Finite Group Databasebeta

← Group #10691785

Character table — Group #10691785

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order122234444446662444661212121212121212444488881212121212121212121288882466121224242424224488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ411111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1
χ91111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iii−i−i1-111-1-1ii−i−i11-1-1i−i11-1-1i−i
χ101111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−i−i−iii1-111-1-1ii−i−i-1-111−ii-1-111−ii
χ111111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−iii−i−i-11-1-111−i−iii-1-111i−i11-1-1−ii
χ121111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−i−i−iii-11-1-111−i−iii11-1-1−ii-1-111i−i
χ131111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiiiii−i−i-11-1-111ii−i−i11-1-1i−i-1-111−ii
χ141111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiii−i−iii-11-1-111ii−i−i-1-111−ii11-1-1i−i
χ151111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiiiii−i−i1-111-1-1−i−iii-1-111i−i-1-111i−i
χ161111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−iii1-111-1-1−i−iii11-1-1−ii11-1-1−ii
χ1722222222222222-2-2-2-2-2-222-2-2222200000000-2-200000000222200000000000000-2-2000000
χ1822222222222222-2-2-2-2-2-222-2-2222200000000-2-200000000-2-2-2-20000000000000022000000
χ192222222-2-2-2-222222-2-2222222-2-2-2-200000000-2-2000000002i2i−2i−2i00000000000000−2i2i000000
χ202222222-2-2-2-222222-2-2222222-2-2-2-200000000-2-200000000−2i−2i2i2i000000000000002i−2i000000
χ2122222-2-222-2-22222-2-2222-2-2-2-222-2-200000000-2200000000000000000000002-22-200000000
χ2222222-2-222-2-22222-2-2222-2-2-2-222-2-200000000-220000000000000000000000-22-2200000000
χ2322222-2-222-2-2222-222-2-2-2-2-22222-2-200002i−2i2i−2i2-20000000000000000002i−2i2i−2i000000000000
χ2422222-2-222-2-2222-222-2-2-2-2-22222-2-20000−2i2i−2i2i2-2000000000000000000−2i2i−2i2i000000000000
χ2522222-2-2-2-2222222-22-222-2-2-2-2-2-22200002-2-222-20000000000000000002-2-22000000000000
χ2622222-2-2-2-2222222-22-222-2-2-2-2-2-2220000-222-22-2000000000000000000-222-2000000000000
χ2722222-2-2-2-222222-22-22-2-2-2-222-2-22200000000-2200000000000000000000002-2-2200000000
χ2822222-2-2-2-222222-22-22-2-2-2-222-2-22200000000-220000000000000000000000-222-200000000
χ292222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ302222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ312222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1111111110000-2-21111-1-1-1-1000000000000
χ322222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000022-1-1-1-11111000000000000
χ332222-122-2-2-2-2-1-1-1-2-22211-1-11111112i2i−2i−2i2i2i−2i−2i-1-1−i−i−i−iiiii00002-2-1-111−i−iii000000000000
χ342222-122-2-2-2-2-1-1-1-2-22211-1-11111112i2i−2i−2i−2i−2i2i2i-1-1−i−i−i−iiiii0000-2211-1-1ii−i−i000000000000
χ352222-122-2-2-2-2-1-1-1-2-22211-1-1111111−2i−2i2i2i2i2i−2i−2i-1-1iiii−i−i−i−i0000-2211-1-1−i−iii000000000000
χ362222-122-2-2-2-2-1-1-1-2-22211-1-1111111−2i−2i2i2i−2i−2i2i2i-1-1iiii−i−i−i−i00002-2-1-111ii−i−i000000000000
χ372222-1-2-222-2-2-1-1-1-222-21111-1-1-1-11100002i−2i2i−2i-1133−3−333−3−3000000−i3i3−i3i3−ii−ii000000000000
χ382222-1-2-222-2-2-1-1-1-222-21111-1-1-1-11100002i−2i2i−2i-11−3−333−3−333000000i3−i3i3−i3−ii−ii000000000000
χ392222-1-2-222-2-2-1-1-1-222-21111-1-1-1-1110000−2i2i−2i2i-1133−3−333−3−3000000i3−i3i3−i3i−ii−i000000000000
χ402222-1-2-222-2-2-1-1-1-222-21111-1-1-1-1110000−2i2i−2i2i-11−3−333−3−333000000−i3i3−i3i3i−ii−i000000000000
χ412222-1-2-2-2-222-1-1-12-22-2-1-1111111-1-100002-2-22-11−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3-111-1000000000000
χ422222-1-2-2-2-222-1-1-12-22-2-1-1111111-1-100002-2-22-11i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3-111-1000000000000
χ432222-1-2-2-2-222-1-1-12-22-2-1-1111111-1-10000-222-2-11−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i31-1-11000000000000
χ442222-1-2-2-2-222-1-1-12-22-2-1-1111111-1-10000-222-2-11i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i31-1-11000000000000
χ4522-2-222-22i−2i2i−2i2-2-20000002-2002i−2i2i−2i1+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000002−2−i2i200
χ4622-2-222-22i−2i2i−2i2-2-20000002-2002i−2i2i−2i1+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−22i2−i200
χ4722-2-222-22i−2i2i−2i2-2-20000002-2002i−2i2i−2i−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−22i2−i200
χ4822-2-222-22i−2i2i−2i2-2-20000002-2002i−2i2i−2i−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000002−2−i2i200
χ4922-2-222-2−2i2i−2i2i2-2-20000002-200−2i2i−2i2i1−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000002−2i2−i200
χ5022-2-222-2−2i2i−2i2i2-2-20000002-200−2i2i−2i2i1−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000−22−i2i200
χ5122-2-222-2−2i2i−2i2i2-2-20000002-200−2i2i−2i2i−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−22−i2i200
χ5222-2-222-2−2i2i−2i2i2-2-20000002-200−2i2i−2i2i−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000002−2i2−i200
χ534444-2444444-2-2-2-4-4-4-422-2-222-2-2-2-200000000220000000000000000000000000000000000
χ544444-244-4-4-4-4-2-2-244-4-4-2-2-2-2-2-2222200000000220000000000000000000000000000000000
χ554444-2-4-444-4-4-2-2-24-4-44-2-22222-2-222000000002-20000000000000000000000000000000000
χ564444-2-4-4-4-444-2-2-2-44-442222-2-222-2-2000000002-20000000000000000000000000000000000
χ5744-4-44-444i−4i−4i4i4-4-4000000-44004i−4i−4i4i00000000000000000000000000000000000000000000
χ5844-4-44-44−4i4i4i−4i4-4-4000000-4400−4i4i4i−4i00000000000000000000000000000000000000000000
χ5944-4-4-24-44i−4i4i−4i-222000000-2200−2i2i−2i2i2+2i−2−2i2−2i−2+2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000
χ6044-4-4-24-44i−4i4i−4i-222000000-2200−2i2i−2i2i−2−2i2+2i−2+2i2−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000
χ6144-4-4-24-4−4i4i−4i4i-222000000-22002i−2i2i−2i2−2i−2+2i2+2i−2−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000
χ6244-4-4-24-4−4i4i−4i4i-222000000-22002i−2i2i−2i−2+2i2−2i−2−2i2+2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000
χ6344-4-4-2-444i−4i−4i4i-2220000002-200−2i2i2i−2i0000000000−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−ζ2200000000000000000000000000
χ6444-4-4-2-444i−4i−4i4i-2220000002-200−2i2i2i−2i0000000000ζ4−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+ζ2200000000000000000000000000
χ6544-4-4-2-44−4i4i4i−4i-2220000002-2002i−2i−2i2i0000000000−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+ζ2200000000000000000000000000
χ6644-4-4-2-44−4i4i4i−4i-2220000002-2002i−2i−2i2i0000000000ζ4+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−ζ2200000000000000000000000000
χ678-88-88000000-8-880000000000000000000000000000000000000000000000000000000000
χ688-88-8-400000044-40000−4i34i30000000000000000000000000000000000000000000000000000
χ698-88-8-400000044-400004i3−4i30000000000000000000000000000000000000000000000000000
χ708-8-888000000-88-80000000000000000000000000000000000000000000000000000000000
χ718-8-88-40000004-440000000043−43000000000000000000000000000000000000000000000000
χ728-8-88-40000004-4400000000−4343000000000000000000000000000000000000000000000000

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