1-1i3−i3−ii−iii−i−333−3i3−i3−i3i30000000000000000
χ6322-2-2-22-2-1−2i−2i2i2i-222-1112i−2i1-1100001-1ii−i−i-1−33−333−33−320-20-1-1−i3i3−2i2i000011i3−i3−iii−i−ii−333−3−i3i3i3−i30000000000000000
χ6422-2-2-22-2-1−2i−2i2i2i-222-1112i−2i1-1100001-1ii−i−i-1−33−333−33−3-202011i3−i32i−2i0000-1-1−i3i3−ii−iii−i3−3−33−i3i3i3−i30000000000000000
χ6522-2-2-2-222000022-22-2-200-2-222i−2i−2i2i220000-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000022-2-22i−2i000000
χ6622-2-2-2-222000022-22-2-200-2-222i−2i−2i2i220000-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000-2-222−2i2i000000
χ6722-2-2-2-222000022-22-2-200-2-22−2i2i2i−2i220000-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000022-2-2−2i2i000000
χ6822-2-2-2-222000022-22-2-200-2-22−2i2i2i−2i220000-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000-2-2222i−2i000000
χ6944444-4-440000-44-4444004-4-40000-440000-400000000000000000000000000000000000000000000000000000000
χ7044444-4-4-20000-44-4-2-2-200-22200002-200002−2i32i32i3−2i3−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ7144444-4-4-20000-44-4-2-2-200-22200002-2000022i3−2i3−2i32i32i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ724444-44-4400004-4-444400-44-400004-40000-400000000000000000000000000000000000000000000000000000000
χ734444-44-4-200004-4-4-2-2-2002-220000-2200002−2i32i32i3−2i32i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ744444-44-4-200004-4-4-2-2-2002-220000-22000022i3−2i3−2i32i3−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ7544-4-4444-20000-4-4-4-22200-2-2-24i−4i4i−4i2200002−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ7644-4-4444-20000-4-4-4-22200-2-2-2−4i4i−4i4i22000022i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ7744-4-4-4-44-2000044-4-2220022-24i−4i−4i4i-2-200002−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ7844-4-4-4-44-2000044-4-2220022-2−4i4i4i−4i-2-2000022i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ794-44i−4i00042+2i−2−2i2−2i−2+2i000-44i−4i000000000002+2i−2−2i2−2i−2+2i000000000000000000000000000000000000000002-22i−2i2-22i−2i00000000
χ804-44i−4i00042+2i−2−2i2−2i−2+2i000-44i−4i000000000002+2i−2−2i2−2i−2+2i00000000000000000000000000000000000000000-22−2i2i-22−2i2i00000000
χ814-44i−4i0004−2−2i2+2i−2+2i2−2i000-44i−4i00000000000−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000000002-22i−2i-22−2i2i00000000
χ824-44i−4i0004−2−2i2+2i−2+2i2−2i000-44i−4i00000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000000000000000000-22−2i2i2-22i−2i00000000
χ834-4−4i4i00042−2i−2+2i2+2i−2−2i000-4−4i4i000000000002−2i−2+2i2+2i−2−2i000000000000000000000000000000000000000002-2−2i2i2-2−2i2i00000000
χ844-4−4i4i00042−2i−2+2i2+2i−2−2i000-4−4i4i000000000002−2i−2+2i2+2i−2−2i00000000000000000000000000000000000000000-222i−2i-222i−2i00000000
χ854-4−4i4i0004−2+2i2−2i−2−2i2+2i000-4−4i4i00000000000−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000000002-2−2i2i-222i−2i00000000
χ864-4−4i4i0004−2+2i2−2i−2−2i2+2i000-4−4i4i00000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000000000000000000-222i−2i2-2−2i2i00000000
χ878-88i−8i000-44+4i−4−4i4−4i−4+4i0004−4i4i00000000000−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000000000000000000000000
χ888-88i−8i000-4−4−4i4+4i−4+4i4−4i0004−4i4i000000000002+2i−2−2i2−2i−2+2i000000000000000000000000000000000000000000000000000000000
χ898-8−8i8i000-44−4i−4+4i4+4i−4−4i00044i−4i00000000000−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000000000000000000000000
χ908-8−8i8i000-4−4+4i4−4i−4−4i4+4i00044i−4i000000000002−2i−2+2i2+2i−2−2i000000000000000000000000000000000000000000000000000000000

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