Finite Group Databasebeta

← Group #10711997

Character table — Group #10711997

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111222222444444448888888888888816161616161616161616161616162424242424242424242424244848
order1222223666222244664444666612121212121244881212121212122424242444444444444444
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ5111111111111111111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1
χ6111111111111111111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111
χ7111111111111111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-1-1-11111111111-1-111-1-1-1-1
χ8111111111111111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111
χ91-11-11-11-11-1-1-1111-11-1i−ii−i1-1-111ii−i−i-11-1i−ii−i11-1-1ii−i−ii−i1-1i−ii−i1-1i−i1-1
χ101-11-11-11-11-1-1-1111-11-1i−ii−i1-1-111ii−i−i-11-1i−ii−i11-1-1ii−i−i−ii-11−ii−ii-11−ii-11
χ111-11-11-11-11-1-1-1111-11-1i−ii−i1-1-111ii−i−i-1-11−iii−i-1-111−i−iiii−i-11i−i−ii-11−ii1-1
χ121-11-11-11-11-1-1-1111-11-1i−ii−i1-1-111ii−i−i-1-11−iii−i-1-111−i−iii−ii1-1−iii−i1-1i−i-11
χ131-11-11-11-11-1-1-1111-11-1−ii−ii1-1-111−i−iii-11-1−ii−ii11-1-1−i−iiii−i-11i−ii−i-11i−i-11
χ141-11-11-11-11-1-1-1111-11-1−ii−ii1-1-111−i−iii-11-1−ii−ii11-1-1−i−iii−ii1-1−ii−ii1-1−ii1-1
χ151-11-11-11-11-1-1-1111-11-1−ii−ii1-1-111−i−iii-1-11i−i−ii-1-111ii−i−ii−i1-1i−i−ii1-1−ii-11
χ161-11-11-11-11-1-1-1111-11-1−ii−ii1-1-111−i−iii-1-11i−i−ii-1-111ii−i−i−ii-11−iii−i-11i−i1-1
χ1722222222222-22-2-2-2220000-22-22-20000-2000000000000000000002200-2-200
χ1822222222222-22-2-2-2220000-22-22-20000-200000000000000000000-2-2002200
χ192222222222-22-22-2-22222-2-22-22-2-22222-20000-2-20000000000000000000000
χ202222222222-22-22-2-222-2-2222-22-2-2-2-2-2-2-20000220000000000000000000000
χ212222222222-2-2-2-222220000-2-2-2-22000020000000000000000220000-2-20000
χ222222222222-2-2-2-222220000-2-2-2-22000020000000000000000-2-20000220000
χ23222222-1-1-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000000000
χ24222222-1-1-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000000000
χ25222222-1-1-1-1222222-1-1-2-2-2-2-1-1-1-1-11111-122-2-211-1-1-1-1111100000000000000
χ26222222-1-1-1-1222222-1-1-2-2-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-100000000000000
χ27222222-1-1-1-1-22-22-2-2-1-122-2-2-11-111-1-1-1-110000113−33−33−33−300000000000000
χ28222222-1-1-1-1-22-22-2-2-1-122-2-2-11-111-1-1-1-11000011−33−33−33−3300000000000000
χ29222222-1-1-1-1-22-22-2-2-1-1-2-222-11-111111110000-1-13−33−3−33−3300000000000000
χ30222222-1-1-1-1-22-22-2-2-1-1-2-222-11-111111110000-1-1−33−333−33−300000000000000
χ312-22-22-22-22-222-2-22-22-20000-222-220000-200000000000000002-20000-220000
χ322-22-22-22-22-222-2-22-22-20000-222-220000-20000000000000000-2200002-20000
χ332-22-22-22-22-22-2-22-222-22i−2i−2i2i22-2-2-22i2i−2i−2i20000−2i2i0000000000000000000000
χ342-22-22-22-22-22-2-22-222-2−2i2i2i−2i22-2-2-2−2i−2i2i2i200002i−2i0000000000000000000000
χ352-22-22-22-22-2-222-2-222-20000-2-222-200002000000000000000000002i−2i00−2i2i00
χ362-22-22-22-22-2-222-2-222-20000-2-222-20000200000000000000000000−2i2i002i−2i00
χ372-22-22-2-11-112-2-22-22-112i−2i−2i2i-1-1111−i−iii-10000i−i3−3−33i3−i3−i3i300000000000000
χ382-22-22-2-11-112-2-22-22-112i−2i−2i2i-1-1111−i−iii-10000i−i−333−3−i3i3i3−i300000000000000
χ392-22-22-2-11-112-2-22-22-11−2i2i2i−2i-1-1111ii−i−i-10000−ii3−3−33−i3i3i3−i300000000000000
χ402-22-22-2-11-112-2-22-22-11−2i2i2i−2i-1-1111ii−i−i-10000−ii−333−3i3−i3−i3i300000000000000
χ412-22-22-2-11-11-2-2222-2-112i−2i2i−2i-111-1-1−i−iii12-22i−2i−ii-1-111−i−iii00000000000000
χ422-22-22-2-11-11-2-2222-2-112i−2i2i−2i-111-1-1−i−iii1-22−2i2i−ii11-1-1ii−i−i00000000000000
χ432-22-22-2-11-11-2-2222-2-11−2i2i−2i2i-111-1-1ii−i−i12-2−2i2ii−i-1-111ii−i−i00000000000000
χ442-22-22-2-11-11-2-2222-2-11−2i2i−2i2i-111-1-1ii−i−i1-222i−2ii−i11-1-1−i−iii00000000000000
χ45444444-2-2-2-24-44-4-4-4-2-200002-22-22000020000000000000000000000000000
χ46444444-2-2-2-2-4-4-4-444-2-200002222-20000-20000000000000000000000000000
χ474444-4-44444000000-4-400000000000000000000000000002200-2-200000000
χ484444-4-44444000000-4-40000000000000000000000000000-2-2002200000000
χ494-44-44-4-22-2244-4-44-4-2200002-2-22-2000020000000000000000000000000000
χ504-44-44-4-22-22-444-4-44-22000022-2-220000-20000000000000000000000000000
χ514-44-4-444-44-4000000-4400000000000000000000000000002i−2i00−2i2i00000000
χ524-44-4-444-44-4000000-440000000000000000000000000000−2i2i002i−2i00000000
χ538888-8-8-4-4-4-400000044000000000000000000000000000000000000000000
χ5488-8-80088-8-800000000000000000000000000000000000000000000000000
χ5588-8-800-4-4440000000000000000023−2323−2300000000000000000000000000000
χ5688-8-800-4-44400000000000000000−2323−232300000000000000000000000000000
χ578-88-8-88-44-440000004-4000000000000000000000000000000000000000000
χ588-8-88008-8-8800000000000000000000000000000000000000000000000000
χ598-8-8800-444-400000000000000000−2i32i32i3−2i300000000000000000000000000000
χ608-8-8800-444-4000000000000000002i3−2i3−2i32i300000000000000000000000000000

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