Finite Group Databasebeta

← Group #10694607

Character table — Group #10694607

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212888812122424242424242424888888884488121212122424242444444488
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ91111-1-11-1-1-1-111-1-111111-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i1111-1-1-1-11-1i−i11-1-1ii−i−iii−i−i1-1i−i
χ101111-1-11-1-1-1-111-1-111111-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i1111-1-1-1-1-11−ii-1-111−i−iiiii−i−i-11−ii
χ111111-1-11-1-1-1-111-1-111111-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i-1-1-1-111111-1i−i11-1-1ii−i−i−i−iii-11−ii
χ121111-1-11-1-1-1-111-1-111111-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i-1-1-1-11111-11−ii-1-111−i−iii−i−iii1-1i−i
χ131111-1-11-1-1-1-111-1-111111-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii1111-1-1-1-11-1−ii11-1-1−i−iii−i−iii1-1−ii
χ141111-1-11-1-1-1-111-1-111111-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii1111-1-1-1-1-11i−i-1-111ii−i−i−i−iii-11i−i
χ151111-1-11-1-1-1-111-1-111111-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii-1-1-1-111111-1−ii11-1-1−i−iiiii−i−i-11i−i
χ161111-1-11-1-1-1-111-1-111111-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii-1-1-1-11111-11i−i-1-111ii−i−iii−i−i1-1−ii
χ17222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-22i−2i2i−2i2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ18222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-2−2i2i−2i2i2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ192222222-2-22222-2-2222-2-222-2-22222-2-20000-2-20000000022-2-222-2-200000000000000000000
χ202222222-2-22222-2-2222-2-222-2-22222-2-20000-2-200000000-2-222-2-22200000000000000000000
χ212222222-2-2-2-2-2-222222-2222-2-2-2-2-2-2220000-2200000000000000000000000000002-22-20000
χ222222222-2-2-2-2-2-222222-2222-2-2-2-2-2-2220000-220000000000000000000000000000-22-220000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ25222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ26222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ27222222-122-2-2-2-2-2-2-1-1-12-2-1-1-1-11111112i−2i2i−2i-11−i−iii−i−iii000000000000−i3i3−i3i33−33−300000000
χ28222222-122-2-2-2-2-2-2-1-1-12-2-1-1-1-11111112i−2i2i−2i-11−i−iii−i−iii000000000000i3−i3i3−i3−33−3300000000
χ29222222-122-2-2-2-2-2-2-1-1-12-2-1-1-1-1111111−2i2i−2i2i-11ii−i−iii−i−i000000000000−i3i3−i3i3−33−3300000000
χ30222222-122-2-2-2-2-2-2-1-1-12-2-1-1-1-1111111−2i2i−2i2i-11ii−i−iii−i−i000000000000i3−i3i3−i33−33−300000000
χ312222-2-222222-2-2-2-2222-22-2-222-2-222-2-20000-2200000000000000000000000000002i−2i−2i2i0000
χ322222-2-222222-2-2-2-2222-22-2-222-2-222-2-20000-220000000000000000000000000000−2i2i2i−2i0000
χ332222-2-2222-2-22222222-2-2-2-22222-2-2220000-2-20000000022-2-2-2-22200000000000000000000
χ342222-2-2222-2-22222222-2-2-2-22222-2-2220000-2-200000000-2-22222-2-200000000000000000000
χ352222-2-22-2-222-2-2222222-2-2-2-2-2-2-222222-2-222-222-2-2-2-2220000000000000000000000000000
χ362222-2-22-2-222-2-2222222-2-2-2-2-2-2-22222-222-22-2-2-22222-2-20000000000000000000000000000
χ372222-2-2-1-2-222-2-222-1-1-12-2111111-1-1-1-12-2-22-11-1-11111-1-1000000000000−i3i3i3−i3−i3i3i3−i300000000
χ382222-2-2-1-2-222-2-222-1-1-12-2111111-1-1-1-12-2-22-11-1-11111-1-1000000000000i3−i3−i3i3i3−i3−i3i300000000
χ392222-2-2-1-2-222-2-222-1-1-12-2111111-1-1-1-1-222-2-1111-1-1-1-111000000000000−i3i3i3−i3i3−i3−i3i300000000
χ402222-2-2-1-2-222-2-222-1-1-12-2111111-1-1-1-1-222-2-1111-1-1-1-111000000000000i3−i3−i3i3−i3i3i3−i300000000
χ412222-2-2-1-2-2-2-222-2-2-1-1-1221111-1-111112i2i−2i−2i-1-1−i−i−i−iiiii000000002-22i−2i-1-111−i−iii00000000
χ422222-2-2-1-2-2-2-222-2-2-1-1-1221111-1-111112i2i−2i−2i-1-1−i−i−i−iiiii00000000-22−2i2i11-1-1ii−i−i00000000
χ432222-2-2-1-2-2-2-222-2-2-1-1-1221111-1-11111−2i−2i2i2i-1-1iiii−i−i−i−i000000002-2−2i2i-1-111ii−i−i00000000
χ442222-2-2-1-2-2-2-222-2-2-1-1-1221111-1-11111−2i−2i2i2i-1-1iiii−i−i−i−i00000000-222i−2i11-1-1−i−iii00000000
χ45444444-2-4-44444-4-4-2-2-2-4-4-2-222-2-2-2-222000022000000000000000000000000000000000000
χ46444444-2-4-4-4-4-4-444-2-2-2-44-2-2222222-2-200002-2000000000000000000000000000000000000
χ474444-4-4-24444-4-4-4-4-2-2-2-4422-2-222-2-22200002-2000000000000000000000000000000000000
χ484444-4-4-244-4-44444-2-2-2-4-422-2-2-2-222-2-2000022000000000000000000000000000000000000
χ4944-4-44-44000000004-4-4004-400000000000000000000000022−220022−2200000000000000000000
χ5044-4-44-44000000004-4-4004-4000000000000000000000000−222200−222200000000000000000000
χ5144-4-4-444000000004-4-400-4400000000000000000000000022−2200−222200000000000000000000
χ5244-4-4-444000000004-4-400-44000000000000000000000000−22220022−2200000000000000000000
χ534-44-4004004i−4i0000-44-4000000004i−4i000000000000000022−2200−2i22i20000000000000000000000
χ544-44-4004004i−4i0000-44-4000000004i−4i0000000000000000−2222002i2−2i20000000000000000000000
χ554-44-400400−4i4i0000-44-400000000−4i4i000000000000000022−22002i2−2i20000000000000000000000
χ564-44-400400−4i4i0000-44-400000000−4i4i0000000000000000−222200−2i22i20000000000000000000000
χ574-4-440044i−4i004-44i−4i-4-4400004i−4i4-4004i−4i000000000000000000000000000000000000000000
χ584-4-440044i−4i00-44−4i4i-4-4400004i−4i-4400−4i4i000000000000000000000000000000000000000000
χ594-4-44004−4i4i004-4−4i4i-4-440000−4i4i4-400−4i4i000000000000000000000000000000000000000000
χ604-4-44004−4i4i00-444i−4i-4-440000−4i4i-44004i−4i000000000000000000000000000000000000000000
χ614-4-4400-24i−4i004-44i−4i22-20000−2i2i-2200−2i2i000000−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
χ624-4-4400-24i−4i004-44i−4i22-20000−2i2i-2200−2i2i000000ζ4−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
χ634-4-4400-24i−4i00-44−4i4i22-20000−2i2i2-2002i−2i000000−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+ζ220000000000000000000000000000
χ644-4-4400-24i−4i00-44−4i4i22-20000−2i2i2-2002i−2i000000ζ4+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−ζ220000000000000000000000000000
χ654-4-4400-2−4i4i004-4−4i4i22-200002i−2i-22002i−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
χ664-4-4400-2−4i4i004-4−4i4i22-200002i−2i-22002i−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
χ674-4-4400-2−4i4i00-444i−4i22-200002i−2i2-200−2i2i000000−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−ζ220000000000000000000000000000
χ684-4-4400-2−4i4i00-444i−4i22-200002i−2i2-200−2i2i000000ζ4−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+ζ220000000000000000000000000000
χ6988-8-88-8-400000000-44400-4400000000000000000000000000000000000000000000000000
χ7088-8-8-88-400000000-444004-400000000000000000000000000000000000000000000000000
χ718-88-800-4008i−8i00004-4400000000−4i4i00000000000000000000000000000000000000000000
χ728-88-800-400−8i8i00004-44000000004i−4i00000000000000000000000000000000000000000000

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