Finite Group Databasebeta

← Group #10692340

Character table — Group #10692340

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444448888888812121212121212121616161616161616161616161616161624242424242424244848
order122234444446662444121212121212688881212124444888888882424242424242424242424242488888822
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
χ9111111-11-1-1-111111-1-11-1-11-1-11ii−i−i1-1-111-1-1ii−i−ii−i1-1ii−i−iii−i−i11-1-11-1i−iii−i−i1-1
χ10111111-11-1-1-111111-1-11-1-11-1-11ii−i−i1-1-111-1-1ii−i−i−ii-11ii−i−i−i−iii-1-1111-1i−i−i−iii-11
χ11111111-11-1-1-111111-1-11-1-11-1-11ii−i−i1-1-1-1-111−i−iiii−i1-1ii−i−iii−i−i11-1-1-11−ii−i−iii-11
χ12111111-11-1-1-111111-1-11-1-11-1-11ii−i−i1-1-1-1-111−i−iii−ii-11ii−i−i−i−iii-1-111-11−iiii−i−i1-1
χ13111111-11-1-1-111111-1-11-1-11-1-11−i−iii1-1-111-1-1−i−iiii−i-11−i−iiiii−i−i-1-1111-1−iiii−i−i-11
χ14111111-11-1-1-111111-1-11-1-11-1-11−i−iii1-1-111-1-1−i−iii−ii1-1−i−iii−i−iii11-1-11-1−ii−i−iii1-1
χ15111111-11-1-1-111111-1-11-1-11-1-11−i−iii1-1-1-1-111ii−i−ii−i-11−i−iiiii−i−i-1-111-11i−i−i−iii1-1
χ16111111-11-1-1-111111-1-11-1-11-1-11−i−iii1-1-1-1-111ii−i−i−ii1-1−i−iii−i−iii11-1-1-11i−iii−i−i-11
χ17222222222-2-2222-2-2-2222-222-2-20000-22-222-2-200000000000000000000-2200000000
χ18222222222-2-2222-2-2-2222-222-2-20000-22-2-2-222000000000000000000002-200000000
χ19222222-22-222222-2-22-22-222-22-20000-2-22222200000000000000000000-2-200000000
χ20222222-22-222222-2-22-22-222-22-20000-2-22-2-2-2-2000000000000000000002200000000
χ2122222-22-2222222-22-2-2-222-222-200002-2-200002222000000000000000000-2-2000000
χ2222222-22-2222222-22-2-2-222-222-200002-2-20000-2-2-2-200000000000000000022000000
χ2322222-22-22-2-22222-22-2-22-2-22-222i−2i2i−2i-2-220000000000002i−2i2i−2i000000000000000000
χ2422222-22-22-2-22222-22-2-22-2-22-22−2i2i−2i2i-2-22000000000000−2i2i−2i2i000000000000000000
χ2522222-2-2-2-2222222-2-22-2-22-2-2222-2-22-22-20000000000002-2-22000000000000000000
χ2622222-2-2-2-2222222-2-22-2-22-2-222-222-2-22-2000000000000-222-2000000000000000000
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
χ332222-12-22-2-2-2-1-1-122-2-2-111-111-12i2i−2i−2i-111000000002i−2i2-2−i−iii−i−iii-1-1110000000000
χ342222-12-22-2-2-2-1-1-122-2-2-111-111-12i2i−2i−2i-11100000000−2i2i-22−i−iiiii−i−i11-1-10000000000
χ352222-12-22-2-2-2-1-1-122-2-2-111-111-1−2i−2i2i2i-111000000002i−2i-22ii−i−i−i−iii11-1-10000000000
χ362222-12-22-2-2-2-1-1-122-2-2-111-111-1−2i−2i2i2i-11100000000−2i2i2-2ii−i−iii−i−i-1-1110000000000
χ372222-1-22-22-2-2-1-1-12-22-21-111-11-12i−2i2i−2i11-1000000000000−ii−ii−i3i3−i3i33−33−30000000000
χ382222-1-22-22-2-2-1-1-12-22-21-111-11-12i−2i2i−2i11-1000000000000−ii−iii3−i3i3−i3−33−330000000000
χ392222-1-22-22-2-2-1-1-12-22-21-111-11-1−2i2i−2i2i11-1000000000000i−ii−i−i3i3−i3i3−33−330000000000
χ402222-1-22-22-2-2-1-1-12-22-21-111-11-1−2i2i−2i2i11-1000000000000i−ii−ii3−i3i3−i33−33−30000000000
χ412222-1-2-2-2-222-1-1-12-2-2211-111-1-12-2-221-11000000000000-111-13−3−33−333−30000000000
χ422222-1-2-2-2-222-1-1-12-2-2211-111-1-12-2-221-11000000000000-111-1−333−33−3−330000000000
χ432222-1-2-2-2-222-1-1-12-2-2211-111-1-1-222-21-110000000000001-1-113−3−333−3−330000000000
χ442222-1-2-2-2-222-1-1-12-2-2211-111-1-1-222-21-110000000000001-1-11−333−3−333−30000000000
χ454444-24444-4-4-2-2-2-4-4-44-2-22-2-22200002-220000000000000000000000000000000000
χ464444-24-44-444-2-2-2-4-44-4-22-2-22-22000022-20000000000000000000000000000000000
χ474444-2-44-4444-2-2-2-44-4-42-2-22-2-220000-2220000000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-2-444422222220000-2-2-20000000000000000000000000000000000
χ4944-4-4400004-44-4-4000000400-40000000000000000000000000000000000002i−2i2i−2i00
χ5044-4-4400004-44-4-4000000400-4000000000000000000000000000000000000−2i2i−2i2i00
χ5144-4-440000-444-4-4000000-40040000000000000000000000000000000000002-2-2200
χ5244-4-440000-444-4-4000000-4004000000000000000000000000000000000000-222-200
χ534-44-44040-400-44-400000400-40000000000000−2i22i2−2i22i200000000000000000000000000
χ544-44-44040-400-44-400000400-400000000000002i2−2i22i2−2i200000000000000000000000000
χ554-44-440-40400-44-400000-4004000000000000022−22−222200000000000000000000000000
χ564-44-440-40400-44-400000-40040000000000000−222222−2200000000000000000000000000
χ574-4-44440-4000-4-440000400-40000000000004i−4i000000000000000000000000000000
χ584-4-44440-4000-4-440000400-4000000000000−4i4i000000000000000000000000000000
χ594-4-444-404000-4-440000-400400000000004-400000000000000000000000000000000
χ604-4-444-404000-4-440000-40040000000000-4400000000000000000000000000000000
χ6188-8-8-400008-8-444000000-4004000000000000000000000000000000000000000000
χ6288-8-8-40000-88-444000000400-4000000000000000000000000000000000000000000
χ638-88-8-4080-8004-4400000-40040000000000000000000000000000000000000000000
χ648-88-8-40-808004-4400000400-40000000000000000000000000000000000000000000
χ658-8-88-480-800044-40000-400400000000000000000000000000000000000000000000
χ668-8-88-4-80800044-40000400-400000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).