Finite Group Databasebeta

← Group #10692016

Character table — Group #10692016

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12223444444446662446612121212121212128888121224242424242424244488121212122424242424448888888888
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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ911111-1-1-1-111-1-1111-111-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−iii−i−i1-1
χ1011111-1-1-1-111-1-1111-111-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i1-1i−i11-1-1ii−i−i-1-111−i−iii−i−iii-11
χ1111111-1-1-1-111-1-1111-111-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i-11−ii-1-111−i−iii11-1-1−i−iiiii−i−i-11
χ1211111-1-1-1-111-1-1111-111-1-1-1-111-1-1-1-1ii−i−i11iiii−i−i−i−i-11−ii-1-111−i−iii-1-111ii−i−i−i−iii1-1
χ1311111-1-1-1-111-1-1111-111-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-1−i−iii−i−iii1-1
χ1411111-1-1-1-111-1-1111-111-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii1-1−ii11-1-1−i−iii-1-111ii−i−iii−i−i-11
χ1511111-1-1-1-111-1-1111-111-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii-11i−i-1-111ii−i−i11-1-1ii−i−i−i−iii-11
χ1611111-1-1-1-111-1-1111-111-1-1-1-111-1-1-1-1−i−iii11−i−i−i−iiiii-11i−i-1-111ii−i−i-1-111−i−iiiii−i−i1-1
χ1722222222222-2-2222-2-2-2-2-2222222-2-20000-2-2000000000000000000002-22-20000000000
χ1822222222222-2-2222-2-2-2-2-2222222-2-20000-2-200000000000000000000-22-220000000000
χ192222222-2-2-2-222222-22-2-2-2-2-2-2-222222-22-22-222-2-222-2-200000000000000000000000000
χ202222222-2-2-2-222222-22-2-2-2-2-2-2-22222-22-222-2-2-222-2-22200000000000000000000000000
χ212222222-2-2-2-2-2-22222-2222-2-2-2-222-2-20000-2200000000000000000000000000002i−2i2i−2i00
χ222222222-2-2-2-2-2-22222-2222-2-2-2-222-2-20000-220000000000000000000000000000−2i2i−2i2i00
χ2322222-2-222-2-222222-2-22-2-222-2-2-2-2220000-2200000000000000000000000000002-2-2200
χ2422222-2-222-2-222222-2-22-2-222-2-2-2-2220000-220000000000000000000000000000-222-200
χ2522222-2-222-2-2-2-222222-22222-2-2-2-2-2-22i−2i−2i2i2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ2622222-2-222-2-2-2-222222-22222-2-2-2-2-2-2−2i2i2i−2i2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ2722222-2-2-2-222222222-2-222-2-222-2-2220000-2-2000000000000000000002-2-220000000000
χ2822222-2-2-2-222222222-2-222-2-222-2-2220000-2-200000000000000000000-222-20000000000
χ292222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ302222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ312222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ322222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ332222-122-2-2-2-222-1-1-1-22-2111111-1-1-1-12-22-2-11-1-111-1-1110000−i3i3−i3i3−i3i3−i3i300000000000000
χ342222-122-2-2-2-222-1-1-1-22-2111111-1-1-1-12-22-2-11-1-111-1-1110000i3−i3i3−i3i3−i3i3−i300000000000000
χ352222-122-2-2-2-222-1-1-1-22-2111111-1-1-1-1-22-22-1111-1-111-1-10000−i3i3−i3i3i3−i3i3−i300000000000000
χ362222-122-2-2-2-222-1-1-1-22-2111111-1-1-1-1-22-22-1111-1-111-1-10000i3−i3i3−i3−i3i3−i3i300000000000000
χ372222-1-2-222-2-2-2-2-1-1-122-2-1-1-1-11111112i−2i−2i2i-11−i−iiiii−i−i0000−i3i3i3−i33−3−3300000000000000
χ382222-1-2-222-2-2-2-2-1-1-122-2-1-1-1-11111112i−2i−2i2i-11−i−iiiii−i−i0000i3−i3−i3i3−333−300000000000000
χ392222-1-2-222-2-2-2-2-1-1-122-2-1-1-1-1111111−2i2i2i−2i-11ii−i−i−i−iii0000−i3i3i3−i3−333−300000000000000
χ402222-1-2-222-2-2-2-2-1-1-122-2-1-1-1-1111111−2i2i2i−2i-11ii−i−i−i−iii0000i3−i3−i3i33−3−3300000000000000
χ412222-1-2-2-2-222-2-2-1-1-1-2221111-1-111112i2i−2i−2i-1-1−i−i−i−iiiii2-22i−2i-1-111−i−iii00000000000000
χ422222-1-2-2-2-222-2-2-1-1-1-2221111-1-111112i2i−2i−2i-1-1−i−i−i−iiiii-22−2i2i11-1-1ii−i−i00000000000000
χ432222-1-2-2-2-222-2-2-1-1-1-2221111-1-11111−2i−2i2i2i-1-1iiii−i−i−i−i2-2−2i2i-1-111ii−i−i00000000000000
χ442222-1-2-2-2-222-2-2-1-1-1-2221111-1-11111−2i−2i2i2i-1-1iiii−i−i−i−i-222i−2i11-1-1−i−iii00000000000000
χ454444-2444444-4-4-2-2-2-4-4-422-2-2-2-2-2-2220000220000000000000000000000000000000000
χ464444-244-4-4-4-4-4-4-2-2-24-44-2-22222-2-22200002-20000000000000000000000000000000000
χ474444-2-4-444-4-444-2-2-2-4-4422-2-22222-2-200002-20000000000000000000000000000000000
χ484444-2-4-4-4-44444-2-2-24-4-4-2-222-2-222-2-20000220000000000000000000000000000000000
χ494-44-440000004i−4i-44-4000000000004i−4i0000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ504-44-440000004i−4i-44-4000000000004i−4i000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ514-44-44000000−4i4i-44-400000000000−4i4i000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ524-44-44000000−4i4i-44-400000000000−4i4i0000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ534-4-4444i−4i4i−4i4-400-4-44000004i−4i4-44i−4i000000000000000000000000000000000000000000
χ544-4-4444i−4i−4i4i-4400-4-4400000−4i4i-444i−4i000000000000000000000000000000000000000000
χ554-4-444−4i4i4i−4i-4400-4-44000004i−4i-44−4i4i000000000000000000000000000000000000000000
χ564-4-444−4i4i−4i4i4-400-4-4400000−4i4i4-4−4i4i000000000000000000000000000000000000000000
χ574-4-44-24i−4i4i−4i4-40022-200000−2i2i-22−2i2i00000000−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
χ584-4-44-24i−4i4i−4i4-40022-200000−2i2i-22−2i2i00000000ζ4−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
χ594-4-44-24i−4i−4i4i-440022-2000002i−2i2-2−2i2i00000000−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
χ604-4-44-24i−4i−4i4i-440022-2000002i−2i2-2−2i2i00000000ζ4−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
χ614-4-44-2−4i4i4i−4i-440022-200000−2i2i2-22i−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
χ624-4-44-2−4i4i4i−4i-440022-200000−2i2i2-22i−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
χ634-4-44-2−4i4i−4i4i4-40022-2000002i−2i-222i−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
χ644-4-44-2−4i4i−4i4i4-40022-2000002i−2i-222i−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
χ6588-8-88000000008-8-800000000000000000000000000000000000000000000000000000
χ6688-8-8-400000000-444000−4i34i3000000000000000000000000000000000000000000000000
χ6788-8-8-400000000-4440004i3−4i3000000000000000000000000000000000000000000000000
χ688-88-8-40000008i−8i4-4400000000000−4i4i0000000000000000000000000000000000000000
χ698-88-8-4000000−8i8i4-44000000000004i−4i0000000000000000000000000000000000000000

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