Finite Group Databasebeta

← Group #10692009

Character table — Group #10692009

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order122234444444466624466121212121212121288881212242424242424242424668812122424242424448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111
χ911111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i1-111i−i-1-1ii−i−i1-1-11ii−i−iii−i−i1-1
χ1011111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i1-111i−i-1-1ii−i−i-111-1−i−iii−i−iii-11
χ1111111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i-11-1-1−ii11−i−iii1-1-11−i−iiiii−i−i-11
χ1211111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i-11-1-1−ii11−i−iii-111-1ii−i−i−i−iii1-1
χ1311111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii1-111−ii-1-1−i−iii1-1-11−i−iii−i−iii1-1
χ1411111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii1-111−ii-1-1−i−iii-111-1ii−i−iii−i−i-11
χ1511111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii-11-1-1i−i11ii−i−i1-1-11ii−i−i−i−iii-11
χ1611111-1-111-1-1-1-1111-111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii-11-1-1i−i11ii−i−i-111-1−i−iiiii−i−i1-1
χ1722222222222-2-2222-2-2-2-2-2222222-2-20000-2-20000000000000000000022-2-20000000000
χ1822222222222-2-2222-2-2-2-2-2222222-2-20000-2-200000000000000000000-2-2220000000000
χ192222222-2-2-2-222222-2-22-2-2-2-2-2-222222-22-2-2222-2-222-2-200000000000000000000000000
χ202222222-2-2-2-222222-2-22-2-2-2-2-2-22222-22-22-22-2-222-2-22200000000000000000000000000
χ212222222-2-2-2-2-2-222222-222-2-2-2-222-2-200002-200000000000000000000000000002i−2i2i−2i00
χ222222222-2-2-2-2-2-222222-222-2-2-2-222-2-200002-20000000000000000000000000000−2i2i−2i2i00
χ2322222-2-222-2-2222222-2-22222-2-2-2-2220000-2-2000000000000000000002-22-20000000000
χ2422222-2-222-2-2222222-2-22222-2-2-2-2220000-2-200000000000000000000-22-220000000000
χ2522222-2-2-2-22222222-22-2-2-2-2-222-2-22200002-200000000000000000000000000002-2-2200
χ2622222-2-2-2-22222222-22-2-2-2-2-222-2-22200002-20000000000000000000000000000-222-200
χ2722222-2-2-2-222-2-22222-2222-2-222-2-2-2-22i−2i−2i2i-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ2822222-2-2-2-222-2-22222-2222-2-222-2-2-2-2−2i2i2i−2i-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ292222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100000000000000
χ302222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-211111100000000000000
χ312222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-1111100000000000000
χ322222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-100000000000000
χ332222-122-2-2-2-222-1-1-1-2-22111111-1-1-1-12-22-21-1-1-111-1-11100−i3i300−i3i3−i3i3−i3i300000000000000
χ342222-122-2-2-2-222-1-1-1-2-22111111-1-1-1-12-22-21-1-1-111-1-11100i3−i300i3−i3i3−i3i3−i300000000000000
χ352222-122-2-2-2-222-1-1-1-2-22111111-1-1-1-1-22-221-111-1-111-1-100−i3i300−i3i3i3−i3i3−i300000000000000
χ362222-122-2-2-2-222-1-1-1-2-22111111-1-1-1-1-22-221-111-1-111-1-100i3−i300i3−i3−i3i3−i3i300000000000000
χ372222-1-2-222-2-2-2-2-1-1-1-22211-1-11111112i2i−2i−2i-1-1−i−i−i−iiiii2-2-1-12i−2i11−i−iii00000000000000
χ382222-1-2-222-2-2-2-2-1-1-1-22211-1-11111112i2i−2i−2i-1-1−i−i−i−iiiii-2211−2i2i-1-1ii−i−i00000000000000
χ392222-1-2-222-2-2-2-2-1-1-1-22211-1-1111111−2i−2i2i2i-1-1iiii−i−i−i−i2-2-1-1−2i2i11ii−i−i00000000000000
χ402222-1-2-222-2-2-2-2-1-1-1-22211-1-1111111−2i−2i2i2i-1-1iiii−i−i−i−i-22112i−2i-1-1−i−iii00000000000000
χ412222-1-2-2-2-222-2-2-1-1-12-22-1-111-1-111112i−2i−2i2i1-1−i−iiiii−i−i00−i3i300i3−i33−3−3300000000000000
χ422222-1-2-2-2-222-2-2-1-1-12-22-1-111-1-111112i−2i−2i2i1-1−i−iiiii−i−i00i3−i300−i3i3−333−300000000000000
χ432222-1-2-2-2-222-2-2-1-1-12-22-1-111-1-11111−2i2i2i−2i1-1ii−i−i−i−iii00−i3i300i3−i3−333−300000000000000
χ442222-1-2-2-2-222-2-2-1-1-12-22-1-111-1-11111−2i2i2i−2i1-1ii−i−i−i−iii00i3−i300−i3i33−3−3300000000000000
χ454444-2444444-4-4-2-2-2-4-4-422-2-2-2-2-2-2220000220000000000000000000000000000000000
χ464444-244-4-4-4-4-4-4-2-2-244-4-2-22222-2-2220000-220000000000000000000000000000000000
χ474444-2-4-444-4-444-2-2-24-4-4-2-2-2-22222-2-20000220000000000000000000000000000000000
χ484444-2-4-4-4-44444-2-2-2-44-42222-2-222-2-20000-220000000000000000000000000000000000
χ4944-4-440000004i−4i4-4-4000000000004i−4i0000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ5044-4-440000004i−4i4-4-4000000000004i−4i000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ5144-4-44000000−4i4i4-4-400000000000−4i4i000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ5244-4-44000000−4i4i4-4-400000000000−4i4i0000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ534-44-444i−4i4-44i−4i00-44-4000004-44i−4i4i−4i000000000000000000000000000000000000000000
χ544-44-444i−4i-44−4i4i00-44-400000-44−4i4i4i−4i000000000000000000000000000000000000000000
χ554-44-44−4i4i4-4−4i4i00-44-4000004-4−4i4i−4i4i000000000000000000000000000000000000000000
χ564-44-44−4i4i-444i−4i00-44-400000-444i−4i−4i4i000000000000000000000000000000000000000000
χ574-44-4-24i−4i4-44i−4i002-2200000-22−2i2i−2i2i00000000−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+ζ2200000000000000000000000000
χ584-44-4-24i−4i4-44i−4i002-2200000-22−2i2i−2i2i00000000ζ4+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−ζ2200000000000000000000000000
χ594-44-4-24i−4i-44−4i4i002-22000002-22i−2i−2i2i00000000−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
χ604-44-4-24i−4i-44−4i4i002-22000002-22i−2i−2i2i00000000ζ4+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
χ614-44-4-2−4i4i4-4−4i4i002-2200000-222i−2i2i−2i00000000−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−ζ2200000000000000000000000000
χ624-44-4-2−4i4i4-4−4i4i002-2200000-222i−2i2i−2i00000000ζ4−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+ζ2200000000000000000000000000
χ634-44-4-2−4i4i-444i−4i002-22000002-2−2i2i2i−2i00000000−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
χ644-44-4-2−4i4i-444i−4i002-22000002-2−2i2i2i−2i00000000ζ4−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
χ6588-8-8-40000008i−8i-44400000000000−4i4i0000000000000000000000000000000000000000
χ6688-8-8-4000000−8i8i-444000000000004i−4i0000000000000000000000000000000000000000
χ678-8-88800000000-8-8800000000000000000000000000000000000000000000000000000
χ688-8-88-40000000044-4000−4i34i3000000000000000000000000000000000000000000000000
χ698-8-88-40000000044-40004i3−4i3000000000000000000000000000000000000000000000000

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