Finite Group Databasebeta

← Group #10692242

Character table — Group #10692242

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444448888888812121212121212121616161616161616161616161616161624242424242424244848
order122222344446662244661212121266888812124444888844881212121224242424242424244488888844
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ91111-1-1111-1-11111-11-1-1-111-1-11-1ii−i−i1-111-1-1ii−i−ii−i1-1ii−i−iii−i−i11-1-1-11i−iii−i−i1-1
χ101111-1-1111-1-11111-11-1-1-111-1-11-1ii−i−i1-111-1-1ii−i−i−ii-11−i−iiiii−i−i-1-111-11i−i−i−iii-11
χ111111-1-1111-1-11111-11-1-1-111-1-11-1ii−i−i1-1-1-111−i−iiii−i1-1ii−i−iii−i−i11-1-11-1−ii−i−iii-11
χ121111-1-1111-1-11111-11-1-1-111-1-11-1ii−i−i1-1-1-111−i−iii−ii-11−i−iiiii−i−i-1-1111-1−iiii−i−i1-1
χ131111-1-1111-1-11111-11-1-1-111-1-11-1−i−iii1-111-1-1−i−iiii−i-11ii−i−i−i−iii-1-111-11−iiii−i−i-11
χ141111-1-1111-1-11111-11-1-1-111-1-11-1−i−iii1-111-1-1−i−iii−ii1-1−i−iii−i−iii11-1-1-11−ii−i−iii1-1
χ151111-1-1111-1-11111-11-1-1-111-1-11-1−i−iii1-1-1-111ii−i−ii−i-11ii−i−i−i−iii-1-1111-1i−i−i−iii1-1
χ161111-1-1111-1-11111-11-1-1-111-1-11-1−i−iii1-1-1-111ii−i−i−ii1-1−i−iii−i−iii11-1-11-1i−iii−i−i-11
χ17222222222-2-2222-2-2-222222-2-2-2-20000-2222-2-2000000000000000000002-200000000
χ18222222222-2-2222-2-2-222222-2-2-2-20000-22-2-22200000000000000000000-2200000000
χ192222222-2-222222-2-22-222-2-222-2-200002-200002222000000000000000000-2-2000000
χ202222222-2-222222-2-22-222-2-222-2-200002-20000-2-2-2-200000000000000000022000000
χ212222222-2-2-2-222222-2-222-2-2-2-2222i−2i2i−2i-2-200000000000000002i−2i2i−2i00000000000000
χ222222222-2-2-2-222222-2-222-2-2-2-222−2i2i−2i2i-2-20000000000000000−2i2i−2i2i00000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-12222-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-12222-1-100000000-2-2-2-21111-1-1-1-111110000000000
χ25222222-12222-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-10000000022-2-2-1-1-1-1111111110000000000
χ26222222-12222-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-100000000-2-22211111111-1-1-1-10000000000
χ27222222-1-2-2-2-2-1-1-122-2-2-1-11111-1-12i−2i2i−2i11000000000000−i3i3−i3i3−ii−ii3−33−30000000000
χ28222222-1-2-2-2-2-1-1-122-2-2-1-11111-1-12i−2i2i−2i11000000000000i3−i3i3−i3−ii−ii−33−330000000000
χ29222222-1-2-2-2-2-1-1-122-2-2-1-11111-1-1−2i2i−2i2i11000000000000−i3i3−i3i3i−ii−i−33−330000000000
χ30222222-1-2-2-2-2-1-1-122-2-2-1-11111-1-1−2i2i−2i2i11000000000000i3−i3i3−i3i−ii−i3−33−30000000000
χ312222-2-222222222-22-2-2-2-22222-220000-2-2222200000000000000000000-2-200000000
χ322222-2-222222222-22-2-2-2-22222-220000-2-2-2-2-2-2000000000000000000002200000000
χ332222-2-22-2-2222222-2-22-2-2-2-2222-22-2-22-2200000000000000002-2-2200000000000000
χ342222-2-22-2-2222222-2-22-2-2-2-2222-2-222-2-220000000000000000-222-200000000000000
χ352222-2-22-2-2-2-2222-2222-2-2-2-2-2-2-2200002200002i2i−2i−2i000000000000000000−2i2i000000
χ362222-2-22-2-2-2-2222-2222-2-2-2-2-2-2-220000220000−2i−2i2i2i0000000000000000002i−2i000000
χ372222-2-2-122-2-2-1-1-12-22-211-1-111-112i2i−2i−2i-11000000002i−2i2-2−i−iii−i−iii-1-1110000000000
χ382222-2-2-122-2-2-1-1-12-22-211-1-111-112i2i−2i−2i-1100000000−2i2i-22ii−i−i−i−iii11-1-10000000000
χ392222-2-2-122-2-2-1-1-12-22-211-1-111-11−2i−2i2i2i-11000000002i−2i-22−i−iiiii−i−i11-1-10000000000
χ402222-2-2-122-2-2-1-1-12-22-211-1-111-11−2i−2i2i2i-1100000000−2i2i2-2ii−i−iii−i−i-1-1110000000000
χ412222-2-2-1-2-222-1-1-12-2-221111-1-1-112-2-221-10000000000003−3−33-111-1−333−30000000000
χ422222-2-2-1-2-222-1-1-12-2-221111-1-1-112-2-221-1000000000000−333−3-111-13−3−330000000000
χ432222-2-2-1-2-222-1-1-12-2-221111-1-1-11-222-21-10000000000003−3−331-1-113−3−330000000000
χ442222-2-2-1-2-222-1-1-12-2-221111-1-1-11-222-21-1000000000000−333−31-1-11−333−30000000000
χ45444444-244-4-4-2-2-2-4-4-44-2-2-2-2222200002-20000000000000000000000000000000000
χ46444444-2-4-444-2-2-2-4-44-4-2-222-2-2220000-220000000000000000000000000000000000
χ474444-4-4-24444-2-2-2-44-4-422-2-2-2-22-20000220000000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-2-2-2-44442222222-20000-2-20000000000000000000000000000000000
χ4944-4-44-4400004-4-400004-4000000000000000022−2222−2200000000000000000000000000
χ5044-4-44-4400004-4-400004-40000000000000000−2222−222200000000000000000000000000
χ5144-4-4-44400004-4-40000-440000000000000000−2i22i22i2−2i200000000000000000000000000
χ5244-4-4-44400004-4-40000-4400000000000000002i2−2i2−2i22i200000000000000000000000000
χ534-44-40044-400-4-440000004-40000000000004i−4i000000000000000000000000000000
χ544-44-40044-400-4-440000004-4000000000000−4i4i000000000000000000000000000000
χ554-44-4004-4400-4-44000000-4400000000004i−4i00000000000000000000000000000000
χ564-44-4004-4400-4-44000000-440000000000−4i4i00000000000000000000000000000000
χ574-4-44004004i−4i-44-4000000004i−4i000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ584-4-44004004i−4i-44-4000000004i−4i0000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ594-4-4400400−4i4i-44-400000000−4i4i0000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ604-4-4400400−4i4i-44-400000000−4i4i000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ6188-8-88-8-40000-4440000-440000000000000000000000000000000000000000000000
χ6288-8-8-88-40000-44400004-40000000000000000000000000000000000000000000000
χ638-88-800-48-80044-4000000-4400000000000000000000000000000000000000000000
χ648-88-800-4-880044-40000004-400000000000000000000000000000000000000000000
χ658-8-8800-4008i−8i4-4400000000−4i4i000000000000000000000000000000000000000000
χ668-8-8800-400−8i8i4-44000000004i−4i000000000000000000000000000000000000000000

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