Finite Group Databasebeta

← Group #10692277

Character table — Group #10692277

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444448888888812121212121212121616161616161616161616161616161624242424242424244848
order122234444446662444121212121212688881212122244888888882424242424242424242424244488888844
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1
χ61111111111111111111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ71111111111111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ81111111111111111111111111-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ9111111-1-11-1-111111-1-11-1-1-1-111ii−i−i1-1-111-1-1ii−i−ii−i1-1ii−i−iii−i−i11-1-11-1i−iii−i−i1-1
χ10111111-1-11-1-111111-1-11-1-1-1-111ii−i−i1-1-111-1-1ii−i−i−ii-11ii−i−i−i−iii-1-1111-1i−i−i−iii-11
χ11111111-1-11-1-111111-1-11-1-1-1-111ii−i−i1-1-1-1-111−i−iiii−i1-1ii−i−iii−i−i11-1-1-11−ii−i−iii-11
χ12111111-1-11-1-111111-1-11-1-1-1-111ii−i−i1-1-1-1-111−i−iii−ii-11ii−i−i−i−iii-1-111-11−iiii−i−i1-1
χ13111111-1-11-1-111111-1-11-1-1-1-111−i−iii1-1-111-1-1−i−iiii−i-11−i−iiiii−i−i-1-1111-1−iiii−i−i-11
χ14111111-1-11-1-111111-1-11-1-1-1-111−i−iii1-1-111-1-1−i−iii−ii1-1−i−iii−i−iii11-1-11-1−ii−i−iii1-1
χ15111111-1-11-1-111111-1-11-1-1-1-111−i−iii1-1-1-1-111ii−i−ii−i-11−i−iiiii−i−i-1-111-11i−i−i−iii1-1
χ16111111-1-11-1-111111-1-11-1-1-1-111−i−iii1-1-1-1-111ii−i−i−ii1-1−i−iii−i−iii11-1-1-11i−iii−i−i-11
χ17222222222-2-2222-2-2-22222-2-22-20000-22-222-2-200000000000000000000-2200000000
χ18222222222-2-2222-2-2-22222-2-22-20000-22-2-2-222000000000000000000002-200000000
χ19222222-2-2222222-2-22-22-2-2222-20000-2-22222200000000000000000000-2-200000000
χ20222222-2-2222222-2-22-22-2-2222-20000-2-22-2-2-2-2000000000000000000002200000000
χ2122222-222-222222-22-2-2-22222-2-200002-2-200002222000000000000000000-2-2000000
χ2222222-222-222222-22-2-2-22222-2-200002-2-20000-2-2-2-200000000000000000022000000
χ2322222-222-2-2-22222-22-2-222-2-2-222i−2i2i−2i-2-220000000000002i−2i2i−2i000000000000000000
χ2422222-222-2-2-22222-22-2-222-2-2-22−2i2i−2i2i-2-22000000000000−2i2i−2i2i000000000000000000
χ2522222-2-2-2-2222222-2-22-2-2-222-222-2-22-22-20000000000002-2-22000000000000000000
χ2622222-2-2-2-2222222-2-22-2-2-222-22-222-2-22-2000000000000-222-2000000000000000000
χ2722222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-2000022200002i2i−2i−2i000000000000000000−2i2i000000
χ2822222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-200002220000−2i−2i2i2i0000000000000000002i−2i000000
χ292222-1222222-1-1-12222-1-1-1-1-1-1-12222-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ302222-1222222-1-1-12222-1-1-1-1-1-1-12222-1-1-100000000-2-2-2-2-1-1-1-1111111110000000000
χ312222-1222222-1-1-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-10000000022-2-21111-1-1-1-111110000000000
χ322222-1222222-1-1-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-100000000-2-22211111111-1-1-1-10000000000
χ332222-12-2-22-2-2-1-1-122-2-2-11111-1-12i2i−2i−2i-111000000002i−2i2-2−i−iii−i−iii-1-1110000000000
χ342222-12-2-22-2-2-1-1-122-2-2-11111-1-12i2i−2i−2i-11100000000−2i2i-22−i−iiiii−i−i11-1-10000000000
χ352222-12-2-22-2-2-1-1-122-2-2-11111-1-1−2i−2i2i2i-111000000002i−2i-22ii−i−i−i−iii11-1-10000000000
χ362222-12-2-22-2-2-1-1-122-2-2-11111-1-1−2i−2i2i2i-11100000000−2i2i2-2ii−i−iii−i−i-1-1110000000000
χ372222-1-222-2-2-2-1-1-12-22-21-1-1111-12i−2i2i−2i11-1000000000000−ii−ii−i3i3−i3i33−33−30000000000
χ382222-1-222-2-2-2-1-1-12-22-21-1-1111-12i−2i2i−2i11-1000000000000−ii−iii3−i3i3−i3−33−330000000000
χ392222-1-222-2-2-2-1-1-12-22-21-1-1111-1−2i2i−2i2i11-1000000000000i−ii−i−i3i3−i3i3−33−330000000000
χ402222-1-222-2-2-2-1-1-12-22-21-1-1111-1−2i2i−2i2i11-1000000000000i−ii−ii3−i3i3−i33−33−30000000000
χ412222-1-2-2-2-222-1-1-12-2-22111-1-11-12-2-221-11000000000000-111-13−3−33−333−30000000000
χ422222-1-2-2-2-222-1-1-12-2-22111-1-11-12-2-221-11000000000000-111-1−333−33−3−330000000000
χ432222-1-2-2-2-222-1-1-12-2-22111-1-11-1-222-21-110000000000001-1-113−3−333−3−330000000000
χ442222-1-2-2-2-222-1-1-12-2-22111-1-11-1-222-21-110000000000001-1-11−333−3−333−30000000000
χ454444-24444-4-4-2-2-2-4-4-44-2-2-222-2200002-220000000000000000000000000000000000
χ464444-24-4-4444-2-2-2-4-44-4-222-2-2-22000022-20000000000000000000000000000000000
χ474444-2-444-444-2-2-2-44-4-42-2-2-2-2220000-2220000000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-2-444422222220000-2-2-20000000000000000000000000000000000
χ4944-4-44400-4004-4-4000040000-4000000004-400000000000000000000000000000000
χ5044-4-44400-4004-4-4000040000-400000000-4400000000000000000000000000000000
χ5144-4-44-4004004-4-40000-40000400000000004i−4i000000000000000000000000000000
χ5244-4-44-4004004-4-40000-4000040000000000−4i4i000000000000000000000000000000
χ534-44-4400004i−4i-44-400000004i−4i00000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ544-44-4400004i−4i-44-400000004i−4i0000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ554-44-440000−4i4i-44-40000000−4i4i0000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ564-44-440000−4i4i-44-40000000−4i4i00000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ574-4-44404i−4i000-4-44000004i−4i0000000000000002+2i−2−2i2−2i−2+2i00000000000000000000000000
χ584-4-44404i−4i000-4-44000004i−4i000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000
χ594-4-4440−4i4i000-4-4400000−4i4i0000000000000002−2i−2+2i2+2i−2−2i00000000000000000000000000
χ604-4-4440−4i4i000-4-4400000−4i4i000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000
χ6188-8-8-4800-800-4440000-400004000000000000000000000000000000000000000000
χ6288-8-8-4-800800-444000040000-4000000000000000000000000000000000000000000
χ638-88-8-400008i−8i4-440000000−4i4i0000000000000000000000000000000000000000000
χ648-88-8-40000−8i8i4-4400000004i−4i0000000000000000000000000000000000000000000
χ658-8-88-408i−8i00044-400000−4i4i000000000000000000000000000000000000000000000
χ668-8-88-40−8i8i00044-4000004i−4i000000000000000000000000000000000000000000000

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