Finite Group Databasebeta

← Group #72310948

Character table — Group #72310948

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112444888888888888881616161616161616161616161616323232323232323232323264646464646464646464646464128128128128
order12222222222222222244224444444444442444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-11-111-1-1-1-1111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-11-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ611111111111111-1-1-1-111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ711111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-11-111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ811111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-11-111-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ911111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11-1-11111-1-111-111-1-111-1-111-1-11-11-1
χ1011111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11-1-11111-1-111-111-1-1-1-111-1-111-11-11
χ1111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111-1-11111-1-1-11111-1-111-1-1-11-11
χ1211111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111-1-11111-1-1-111-1-111-1-1111-11-1
χ1311111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11-1-11111-1-1-1-11-1-111ii−i−i−i−iiii−i−ii
χ1411111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11-1-11111-1-1-1-11-1-111−i−iiiii−i−i−iii−i
χ1511111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111-1-111-1-1111-1-1ii−i−i−i−iii−iii−i
χ1611111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111-1-111-1-1111-1-1−i−iiiii−i−ii−i−ii
χ172222222222222222222222222222-2-200000-20-2-20000-2-2-20000000000000000
χ1822222222222222-2-2-2-222-2-222-2-2-2-2-2-200000-20-2-200002220000000000000000
χ1922222222-2-2-2-222222222-2-2-2-222-2-2220000020-2-20000-2-220000000000000000
χ2022222222-2-2-2-222-2-2-2-22222-2-2-2-222220000020-2-2000022-20000000000000000
χ21222222-2-200002222-2-2-2-200002-2000000220022-200-2-22-20002-2000000000000
χ22222222-2-200002222-2-2-2-200002-2000000-2-200-22-200222-2000-22000000000000
χ23222222-2-200002222-2-2-2-200002-200002200200-22-2-200-2202-200000000000000
χ24222222-2-200002222-2-2-2-200002-20000-2-200-200-222200-220-2200000000000000
χ25222222-2-2000022-2-222-2-20000-22000000220022-200-2-2-22000-22000000000000
χ26222222-2-2000022-2-222-2-20000-22000000-2-200-22-20022-220002-2000000000000
χ27222222-2-2000022-2-222-2-20000-2200002200200-22-2-2002-20-2200000000000000
χ28222222-2-2000022-2-222-2-20000-220000-2-200-200-2222002-202-200000000000000
χ294444444444-4-4-4-40000-4-4004-400000000000000000000000000000000000000
χ3044444444-4-444-4-40000-4-400-4400000000000000000000000000000000000000
χ31444444-4-40000-4-4000044000000004400000-400000000000000000000000000
χ32444444-4-40000-4-400004400000000-4-400000400000000000000000000000000
χ334444-4-40000004-400440000000-40000000000000000000000002-2002-2000000
χ344444-4-40000004-400440000000-4000000000000000000000000-2200-22000000
χ354444-4-40000004-400-4-4000000040000000000000000000000002i−2i00−2i2i000000
χ364444-4-40000004-400-4-400000004000000000000000000000000−2i2i002i−2i000000
χ374444-4-4000000-444400000000-40000000000000000000000000002-2002-20000
χ384444-4-4000000-444400000000-4000000000000000000000000000-2200-220000
χ394444-4-4000000-44-4-40000000040000000000000000000000000002i−2i00−2i2i0000
χ404444-4-4000000-44-4-4000000004000000000000000000000000000−2i2i002i−2i0000
χ41444-4-444-4004400000000000-40000002222-20-2002-22-20000000000000000000
χ42444-4-444-4004400000000000-4000000-2-2-2-220200-22-220000000000000000000
χ43444-4-444-400-4-400000000000400000022-2-2-202002-2-220000000000000000000
χ44444-4-444-400-4-4000000000004000000-2-22220-200-222-20000000000000000000
χ45444-4-44-4444000000000000-400000002222-20-200-22-220000000000000000000
χ46444-4-44-4444000000000000-40000000-2-2-2-2202002-22-20000000000000000000
χ47444-4-44-44-4-40000000000004000000022-2-2-20200-222-20000000000000000000
χ48444-4-44-44-4-400000000000040000000-2-22220-2002-2-220000000000000000000
χ49888-88-800000000000000440000-4-40000000000000000000000000000000000
χ50888-88-800000000000000-4-40000440000000000000000000000000000000000
χ5188-8000004-44-4004-44-44-40000004-40000000000000000000000000000000000
χ5288-8000004-44-400-44-444-4000000-440000000000000000000000000000000000
χ5388-8000004-4-44004-4-44-444-40000000000000000000000000000000000000000
χ5488-8000004-4-4400-444-4-44-440000000000000000000000000000000000000000
χ5588-800000-444-4004-4-44-44-440000000000000000000000000000000000000000
χ5688-800000-444-400-444-4-444-40000000000000000000000000000000000000000
χ5788-800000-44-44004-44-44-4000000-440000000000000000000000000000000000
χ5888-800000-44-4400-44-444-40000004-40000000000000000000000000000000000
χ5916-16000000000000000000000000004i−4i4-44i−4i0000000000000000000000000000
χ6016-16000000000000000000000000004i−4i-44−4i4i0000000000000000000000000000
χ6116-1600000000000000000000000000−4i4i4-4−4i4i0000000000000000000000000000
χ6216-1600000000000000000000000000−4i4i-444i−4i0000000000000000000000000000

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