Finite Group Databasebeta

← Group #10691309

Character table — Group #10691309

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order1222444434444444466612121212241212121212121212688888888122424242424242424242424242424242488888888246612122444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ91111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1ii−i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-111-1-111-1-1i−i
χ101111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1ii−i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-111-1-1-1-111-1-111−ii
χ111111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1ii−i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-1-11111-1-1−ii
χ121111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1ii−i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-1-11111-1-1-1-111i−i
χ131111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1−i−iiiii−i−i1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-1-11111-1-1-1-111−ii
χ141111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1−i−iiiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11-1-111-1-11111-1-1i−i
χ151111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1−i−iii−i−iii1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1-1-111-1-111i−i
χ161111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1−i−iii−i−iii1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-111-1-111-1-111-1-1−ii
χ1722222222222-2-2-2-2222222222-2-222-2-222-2-2-200000000-2000000000000000022-2-222-2-20000000000000000
χ1822222222222-2-2-2-2222222222-2-222-2-222-2-2-200000000-20000000000000000-2-222-2-2220000000000000000
χ19222222222-2-22222-2-22222222-2-2-2-222-2-222-200000000-20000000000000000000000000000002-2-22000000
χ20222222222-2-22222-2-22222222-2-2-2-222-2-222-200000000-2000000000000000000000000000000-222-2000000
χ21222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2200002i−2i2i−2i2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ22222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-220000−2i2i−2i2i200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
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
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-100002i−2i2i−2i-133−3−333−3−3−i−iii−i−iii0000000000−i3i3−i3i30000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-100002i−2i2i−2i-1−3−333−3−333−i−iii−i−iii0000000000i3−i3i3−i30000000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-10000−2i2i−2i2i-133−3−333−3−3ii−i−iii−i−i0000000000i3−i3i3−i30000000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-10000−2i2i−2i2i-1−3−333−3−333ii−i−iii−i−i0000000000−i3i3−i3i30000000000
χ312222-2-2-2-222222-2-2-2-2222-2-2-2-22-222-2-2-2-222200000000-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-222222-2-2-2-2222-2-2-2-22-222-2-2-2-222200000000-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-22-2-222-2-222222-2-2-2-2-22-2-2-2-22222-200002-2-2220000000022-2-2-2-222000000000000000000000000
χ342222-2-2-2-22-2-222-2-222222-2-2-2-2-22-2-2-2-22222-20000-222-2200000000-2-22222-2-2000000000000000000000000
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-22-2-2-22222-2-2200000000-20000000000000000000000000000002-22-2000000
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-22-2-2-22222-2-2200000000-2000000000000000000000000000000-22-22000000
χ372222-2-2-2-2-122-2-222-2-2-1-1-11111-22-1-1-1-1111112i2i−2i−2i2i2i−2i−2i-1−i−i−i−iiiii−i−i−i−iiiii000000002-2-1-1110000000000
χ382222-2-2-2-2-122-2-222-2-2-1-1-11111-22-1-1-1-1111112i2i−2i−2i−2i−2i2i2i-1−i−i−i−iiiiiiiii−i−i−i−i00000000-2211-1-10000000000
χ392222-2-2-2-2-122-2-222-2-2-1-1-11111-22-1-1-1-111111−2i−2i2i2i2i2i−2i−2i-1iiii−i−i−i−i−i−i−i−iiiii00000000-2211-1-10000000000
χ402222-2-2-2-2-122-2-222-2-2-1-1-11111-22-1-1-1-111111−2i−2i2i2i−2i−2i2i2i-1iiii−i−i−i−iiiii−i−i−i−i000000002-2-1-1110000000000
χ412222-2-2-2-2-1-2-222-2-222-1-1-11111-221111-1-1-1-1100002-2-22-1−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000−i3i3i3−i30000000000
χ422222-2-2-2-2-1-2-222-2-222-1-1-11111-221111-1-1-1-1100002-2-22-1i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000i3−i3−i3i30000000000
χ432222-2-2-2-2-1-2-222-2-222-1-1-11111-221111-1-1-1-110000-222-2-1−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000i3−i3−i3i30000000000
χ442222-2-2-2-2-1-2-222-2-222-1-1-11111-221111-1-1-1-110000-222-2-1i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000−i3i3i3−i30000000000
χ4522-2-22i−2i2i−2i22-200002i−2i2-2-22i2i−2i−2i002-2002i−2i0001+i−1−i1−i−1+i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000002−2−i2i200
χ4622-2-22i−2i2i−2i22-200002i−2i2-2-22i2i−2i−2i002-2002i−2i0001+i−1−i1−i−1+i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000−22i2−i200
χ4722-2-22i−2i2i−2i22-200002i−2i2-2-22i2i−2i−2i002-2002i−2i000−1−i1+i−1+i1−i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000−22i2−i200
χ4822-2-22i−2i2i−2i22-200002i−2i2-2-22i2i−2i−2i002-2002i−2i000−1−i1+i−1+i1−i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000002−2−i2i200
χ4922-2-2−2i2i−2i2i22-20000−2i2i2-2-2−2i−2i2i2i002-200−2i2i0001−i−1+i1+i−1−i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000002−2i2−i200
χ5022-2-2−2i2i−2i2i22-20000−2i2i2-2-2−2i−2i2i2i002-200−2i2i0001−i−1+i1+i−1−i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000−22−i2i200
χ5122-2-2−2i2i−2i2i22-20000−2i2i2-2-2−2i−2i2i2i002-200−2i2i000−1+i1−i−1−i1+i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000−22−i2i200
χ5222-2-2−2i2i−2i2i22-20000−2i2i2-2-2−2i−2i2i2i002-200−2i2i000−1+i1−i−1−i1+i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000002−2i2−i200
χ5344444444-244-4-4-4-444-2-2-2-2-2-2-2-4-4-2-222-2-22220000000020000000000000000000000000000000000000000
χ5444444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-422-2-222-2-220000000020000000000000000000000000000000000000000
χ554444-4-4-4-4-24444-4-4-4-4-2-2-222224-4-2-22222-2-2-20000000020000000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-4-4-44444-2-2-222224-422-2-2-2-222-20000000020000000000000000000000000000000000000000
χ5744-4-44i−4i4i−4i4-440000−4i4i4-4-44i4i−4i−4i00-4400−4i4i0000000000000000000000000000000000000000000000000000
χ5844-4-44i−4i4i−4i-24-400004i−4i-222−2i−2i2i2i00-2200−2i2i0002+2i−2−2i2−2i−2+2i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000000000
χ5944-4-44i−4i4i−4i-24-400004i−4i-222−2i−2i2i2i00-2200−2i2i000−2−2i2+2i−2+2i2−2i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000000000
χ6044-4-44i−4i4i−4i-2-440000−4i4i-222−2i−2i2i2i002-2002i−2i000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000000000000000000000
χ6144-4-44i−4i4i−4i-2-440000−4i4i-222−2i−2i2i2i002-2002i−2i000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000000000000000000
χ6244-4-4−4i4i−4i4i4-4400004i−4i4-4-4−4i−4i4i4i00-44004i−4i0000000000000000000000000000000000000000000000000000
χ6344-4-4−4i4i−4i4i-24-40000−4i4i-2222i2i−2i−2i00-22002i−2i0002−2i−2+2i2+2i−2−2i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000000000
χ6444-4-4−4i4i−4i4i-24-40000−4i4i-2222i2i−2i−2i00-22002i−2i000−2+2i2−2i−2−2i2+2i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000000000
χ6544-4-4−4i4i−4i4i-2-4400004i−4i-2222i2i−2i−2i002-200−2i2i000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000000000000000000
χ6644-4-4−4i4i−4i4i-2-4400004i−4i-2222i2i−2i−2i002-200−2i2i000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000000000
χ674-44-44i−4i−4i4i4004i−4i4-400-44-44i−4i4i−4i00004-4004i−4i00000000000000000000000000000000000000000000000000
χ684-44-44i−4i−4i4i400−4i4i-4400-44-44i−4i4i−4i0000-4400−4i4i00000000000000000000000000000000000000000000000000
χ694-44-44i−4i−4i4i-2004i−4i4-4002-22−2i2i−2i2i0000-2200−2i2i000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000
χ704-44-44i−4i−4i4i-2004i−4i4-4002-22−2i2i−2i2i0000-2200−2i2i000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000
χ714-44-44i−4i−4i4i-200−4i4i-44002-22−2i2i−2i2i00002-2002i−2i000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000
χ724-44-44i−4i−4i4i-200−4i4i-44002-22−2i2i−2i2i00002-2002i−2i000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000
χ734-44-4−4i4i4i−4i4004i−4i-4400-44-4−4i4i−4i4i0000-44004i−4i00000000000000000000000000000000000000000000000000
χ744-44-4−4i4i4i−4i400−4i4i4-400-44-4−4i4i−4i4i00004-400−4i4i00000000000000000000000000000000000000000000000000
χ754-44-4−4i4i4i−4i-2004i−4i-44002-222i−2i2i−2i00002-200−2i2i000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000
χ764-44-4−4i4i4i−4i-2004i−4i-44002-222i−2i2i−2i00002-200−2i2i000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000
χ774-44-4−4i4i4i−4i-200−4i4i4-4002-222i−2i2i−2i0000-22002i−2i000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000
χ784-44-4−4i4i4i−4i-200−4i4i4-4002-222i−2i2i−2i0000-22002i−2i000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000
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.