Finite Group Databasebeta

← Group #10691821

Character table — Group #10691821

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12223444444666244466121212121212121244448888121224242424242424248888881212121224242424888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ91111111-1-1-1-1111-11-11-1-1-1-111-1-1-1-111-1-1ii−i−i11iiii−i−i−i−iii−i−ii−i11-1-1ii−i−ii−iii−i−i11-1-11-1
χ101111111-1-1-1-1111-11-11-1-1-1-111-1-1-1-111-1-1ii−i−i11iiii−i−i−i−i−i−iiii−i11-1-1ii−i−i−ii−i−iii-1-111-11
χ111111111-1-1-1-1111-11-11-1-1-1-111-1-1-1-111-1-1−i−iii11−i−i−i−iiiiiii−i−i−ii11-1-1−i−iiii−iii−i−i-1-111-11
χ121111111-1-1-1-1111-11-11-1-1-1-111-1-1-1-111-1-1−i−iii11−i−i−i−iiiii−i−iii−ii11-1-1−i−iii−ii−i−iii11-1-11-1
χ131111111-1-1-1-1111-11-11-1-1-1-111-1-1-1-1-1-111ii−i−i11iiii−i−i−i−iii−i−i−ii-1-111−i−iiii−i−i−iii11-1-1-11
χ141111111-1-1-1-1111-11-11-1-1-1-111-1-1-1-1-1-111ii−i−i11iiii−i−i−i−i−i−iii−ii-1-111−i−iii−iiii−i−i-1-1111-1
χ151111111-1-1-1-1111-11-11-1-1-1-111-1-1-1-1-1-111−i−iii11−i−i−i−iiiiiii−i−ii−i-1-111ii−i−ii−i−i−iii-1-1111-1
χ161111111-1-1-1-1111-11-11-1-1-1-111-1-1-1-1-1-111−i−iii11−i−i−i−iiiii−i−iiii−i-1-111ii−i−i−iiii−i−i11-1-1-11
χ1722222222222222-2-2-2-2-2-2222222-2-200000000-2-20000000022220000000000-2-20000000000
χ1822222222222222-2-2-2-2-2-2222222-2-200000000-2-200000000-2-2-2-20000000000220000000000
χ192222222-2-2-2-22222-22-222-2-222-2-22200000000-2-2000000002i2i−2i−2i0000000000−2i2i0000000000
χ202222222-2-2-2-22222-22-222-2-222-2-22200000000-2-200000000−2i−2i2i2i00000000002i−2i0000000000
χ2122222-2-222-2-222222-2-222-2-2-2-222-2-200000000-220000000000000000000000002i−2i2i−2i000000
χ2222222-2-222-2-222222-2-222-2-2-2-222-2-200000000-22000000000000000000000000−2i2i−2i2i000000
χ2322222-2-222-2-2222-2-222-2-2-2-2-2-222222-22-200002-2000000000000002-22-20000000000000000
χ2422222-2-222-2-2222-2-222-2-2-2-2-2-22222-22-2200002-200000000000000-22-220000000000000000
χ2522222-2-2-2-2222222-2-222222-2-2-2-2-2-22-2-2200002-2000000000000002-2-220000000000000000
χ2622222-2-2-2-2222222-2-222222-2-2-2-2-2-2-222-200002-200000000000000-222-20000000000000000
χ2722222-2-2-2-222222-222-2-2-222-2-2-2-22200000000-220000000000000000000000002-2-22000000
χ2822222-2-2-2-222222-222-2-2-222-2-2-2-22200000000-22000000000000000000000000-222-2000000
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
χ302222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-2-1-1-1-11111000000000000
χ312222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ322222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-1000000000000
χ332222-122-2-2-2-2-1-1-1-22-221111-1-1111122-2-22i2i−2i−2i-1-1−i−i−i−iiiii00002i−2i-1-111−i−iii000000000000
χ342222-122-2-2-2-2-1-1-1-22-221111-1-1111122-2-2−2i−2i2i2i-1-1iiii−i−i−i−i0000−2i2i-1-111ii−i−i000000000000
χ352222-122-2-2-2-2-1-1-1-22-221111-1-11111-2-2222i2i−2i−2i-1-1−i−i−i−iiiii0000−2i2i11-1-1ii−i−i000000000000
χ362222-122-2-2-2-2-1-1-1-22-221111-1-11111-2-222−2i−2i2i2i-1-1iiii−i−i−i−i00002i−2i11-1-1−i−iii000000000000
χ372222-1-2-222-2-2-1-1-1-2-222111111-1-1-1-12-22-20000-11−i3−i3i3i3−i3−i3i3i3000000-11-11−i3i3−i3i3000000000000
χ382222-1-2-222-2-2-1-1-1-2-222111111-1-1-1-12-22-20000-11i3i3−i3−i3i3i3−i3−i3000000-11-11i3−i3i3−i3000000000000
χ392222-1-2-222-2-2-1-1-1-2-222111111-1-1-1-1-22-220000-11−i3−i3i3i3−i3−i3i3i30000001-11-1i3−i3i3−i3000000000000
χ402222-1-2-222-2-2-1-1-1-2-222111111-1-1-1-1-22-220000-11i3i3−i3−i3i3i3−i3−i30000001-11-1−i3i3−i3i3000000000000
χ412222-1-2-2-2-222-1-1-12-2-22-1-1-1-11111112-2-220000-1133−3−3−3−333000000-111-13−3−33000000000000
χ422222-1-2-2-2-222-1-1-12-2-22-1-1-1-11111112-2-220000-11−3−33333−3−3000000-111-1−333−3000000000000
χ432222-1-2-2-2-222-1-1-12-2-22-1-1-1-1111111-222-20000-1133−3−3−3−3330000001-1-11−333−3000000000000
χ442222-1-2-2-2-222-1-1-12-2-22-1-1-1-1111111-222-20000-11−3−33333−3−30000001-1-113−3−33000000000000
χ452-2-2222-22i−2i2i−2i-22-20000002i−2i2-22i−2i0000001+i−1−i1−i−1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000002−2−i2i200
χ462-2-2222-22i−2i2i−2i-22-20000002i−2i2-22i−2i0000001+i−1−i1−i−1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−22i2−i200
χ472-2-2222-22i−2i2i−2i-22-20000002i−2i2-22i−2i000000−1−i1+i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−22i2−i200
χ482-2-2222-22i−2i2i−2i-22-20000002i−2i2-22i−2i000000−1−i1+i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000002−2−i2i200
χ492-2-2222-2−2i2i−2i2i-22-2000000−2i2i2-2−2i2i0000001−i−1+i1+i−1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000002−2i2−i200
χ502-2-2222-2−2i2i−2i2i-22-2000000−2i2i2-2−2i2i0000001−i−1+i1+i−1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000−22−i2i200
χ512-2-2222-2−2i2i−2i2i-22-2000000−2i2i2-2−2i2i000000−1+i1−i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−22−i2i200
χ522-2-2222-2−2i2i−2i2i-22-2000000−2i2i2-2−2i2i000000−1+i1−i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000002−2i2−i200
χ534444-2444444-2-2-2-4-4-4-422-2-2-2-2-2-22200000000220000000000000000000000000000000000
χ544444-244-4-4-4-4-2-2-24-44-4-2-222-2-222-2-200000000220000000000000000000000000000000000
χ554444-2-4-444-4-4-2-2-244-4-4-2-22222-2-222000000002-20000000000000000000000000000000000
χ564444-2-4-4-4-444-2-2-2-444-422-2-22222-2-2000000002-20000000000000000000000000000000000
χ574-4-444-444i−4i−4i4i-44-4000000−4i4i-444i−4i0000000000000000000000000000000000000000000000
χ584-4-444-44−4i4i4i−4i-44-40000004i−4i-44−4i4i0000000000000000000000000000000000000000000000
χ594-4-44-24-44i−4i4i−4i2-22000000−2i2i-22−2i2i0000002+2i−2−2i2−2i−2+2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000
χ604-4-44-24-44i−4i4i−4i2-22000000−2i2i-22−2i2i000000−2−2i2+2i−2+2i2−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000
χ614-4-44-24-4−4i4i−4i4i2-220000002i−2i-222i−2i0000002−2i−2+2i2+2i−2−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000
χ624-4-44-24-4−4i4i−4i4i2-220000002i−2i-222i−2i000000−2+2i2−2i−2−2i2+2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000
χ634-4-44-2-444i−4i−4i4i2-220000002i−2i2-2−2i2i000000000000−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−ζ2200000000000000000000000000
χ644-4-44-2-444i−4i−4i4i2-220000002i−2i2-2−2i2i000000000000ζ4+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+ζ2200000000000000000000000000
χ654-4-44-2-44−4i4i4i−4i2-22000000−2i2i2-22i−2i000000000000−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+ζ2200000000000000000000000000
χ664-4-44-2-44−4i4i4i−4i2-22000000−2i2i2-22i−2i000000000000ζ4−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−ζ2200000000000000000000000000
χ6788-8-88000000-8-880000000000000000000000000000000000000000000000000000000000
χ6888-8-8-400000044-400000000000043−4300000000000000000000000000000000000000000000
χ6988-8-8-400000044-4000000000000−434300000000000000000000000000000000000000000000
χ708-88-880000008-8-80000000000000000000000000000000000000000000000000000000000
χ718-88-8-4000000-4440000−4i34i30000000000000000000000000000000000000000000000000000
χ728-88-8-4000000-44400004i3−4i30000000000000000000000000000000000000000000000000000

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