Finite Group Databasebeta

← Group #72283988

Character table — Group #72283988

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112444888888881616161616161616161616161616161616161616163232323232323232323232646464646464646464646464128128128128
order12222222222244222444444444444444444224444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111111-1-1-1-1111-1-1-1-1
χ31111111111111111111-1-1-1-1111111111111-1-1111-1-11111-11-11-1-1-1-1-11-1-111-1-1
χ41111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1-1-11-11-111111-1-1-1-111
χ5111111111111111-1-11111-1-11111111111111-1-1111111111-1-1-1-11111-11-1-1-1-1-1
χ6111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-11-11111
χ7111111111111111-1-111-1-111111111111111-11-111-1-11111-1-11-11-1-1-1-1-1-11-1-111
χ8111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-11-111-1-1-1-1-1-1-1-11-111111-1-1111-1-1
χ9111111-11-1-11-111111-1-11111iiii−i−i−i−i-1-1-1-111111-1-1ii−i−i-1-1-111ii−i−i-11-1i−ii−i
χ10111111-11-1-11-111111-1-11111−i−i−i−iiiii-1-1-1-111111-1-1−i−iii-1-1-111−i−iii-11-1−ii−ii
χ11111111-11-1-11-111111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-111111ii−i−i1-111-1−i−iii-1-11i−i−ii
χ12111111-11-1-11-111111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-111111−i−iii1-111-1ii−i−i-1-11−iii−i
χ13111111-11-1-11-1111-1-1-1-111-1-1iiii−i−i−i−i-1-1-1-11-1-111-1-1ii−i−i-111-1-1ii−i−i111−ii−ii
χ14111111-11-1-11-1111-1-1-1-111-1-1−i−i−i−iiiii-1-1-1-11-1-111-1-1−i−iii-111-1-1−i−iii111i−ii−i
χ15111111-11-1-11-1111-1-1-1-1-1-111iiii−i−i−i−i-1-1-1-1-11-11111ii−i−i11-1-11−i−iii1-1-1−iii−i
χ16111111-11-1-11-1111-1-1-1-1-1-111−i−i−i−iiiii-1-1-1-1-11-11111−i−iii11-1-11ii−i−i1-1-1i−i−ii
χ172222222222222220022220000000000-2-2-2-2200-2-2-2-200002000000000-200000
χ182222222222222220022-2-20000000000-2-2-2-2-200-2-2220000-2000000000200000
χ1922222222-2-222-2-2-2002-200220000000022-2-20202-20000000020-2000000-20000
χ2022222222-2-222-2-2-2002-200-2-20000000022-2-20-202-200000000-20200000020000
χ2122222222-2-222-2-2-2222-2000000000000-2-222002-22000000020-200000-2000000
χ2222222222-2-222-2-2-2-2-22-2000000000000-2-22200-2-220000000-202000002000000
χ23222222-22222-2-2-2-200-22002200000000-2-2220202-200000000-20-200000020000
χ24222222-22222-2-2-2-200-2200-2-200000000-2-2220-202-200000000202000000-20000
χ25222222-22222-2-2-2-222-2200000000000022-2-2002-220000000-20-2000002000000
χ26222222-22222-2-2-2-2-2-2-2200000000000022-2-200-2-22000000020200000-2000000
χ27222222-22-2-22-222200-2-22200000000002222200-2-2220000-2000000000-200000
χ28222222-22-2-22-222200-2-2-2-200000000002222-200-2-2-2-200002000000000200000
χ292222-2-20200-2022-2000022001+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2i−2i-200002i−2i1+i−1−i1−i−1+i000001+i−1−i1−i−1+i0000000
χ302222-2-20200-2022-2000022001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i−2i2i-20000−2i2i1−i−1+i1+i−1−i000001−i−1+i1+i−1−i0000000
χ312222-2-20200-2022-200002200−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i−2i2i-20000−2i2i−1+i1−i−1−i1+i00000−1+i1−i−1−i1+i0000000
χ322222-2-20200-2022-200002200−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2i−2i-200002i−2i−1−i1+i−1+i1−i00000−1−i1+i−1+i1−i0000000
χ332222-2-20200-2022-20000-2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i2i−2i2i−2i20000−2i2i1+i−1−i1−i−1+i00000−1−i1+i−1+i1−i0000000
χ342222-2-20200-2022-20000-2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2i2i−2i2i200002i−2i1−i−1+i1+i−1−i00000−1+i1−i−1−i1+i0000000
χ352222-2-20200-2022-20000-2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2i2i−2i2i200002i−2i−1+i1−i−1−i1+i000001−i−1+i1+i−1−i0000000
χ362222-2-20200-2022-20000-2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i2i−2i2i−2i20000−2i2i−1−i1+i−1+i1−i000001+i−1−i1−i−1+i0000000
χ374444444-400-4400000-4000002222222200000000000-2-2-2-20000000000000000
χ384444444-400-4400000-400000-2-2-2-2-2-2-2-20000000000022220000000000000000
χ39444444-4-400-4-4000004000002i2i2i2i−2i−2i−2i−2i00000000000−2i−2i2i2i0000000000000000
χ40444444-4-400-4-400000400000−2i−2i−2i−2i2i2i2i2i000000000002i2i−2i−2i0000000000000000
χ414444-4-40400-40-4-4400000000000000004i−4i−4i4i000000000000000000000000000
χ424444-4-40400-40-4-440000000000000000−4i4i4i−4i000000000000000000000000000
χ434444-4-40-44440000000-4000022-2-222-2-200000000000-22-220000000000000000
χ444444-4-40-44440000000-40000-2-222-2-222000000000002-22-20000000000000000
χ454444-4-40-4-4-440000000400002i2i−2i−2i−2i−2i2i2i00000000000−2i2i2i−2i0000000000000000
χ464444-4-40-4-4-44000000040000−2i−2i2i2i2i2i−2i−2i000000000002i−2i−2i2i0000000000000000
χ47888-88-8000000000000000440000000000000-40000000000000000000000000
χ48888-88-8000000000000000-4-4000000000000040000000000000000000000000
χ49888-8-880000000004400000000000000000000-4000000000000000000000000
χ50888-8-88000000000-4-4000000000000000000004000000000000000000000000
χ5188-8000404-40-44-4000000000004i−4i004i−4i0000000000000000000000000000000
χ5288-8000404-40-44-400000000000−4i4i00−4i4i0000000000000000000000000000000
χ5388-800040-440-4-440000000004i−4i004i−4i000000000000000000000000000000000
χ5488-800040-440-4-44000000000−4i4i00−4i4i000000000000000000000000000000000
χ5588-8000-404-404-440000000004-400-44000000000000000000000000000000000
χ5688-8000-404-404-44000000000-44004-4000000000000000000000000000000000
χ5788-8000-40-44044-4000000000004-400-440000000000000000000000000000000
χ5888-8000-40-44044-400000000000-44004-40000000000000000000000000000000
χ5916-1600000000000004-4004-44-4000000000000000000000000000000000000000
χ6016-1600000000000004-400-44-44000000000000000000000000000000000000000
χ6116-160000000000000-44004-4-44000000000000000000000000000000000000000
χ6216-160000000000000-4400-444-4000000000000000000000000000000000000000

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