Finite Group Databasebeta

← Group #72284909

Character table — Group #72284909

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11244488888816161616161616161616161616163232323232323232323232323264646464646464646464646464128128128128
order12222222224422444444444444224444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-11111-1-11-111-111-1-1-1-1111-1-1-1-111111111-1-1-1-1
χ4111111111111111111-1-11111-1-11-111-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111-1-111-111-1-11111-1-1-1-111-1-1
χ61111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111-1-111-111-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-111-11-1-1-111-1-11111-1-1-1111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-111-11-1-1-111-1-11111-1-1-111-1-1-1-1111111-1-1
χ9111111111111-1-1-1-11111111111-11-111111111-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−i
χ10111111111111-1-1-1-11111111111-11-111111111-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii
χ11111111111111-1-1-1-111-1-11111-1-1-1-1-11-111-1-1-1-1-1-1-11111ii−i−iii−i−i−ii−ii
χ12111111111111-1-1-1-111-1-11111-1-1-1-1-11-111-1-1-1-1-1-1-11111−i−iii−i−iiii−ii−i
χ13111111111111-1-1-1-1-1-111-1-1-1-1-1-11-11-111111-1-1-1-11-1-111ii−i−i−i−iiii−i−ii
χ14111111111111-1-1-1-1-1-111-1-1-1-1-1-11-11-111111-1-1-1-11-1-111−i−iiiii−i−i−iii−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-1111-1-1ii−i−i−i−iii−iii−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-1111-1-1−i−iiiii−i−ii−i−ii
χ1722222222222222222200-2-2-2-200-20-220-2-20000-2-220000000000000000
χ182222222222222222-2-200222200202-20-2-20000-2-2-20000000000000000
χ19222222222222-2-2-2-22200-2-2-2-20020220-2-2000022-20000000000000000
χ20222222222222-2-2-2-2-2-200222200-20-2-20-2-200002220000000000000000
χ21222222-2-222-2-22-22-20000000022020002-200-2-22-20002-2000000000000
χ22222222-2-222-2-22-22-200000000-2-20-20002-200222-2000-22000000000000
χ23222222-2-222-2-22-22-2002200000000002-22-2-200-2202-200000000000000
χ24222222-2-222-2-22-22-200-2-20000000000-2-222200-220-2200000000000000
χ25222222-2-222-2-2-22-220000000022020002-200-2-2-22000-22000000000000
χ26222222-2-222-2-2-22-2200000000-2-20-20002-20022-220002-2000000000000
χ27222222-2-222-2-2-22-22002200000000002-22-2-2002-20-2200000000000000
χ28222222-2-222-2-2-22-2200-2-20000000000-2-2222002-202-200000000000000
χ2944444444-4-4-4-400004400000000000-400000000000000000000000000
χ3044444444-4-4-4-40000-4-400000000000400000000000000000000000000
χ31444444-4-4-4-4440000000044-4-400000000000000000000000000000000
χ32444444-4-4-4-44400000000-4-44400000000000000000000000000000000
χ334444-4-4004-400040-400000000000000000000000000002-22-200000000
χ344444-4-4004-400040-40000000000000000000000000000-22-2200000000
χ354444-4-4004-4000-40400000000000000000000000000002i−2i−2i2i00000000
χ364444-4-4004-4000-4040000000000000000000000000000−2i2i2i−2i00000000
χ374444-4-400-440040-40000000000000000000000000000000002-22-20000
χ384444-4-400-440040-4000000000000000000000000000000000-22-220000
χ394444-4-400-4400-4040000000000000000000000000000000002i−2i−2i2i0000
χ404444-4-400-4400-404000000000000000000000000000000000−2i2i2i−2i0000
χ41444-4-4400004-400000022004-4220-200-2002-22-20000000000000000000
χ42444-4-4400004-40000002200-44-2-20200-2002-2-220000000000000000000
χ43444-4-4400004-4000000-2-2004-4-2-20200200-22-220000000000000000000
χ44444-4-4400004-4000000-2-200-44220-200200-222-20000000000000000000
χ45444-4-440000-44000000224-400220-200-200-22-220000000000000000000
χ46444-4-440000-4400000022-4400-2-20200-200-222-20000000000000000000
χ47444-4-440000-44000000-2-24-400-2-202002002-22-20000000000000000000
χ48444-4-440000-44000000-2-2-4400220-2002002-2-220000000000000000000
χ49888-88-80000000000000000000040-4000000000000000000000000000
χ50888-88-800000000000000000000-404000000000000000000000000000
χ511616-160008-8000000000000000000000000000000000000000000000000
χ521616-16000-88000000000000000000000000000000000000000000000000
χ5316-16000000000000004i−4i4i−4i00004-4000000000000000000000000000000
χ5416-16000000000000004i−4i−4i4i0000-44000000000000000000000000000000
χ5516-1600000000000000−4i4i4i−4i0000-44000000000000000000000000000000
χ5616-1600000000000000−4i4i−4i4i00004-4000000000000000000000000000000

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