Finite Group Databasebeta

← Group #10705561

Character table — Group #10705561

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222222222444444448888888888888888888888888888888888888824242424242424242424242424242424
order12224444223446666666121212121212121222444444244444444466661212121212121212121212121212121212121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ141111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ161111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-111
χ17222222222222222222222222222222-2-222-2-2-2-200000000-2-22200000000-2-2-2-222-2-2000000000000000000000000
χ182222222222222222222222222222-2-222-2-222-2-200000000-2-2-2-200000000-2-222-2-222000000000000000000000000
χ192222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000000000000000
χ212222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-20000000011-1-1−i3−i3i3i3−i3−i3i3i31111-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-20000000011-1-1i3i3−i3−i3i3i3−i3−i31111-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ232222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2000000001111−i3−i3i3i3−i3−i3i3i311-1-111-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ242222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2000000001111i3i3−i3−i3i3i3−i3−i311-1-111-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ252222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222222-2-2-2-2-1-11111111111-1-1111111-1-1-1-1-1-1-1-10000000000000000
χ262222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-2-22222-1-111-1-1-1-1-1-1-1-1-1-1111111111111110000000000000000
χ272222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-222-2-2-2-2222-200000000222200000000-2-2-2-2-2-222000000000000000000000000
χ282222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-22-20000000022-2-200000000-2-22222-2-2000000000000000000000000
χ292222-2-2-2-222-1-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-2222-2-222-2-211-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ302222-2-2-2-222-1-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-22-2-222-2-22211-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ312222-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122-2-2-2-2222-200000000-1-1-1-1−i3−i3i3i3i3i3−i3−i3111111-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ322222-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122-2-2-2-2222-200000000-1-1-1-1i3i3−i3−i3−i3−i3i3i3111111-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ332222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-22222-2-22-200000000-1-111−i3−i3i3i3i3i3−i3−i311-1-1-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ342222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-22222-2-22-200000000-1-111i3i3−i3−i3−i3−i3i3i311-1-1-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ352222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-2222-2-2-2-22211111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111110000000000000000
χ362222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-22-2-22222-2-21111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-10000000000000000
χ3722-2-22i2i−2i−2i2-222i−2i22-2-22-2-22i2i2i2i−2i−2i−2i−2i002i−2i002-20000000000000000000000002i−2i002-2000000002−2−i2i2−i2i22−200000000
χ3822-2-22i2i−2i−2i2-222i−2i22-2-22-2-22i2i2i2i−2i−2i−2i−2i002i−2i002-20000000000000000000000002i−2i002-200000000−22i2−i2i2−i2−2200000000
χ3922-2-22i2i−2i−2i2-222i−2i22-2-22-2-22i2i2i2i−2i−2i−2i−2i00−2i2i00-22000000000000000000000000−2i2i00-2200000000−i2i2−222−2i2−i200000000
χ4022-2-22i2i−2i−2i2-222i−2i22-2-22-2-22i2i2i2i−2i−2i−2i−2i00−2i2i00-22000000000000000000000000−2i2i00-2200000000i2−i22−2−22−i2i200000000
χ4122-2-22i2i−2i−2i-222−2i2i-2-2222-2-22i2i−2i−2i2i2i−2i−2i2-2002i−2i000000000000002-20000000000002i−2i0000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ4222-2-22i2i−2i−2i-222−2i2i-2-2222-2-22i2i−2i−2i2i2i−2i−2i2-2002i−2i000000000000002-20000000000002i−2i000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ4322-2-22i2i−2i−2i-222−2i2i-2-2222-2-22i2i−2i−2i2i2i−2i−2i-2200−2i2i00000000000000-22000000000000−2i2i0000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i
χ4422-2-22i2i−2i−2i-222−2i2i-2-2222-2-22i2i−2i−2i2i2i−2i−2i-2200−2i2i00000000000000-22000000000000−2i2i000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i
χ4522-2-2−2i−2i2i2i2-22−2i2i22-2-22-2-2−2i−2i−2i−2i2i2i2i2i002i−2i00-220000000000000000000000002i−2i00-2200000000−i2i22−2−22i2−i200000000
χ4622-2-2−2i−2i2i2i2-22−2i2i22-2-22-2-2−2i−2i−2i−2i2i2i2i2i002i−2i00-220000000000000000000000002i−2i00-2200000000i2−i2−222−2−i2i200000000
χ4722-2-2−2i−2i2i2i2-22−2i2i22-2-22-2-2−2i−2i−2i−2i2i2i2i2i00−2i2i002-2000000000000000000000000−2i2i002-2000000002−2i2−i2i2−i22−200000000
χ4822-2-2−2i−2i2i2i2-22−2i2i22-2-22-2-2−2i−2i−2i−2i2i2i2i2i00−2i2i002-2000000000000000000000000−2i2i002-200000000−22−i2i2−i2i2−2200000000
χ4922-2-2−2i−2i2i2i-2222i−2i-2-2222-2-2−2i−2i2i2i−2i−2i2i2i2-200−2i2i000000000000002-2000000000000−2i2i0000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ5022-2-2−2i−2i2i2i-2222i−2i-2-2222-2-2−2i−2i2i2i−2i−2i2i2i2-200−2i2i000000000000002-2000000000000−2i2i000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ5122-2-2−2i−2i2i2i-2222i−2i-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-22002i−2i00000000000000-220000000000002i−2i0000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ5222-2-2−2i−2i2i2i-2222i−2i-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-22002i−2i00000000000000-220000000000002i−2i000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ5344444444-4-44-4-4-4-4-4-444444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000
χ5444444444-4-4-2-4-42222-2-2-2-2-22222-2-2000000000000000000−2i32i30000000000−2i32i3000000000000000000000000000000
χ5544444444-4-4-2-4-42222-2-2-2-2-22222-2-20000000000000000002i3−2i300000000002i3−2i3000000000000000000000000000000
χ564444-4-4-4-4-4-4444-4-4-4-4444-4-44444-4-400000000000000000000000000000000000000000000000000000000000000
χ574444-4-4-4-4-4-4-2442222-2-2-222-2-2-2-222000000000000000000−2i32i300000000002i3−2i3000000000000000000000000000000
χ584444-4-4-4-4-4-4-2442222-2-2-222-2-2-2-2220000000000000000002i3−2i30000000000−2i32i3000000000000000000000000000000
χ5944-4-44i4i−4i−4i4-4-24i−4i-2-222-222−2i−2i−2i−2i2i2i2i2i004i−4i004-4000000000000000000000000−2i2i00-22000000000000000000000000
χ6044-4-44i4i−4i−4i4-4-24i−4i-2-222-222−2i−2i−2i−2i2i2i2i2i00−4i4i00-440000000000000000000000002i−2i002-2000000000000000000000000
χ6144-4-44i4i−4i−4i-44-2−4i4i22-2-2-222−2i−2i2i2i−2i−2i2i2i4-4004i−4i00000000000000-22000000000000−2i2i00000000000000000000000000
χ6244-4-44i4i−4i−4i-44-2−4i4i22-2-2-222−2i−2i2i2i−2i−2i2i2i-4400−4i4i000000000000002-20000000000002i−2i00000000000000000000000000
χ6344-4-4−4i−4i4i4i4-4-2−4i4i-2-222-2222i2i2i2i−2i−2i−2i−2i004i−4i00-44000000000000000000000000−2i2i002-2000000000000000000000000
χ6444-4-4−4i−4i4i4i4-4-2−4i4i-2-222-2222i2i2i2i−2i−2i−2i−2i00−4i4i004-40000000000000000000000002i−2i00-22000000000000000000000000
χ6544-4-4−4i−4i4i4i-44-24i−4i22-2-2-2222i2i−2i−2i2i2i−2i−2i4-400−4i4i00000000000000-220000000000002i−2i00000000000000000000000000
χ6644-4-4−4i−4i4i4i-44-24i−4i22-2-2-2222i2i−2i−2i2i2i−2i−2i-44004i−4i000000000000002-2000000000000−2i2i00000000000000000000000000
χ674-44-44-44-4004000000-44-44-400004-400000000002i−2i2i−2i0000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ684-44-44-44-4004000000-44-44-400004-40000000000−2i2i−2i2i000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ694-44-44-44-400-200−2i32i3−2i32i32-22-22−2i32i3−2i32i3-2200000000002i−2i2i−2i0000000000000000000000002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ140000000000000000
χ704-44-44-44-400-200−2i32i3−2i32i32-22-22−2i32i3−2i32i3-220000000000−2i2i−2i2i000000000000000000000000−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ140000000000000000
χ714-44-44-44-400-2002i3−2i32i3−2i32-22-222i3−2i32i3−2i3-2200000000002i−2i2i−2i0000000000000000000000002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ220000000000000000
χ724-44-44-44-400-2002i3−2i32i3−2i32-22-222i3−2i32i3−2i3-220000000000−2i2i−2i2i000000000000000000000000−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ220000000000000000
χ734-44-4-44-44004000000-44-4-440000-4400000000002i−2i−2i2i0000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ744-44-4-44-44004000000-44-4-440000-440000000000−2i2i2i−2i000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ754-44-4-44-4400-200−2i32i3−2i32i32-222-22i3−2i32i3−2i32-200000000002i−2i−2i2i0000000000000000000000002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ140000000000000000
χ764-44-4-44-4400-200−2i32i3−2i32i32-222-22i3−2i32i3−2i32-20000000000−2i2i2i−2i000000000000000000000000−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ140000000000000000
χ774-44-4-44-4400-2002i3−2i32i3−2i32-222-2−2i32i3−2i32i32-200000000002i−2i−2i2i0000000000000000000000002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ220000000000000000
χ784-44-4-44-4400-2002i3−2i32i3−2i32-222-2−2i32i3−2i32i32-20000000000−2i2i2i−2i000000000000000000000000−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ220000000000000000
χ794-4-444i−4i−4i4i004000000-4-444i−4i0000−4i4i000000000000002i−2i2-200002i−2i2i−2i2-22-200000000000000000000000000000000
χ804-4-444i−4i−4i4i004000000-4-444i−4i0000−4i4i00000000000000−2i2i-220000−2i2i−2i2i-22-2200000000000000000000000000000000
χ814-4-444i−4i−4i4i00-200−2i32i32i3−2i322-2−2i2i23−23−23232i−2i000000000000002i−2i2-200002ζ14−2ζ142ζ22−2ζ22−1+i31−i3−1−i31+i300000000000000000000000000000000
χ824-4-444i−4i−4i4i00-200−2i32i32i3−2i322-2−2i2i23−23−23232i−2i00000000000000−2i2i-220000−2ζ142ζ14−2ζ222ζ221−i3−1+i31+i3−1−i300000000000000000000000000000000
χ834-4-444i−4i−4i4i00-2002i3−2i3−2i32i322-2−2i2i−232323−232i−2i000000000000002i−2i2-200002ζ22−2ζ222ζ14−2ζ14−1−i31+i3−1+i31−i300000000000000000000000000000000
χ844-4-444i−4i−4i4i00-2002i3−2i3−2i32i322-2−2i2i−232323−232i−2i00000000000000−2i2i-220000−2ζ222ζ22−2ζ142ζ141+i3−1−i31−i3−1+i300000000000000000000000000000000
χ854-4-44−4i4i4i−4i004000000-4-44−4i4i00004i−4i000000000000002i−2i-2200002i−2i2i−2i-22-2200000000000000000000000000000000
χ864-4-44−4i4i4i−4i004000000-4-44−4i4i00004i−4i00000000000000−2i2i2-20000−2i2i−2i2i2-22-200000000000000000000000000000000
χ874-4-44−4i4i4i−4i00-200−2i32i32i3−2i322-22i−2i−232323−23−2i2i000000000000002i−2i-2200002ζ14−2ζ142ζ22−2ζ221−i3−1+i31+i3−1−i300000000000000000000000000000000
χ884-4-44−4i4i4i−4i00-200−2i32i32i3−2i322-22i−2i−232323−23−2i2i00000000000000−2i2i2-20000−2ζ142ζ14−2ζ222ζ22−1+i31−i3−1−i31+i300000000000000000000000000000000
χ894-4-44−4i4i4i−4i00-2002i3−2i3−2i32i322-22i−2i23−23−2323−2i2i000000000000002i−2i-2200002ζ22−2ζ222ζ14−2ζ141+i3−1−i31−i3−1+i300000000000000000000000000000000
χ904-4-44−4i4i4i−4i00-2002i3−2i3−2i32i322-22i−2i23−23−2323−2i2i00000000000000−2i2i2-20000−2ζ222ζ22−2ζ142ζ14−1−i31+i3−1+i31−i300000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.