Finite Group Databasebeta

← Group #10694604

Character table — Group #10694604

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order122222344444444666446612121212121212124444121212121212121212128888888824668812122424242488882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1
χ91111-1-11-1-111-1-1-1-111111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i1111-1-1-1-11-111i−i-1-1ii−i−iii−i−i1-1i−i
χ101111-1-11-1-111-1-1-1-111111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i1111-1-1-1-1-11-1-1−ii11−i−iiiii−i−i-11−ii
χ111111-1-11-1-111-1-1-1-111111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i-1-1-1-111111-111i−i-1-1ii−i−i−i−iii-11−ii
χ121111-1-11-1-111-1-1-1-111111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i-1-1-1-11111-11-1-1−ii11−i−iii−i−iii1-1i−i
χ131111-1-11-1-111-1-1-1-111111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii1111-1-1-1-11-111−ii-1-1−i−iii−i−iii1-1−ii
χ141111-1-11-1-111-1-1-1-111111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii1111-1-1-1-1-11-1-1i−i11ii−i−i−i−iii-11i−i
χ151111-1-11-1-111-1-1-1-111111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii-1-1-1-111111-111−ii-1-1−i−iiiii−i−i-11i−i
χ161111-1-11-1-111-1-1-1-111111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii-1-1-1-11111-11-1-1i−i11ii−i−iii−i−i1-1−ii
χ17222222222-2-2-2-2-2-2222-2222-2-2-2-222-2-20000-2200000000000000000000000000002i−2i2i−2i0000
χ18222222222-2-2-2-2-2-2222-2222-2-2-2-222-2-20000-220000000000000000000000000000−2i2i−2i2i0000
χ192222222-2-22222-2-2222-2-2222222-2-2-2-20000-2-20000000022-2-222-2-200000000000000000000
χ202222222-2-22222-2-2222-2-2222222-2-2-2-20000-2-200000000-2-222-2-22200000000000000000000
χ212222222-2-2-2-2-2-2222222-222-2-2-2-2-2-2222-22-22-222-2-222-2-20000000000000000000000000000
χ222222222-2-2-2-2-2-2222222-222-2-2-2-2-2-222-22-222-2-2-222-2-2220000000000000000000000000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000000022-1-122-1-1-1-1-1-100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-211-2-211111100000000
χ25222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-1-1-2-2-1-1111100000000
χ26222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2112211-1-1-1-100000000
χ27222222-1-2-2-2-2-2-222-1-1-12-2-1-1111111-1-12-22-2-11-1-111-1-1110000000000−i3i300−i3i3−i3i3−i3i300000000
χ28222222-1-2-2-2-2-2-222-1-1-12-2-1-1111111-1-12-22-2-11-1-111-1-1110000000000i3−i300i3−i3i3−i3i3−i300000000
χ29222222-1-2-2-2-2-2-222-1-1-12-2-1-1111111-1-1-22-22-1111-1-111-1-10000000000−i3i300−i3i3i3−i3i3−i300000000
χ30222222-1-2-2-2-2-2-222-1-1-12-2-1-1111111-1-1-22-22-1111-1-111-1-10000000000i3−i300i3−i3−i3i3−i3i300000000
χ312222-2-222222-2-222222-2-2-2-222-2-222220000-2-20000000022-2-2-2-22200000000000000000000
χ322222-2-222222-2-222222-2-2-2-222-2-222220000-2-200000000-2-22222-2-200000000000000000000
χ332222-2-2222-2-222-2-22222-2-2-2-2-22222-2-22i−2i−2i2i2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ342222-2-2222-2-222-2-22222-2-2-2-2-22222-2-2−2i2i2i−2i2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ352222-2-22-2-2-2-22222222-22-2-2-2-222-2-2220000-2200000000000000000000000000002-2-220000
χ362222-2-22-2-2-2-22222222-22-2-2-2-222-2-2220000-220000000000000000000000000000-222-20000
χ372222-2-2-122-2-222-2-2-1-1-12-21111-1-1-1-1112i−2i−2i2i-11−i−iiiii−i−i0000000000−i3i300i3−i33−3−3300000000
χ382222-2-2-122-2-222-2-2-1-1-12-21111-1-1-1-1112i−2i−2i2i-11−i−iiiii−i−i0000000000i3−i300−i3i3−333−300000000
χ392222-2-2-122-2-222-2-2-1-1-12-21111-1-1-1-111−2i2i2i−2i-11ii−i−i−i−iii0000000000−i3i300i3−i3−333−300000000
χ402222-2-2-122-2-222-2-2-1-1-12-21111-1-1-1-111−2i2i2i−2i-11ii−i−i−i−iii0000000000i3−i300−i3i33−3−3300000000
χ412222-2-2-1-2-222-2-2-2-2-1-1-12211-1-11111112i2i−2i−2i-1-1−i−i−i−iiiii000000002-2-1-12i−2i11−i−iii00000000
χ422222-2-2-1-2-222-2-2-2-2-1-1-12211-1-11111112i2i−2i−2i-1-1−i−i−i−iiiii00000000-2211−2i2i-1-1ii−i−i00000000
χ432222-2-2-1-2-222-2-2-2-2-1-1-12211-1-1111111−2i−2i2i2i-1-1iiii−i−i−i−i000000002-2-1-1−2i2i11ii−i−i00000000
χ442222-2-2-1-2-222-2-2-2-2-1-1-12211-1-1111111−2i−2i2i2i-1-1iiii−i−i−i−i00000000-22112i−2i-1-1−i−iii00000000
χ45444444-244-4-4-4-4-4-4-2-2-2-44-2-22222-2-22200002-2000000000000000000000000000000000000
χ46444444-2-4-44444-4-4-2-2-2-4-4-2-2-2-2-2-22222000022000000000000000000000000000000000000
χ474444-4-4-24444-4-444-2-2-2-4-422-2-222-2-2-2-2000022000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-44444-2-2-2-442222-2-222-2-200002-2000000000000000000000000000000000000
χ4944-4-400400004i−4i004-4-40000004i−4i0000000000000000000022−2200−2i22i200000000000000000000
χ5044-4-400400004i−4i004-4-40000004i−4i00000000000000000000−2222002i2−2i200000000000000000000
χ5144-4-40040000−4i4i004-4-4000000−4i4i0000000000000000000022−22002i2−2i200000000000000000000
χ5244-4-40040000−4i4i004-4-4000000−4i4i00000000000000000000−222200−2i22i200000000000000000000
χ534-44-40044i−4i4-4004i−4i-44-400004-4004i−4i4i−4i000000000000000000000000000000000000000000
χ544-44-40044i−4i-4400−4i4i-44-40000-44004i−4i−4i4i000000000000000000000000000000000000000000
χ554-44-4004−4i4i4-400−4i4i-44-400004-400−4i4i−4i4i000000000000000000000000000000000000000000
χ564-44-4004−4i4i-44004i−4i-44-40000-4400−4i4i4i−4i000000000000000000000000000000000000000000
χ574-44-400-24i−4i4-4004i−4i2-220000-2200−2i2i−2i2i000000−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+ζ220000000000000000000000000000
χ584-44-400-24i−4i4-4004i−4i2-220000-2200−2i2i−2i2i000000ζ4+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−ζ220000000000000000000000000000
χ594-44-400-24i−4i-4400−4i4i2-2200002-200−2i2i2i−2i000000−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+ζ220000000000000000000000000000
χ604-44-400-24i−4i-4400−4i4i2-2200002-200−2i2i2i−2i000000ζ4−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−ζ220000000000000000000000000000
χ614-44-400-2−4i4i4-400−4i4i2-220000-22002i−2i2i−2i000000−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−ζ220000000000000000000000000000
χ624-44-400-2−4i4i4-400−4i4i2-220000-22002i−2i2i−2i000000ζ4−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+ζ220000000000000000000000000000
χ634-44-400-2−4i4i-44004i−4i2-2200002-2002i−2i−2i2i000000−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−ζ220000000000000000000000000000
χ644-44-400-2−4i4i-44004i−4i2-2200002-2002i−2i−2i2i000000ζ4+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+ζ220000000000000000000000000000
χ654-4-444-4400000000-4-44004-4000000000000000000000022−220022−220000000000000000000000
χ664-4-444-4400000000-4-44004-40000000000000000000000−222200−22220000000000000000000000
χ674-4-44-44400000000-4-4400-44000000000000000000000022−2200−22220000000000000000000000
χ684-4-44-44400000000-4-4400-440000000000000000000000−22220022−220000000000000000000000
χ6988-8-800-400008i−8i00-444000000−4i4i0000000000000000000000000000000000000000000000
χ7088-8-800-40000−8i8i00-4440000004i−4i0000000000000000000000000000000000000000000000
χ718-8-888-8-40000000044-400-4400000000000000000000000000000000000000000000000000
χ728-8-88-88-40000000044-4004-400000000000000000000000000000000000000000000000000

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