Finite Group Databasebeta

← Group #10693692

Character table — Group #10693692

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order1222444434444444466612121212241212121212121212688888888122424242424242424242424242424242488888888246612128888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1-1-11-1-11111-1-1111-1-1-1-1-111111-1-1-1-1-1i−ii−iii−i−i1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-111-1-111-1-1i−i
χ101111-1-1-1-11-1-11111-1-1111-1-1-1-1-111111-1-1-1-1-1i−ii−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-111-1-1-1-111-1-111−ii
χ111111-1-1-1-11-1-11111-1-1111-1-1-1-1-111111-1-1-1-1-1i−ii−i−i−iii1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-11111-1-1-1-111−ii
χ121111-1-1-1-11-1-11111-1-1111-1-1-1-1-111111-1-1-1-1-1i−ii−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-1-111-1-11111-1-1i−i
χ131111-1-1-1-11-1-11111-1-1111-1-1-1-1-111111-1-1-1-1-1−ii−iiii−i−i1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-1-111-1-11111-1-1−ii
χ141111-1-1-1-11-1-11111-1-1111-1-1-1-1-111111-1-1-1-1-1−ii−iiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11-1-11111-1-1-1-111i−i
χ151111-1-1-1-11-1-11111-1-1111-1-1-1-1-111111-1-1-1-1-1−ii−ii−i−iii1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1-1-111-1-111i−i
χ161111-1-1-1-11-1-11111-1-1111-1-1-1-1-111111-1-1-1-1-1−ii−ii−i−iii1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-111-1-111-1-111-1-1−ii
χ172222222222222-2-2-2-22222222-2-222-2-2-2-222-222-2-20000-222-2-222-2-200000000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-222-2-2-2-222-2-2-2220000-2-2-222-2-22200000000000000000000000000000000
χ19222222222-2-2-2-222222222222-2-2-2-22222-2-2-200000000-2000000000000000022-2-222-2-20000000000000000
χ20222222222-2-2-2-222222222222-2-2-2-22222-2-2-200000000-20000000000000000-2-222-2-2220000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-220000000020000000000000000000000000000002i−2i2i−2i000000
χ22222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22000000002000000000000000000000000000000−2i2i−2i2i000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-22222-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-111111111111111110000000022-1-1-1-10000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-11111-1-1122-2-200001-1-111-1-111−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-11111-1-1122-2-200001-1-111-1-111i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ2922222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-11111-1-11-2-2220000111-1-111-1-1−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ3022222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-11111-1-11-2-2220000111-1-111-1-1i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-22-2-2-222-2-222200000000-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-22-2-2-222-2-222200000000-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-2-22-2-2-2-22222-20000000020000000000000000000000000000002i−2i−2i2i000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-2-22-2-2-2-22222-2000000002000000000000000000000000000000−2i2i2i−2i000000
χ352222-2-2-2-22-2-222-2-222222-2-2-2-22-222-2-222-2-222i−2i−2i2i0000-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ362222-2-2-2-22-2-222-2-222222-2-2-2-22-222-2-222-2-22−2i2i2i−2i0000-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ372222-2-2-2-2-1-2-22222-2-2-1-1-11111-22-1-1-1-1111112i−2i2i−2i2i2i−2i−2i-1−i−i−i−iiiii−i−i−i−iiiii000000002-2-1-1110000000000
χ382222-2-2-2-2-1-2-22222-2-2-1-1-11111-22-1-1-1-1111112i−2i2i−2i−2i−2i2i2i-1−i−i−i−iiiiiiiii−i−i−i−i00000000-2211-1-10000000000
χ392222-2-2-2-2-1-2-22222-2-2-1-1-11111-22-1-1-1-111111−2i2i−2i2i2i2i−2i−2i-1iiii−i−i−i−i−i−i−i−iiiii00000000-2211-1-10000000000
χ402222-2-2-2-2-1-2-22222-2-2-1-1-11111-22-1-1-1-111111−2i2i−2i2i−2i−2i2i2i-1iiii−i−i−i−iiiii−i−i−i−i000000002-2-1-1110000000000
χ412222-2-2-2-2-1-2-222-2-222-1-1-111112-2-1-111-1-111-12i−2i−2i2i00001−i−iiiii−i−i33−3−3−3−3330000000000−i3i3i3−i30000000000
χ422222-2-2-2-2-1-2-222-2-222-1-1-111112-2-1-111-1-111-12i−2i−2i2i00001−i−iiiii−i−i−3−33333−3−30000000000i3−i3−i3i30000000000
χ432222-2-2-2-2-1-2-222-2-222-1-1-111112-2-1-111-1-111-1−2i2i2i−2i00001ii−i−i−i−iii33−3−3−3−3330000000000i3−i3−i3i30000000000
χ442222-2-2-2-2-1-2-222-2-222-1-1-111112-2-1-111-1-111-1−2i2i2i−2i00001ii−i−i−i−iii−3−33333−3−30000000000−i3i3i3−i30000000000
χ4522-2-22i−2i2i−2i200002-22i−2i2-2-22i2i−2i−2i00002-22i−2i00000001+i−1−i1−i−1+i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000−i2i22−200
χ4622-2-22i−2i2i−2i200002-22i−2i2-2-22i2i−2i−2i00002-22i−2i00000001+i−1−i1−i−1+i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000i2−i2−2200
χ4722-2-22i−2i2i−2i200002-22i−2i2-2-22i2i−2i−2i00002-22i−2i0000000−1−i1+i−1+i1−i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000i2−i2−2200
χ4822-2-22i−2i2i−2i200002-22i−2i2-2-22i2i−2i−2i00002-22i−2i0000000−1−i1+i−1+i1−i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000−i2i22−200
χ4922-2-2−2i2i−2i2i200002-2−2i2i2-2-2−2i−2i2i2i00002-2−2i2i00000001−i−1+i1+i−1−i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000i2−i22−200
χ5022-2-2−2i2i−2i2i200002-2−2i2i2-2-2−2i−2i2i2i00002-2−2i2i00000001−i−1+i1+i−1−i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000−i2i2−2200
χ5122-2-2−2i2i−2i2i200002-2−2i2i2-2-2−2i−2i2i2i00002-2−2i2i0000000−1+i1−i−1−i1+i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000−i2i2−2200
χ5222-2-2−2i2i−2i2i200002-2−2i2i2-2-2−2i−2i2i2i00002-2−2i2i0000000−1+i1−i−1−i1+i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000i2−i22−200
χ5344444444-2-4-4-4-44444-2-2-2-2-2-2-2-4-422-2-2-2-22220000000020000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222-200000000-20000000000000000000000000000000000000000
χ554444-4-4-4-4-244-4-444-4-4-2-2-222224-422-2-222-2-2-20000000020000000000000000000000000000000000000000
χ564444-4-4-4-4-244-4-4-4-444-2-2-22222-442222-2-2-2-2200000000-20000000000000000000000000000000000000000
χ5744-4-44i−4i4i−4i40000-44−4i4i4-4-44i4i−4i−4i0000-44−4i4i0000000000000000000000000000000000000000000000000000
χ5844-4-44i−4i4i−4i-200004-44i−4i-222−2i−2i2i2i0000-22−2i2i00000002+2i−2−2i2−2i−2+2i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000
χ5944-4-44i−4i4i−4i-200004-44i−4i-222−2i−2i2i2i0000-22−2i2i0000000−2−2i2+2i−2+2i2−2i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ6044-4-44i−4i4i−4i-20000-44−4i4i-222−2i−2i2i2i00002-22i−2i00000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000
χ6144-4-44i−4i4i−4i-20000-44−4i4i-222−2i−2i2i2i00002-22i−2i00000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000
χ6244-4-4−4i4i−4i4i40000-444i−4i4-4-4−4i−4i4i4i0000-444i−4i0000000000000000000000000000000000000000000000000000
χ6344-4-4−4i4i−4i4i-200004-4−4i4i-2222i2i−2i−2i0000-222i−2i00000002−2i−2+2i2+2i−2−2i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ6444-4-4−4i4i−4i4i-200004-4−4i4i-2222i2i−2i−2i0000-222i−2i0000000−2+2i2−2i−2−2i2+2i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ6544-4-4−4i4i−4i4i-20000-444i−4i-2222i2i−2i−2i00002-2−2i2i00000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000
χ6644-4-4−4i4i−4i4i-20000-444i−4i-2222i2i−2i−2i00002-2−2i2i00000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000
χ674-44-44i−4i−4i4i44i−4i4-40000-44-44i−4i4i−4i004-400004i−4i00000000000000000000000000000000000000000000000000
χ684-44-44i−4i−4i4i4−4i4i-440000-44-44i−4i4i−4i00-440000−4i4i00000000000000000000000000000000000000000000000000
χ694-44-44i−4i−4i4i-24i−4i4-400002-22−2i2i−2i2i00-220000−2i2i0000000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000000000
χ704-44-44i−4i−4i4i-24i−4i4-400002-22−2i2i−2i2i00-220000−2i2i00000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000000000
χ714-44-44i−4i−4i4i-2−4i4i-4400002-22−2i2i−2i2i002-200002i−2i0000000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000000000
χ724-44-44i−4i−4i4i-2−4i4i-4400002-22−2i2i−2i2i002-200002i−2i000000000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000000000
χ734-44-4−4i4i4i−4i44i−4i-440000-44-4−4i4i−4i4i00-4400004i−4i00000000000000000000000000000000000000000000000000
χ744-44-4−4i4i4i−4i4−4i4i4-40000-44-4−4i4i−4i4i004-40000−4i4i00000000000000000000000000000000000000000000000000
χ754-44-4−4i4i4i−4i-24i−4i-4400002-222i−2i2i−2i002-20000−2i2i000000000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000000000
χ764-44-4−4i4i4i−4i-24i−4i-4400002-222i−2i2i−2i002-20000−2i2i0000000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000000000
χ774-44-4−4i4i4i−4i-2−4i4i4-400002-222i−2i2i−2i00-2200002i−2i00000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000000000
χ784-44-4−4i4i4i−4i-2−4i4i4-400002-222i−2i2i−2i00-2200002i−2i0000000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000000000
χ794-4-4444-4-4400000000-4-444-4-44000000000000000000000000000000000000−2i22i200−2i22i2000000000000000000
χ804-4-4444-4-4400000000-4-444-4-440000000000000000000000000000000000002i2−2i2002i2−2i2000000000000000000
χ814-4-44-4-444400000000-4-44-444-400000000000000000000000000000000000022−2200−2222000000000000000000
χ824-4-44-4-444400000000-4-44-444-4000000000000000000000000000000000000−22220022−22000000000000000000
χ838-8-8888-8-8-40000000044-4-444-4000000000000000000000000000000000000000000000000000000000000
χ848-8-88-8-888-40000000044-44-4-44000000000000000000000000000000000000000000000000000000000000

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