Finite Group Databasebeta

← Group #149965

Character table — Group #149965

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444888888888888888888888161616161616323232323232
order12222244444444444444444448888888888888888224444888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111-1-1-1-1-1-11-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i111-111-1-1ii−i−i
χ611111111111-1-1-1-1-1-11-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-11-1-1-111−i−iii
χ711111111111-1-1-1-1-1-11-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii111-111-1-1−i−iii
χ811111111111-1-1-1-1-1-11-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-11-1-1-111ii−i−i
χ9111111-1-1-1-111111-1-11-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-111-11-1i−ii−i
χ10111111-1-1-1-111111-1-11-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii
χ11111111-1-1-1-111111-1-11-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-111-11-1−ii−ii
χ12111111-1-1-1-111111-1-11-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−i
χ13111111-1-1-1-11-1-1-1-111111-111111111-1-1-1-1-1-1-1-111111-1-1-11-1-111-1-11
χ14111111-1-1-1-11-1-1-1-111111-111111111-1-1-1-1-1-1-1-11111-11-1-1-111-1-111-1
χ15111111-1-1-1-11-1-1-1-111111-11111-1-1-1-111111111-1-1-1-11-1-1-11-1-11-111-1
χ16111111-1-1-1-11-1-1-1-111111-11111-1-1-1-111111111-1-1-1-1-11-1-1-111-11-1-11
χ17222222222222222222222-2-2-2-2000000000000000000-2-200000000
χ1822222222222-2-2-2-2-2-22-2-22-2-222000000000000000000-2200000000
χ19222222-2-2-2-222222-2-22-2-2-2-2-2220000000000000000002-200000000
χ20222222-2-2-2-22-2-2-2-222222-2-2-2-2-20000000000000000002200000000
χ212-2-222-20000200002i−2i-22i−2i02-22i−2i00002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000
χ222-2-222-20000200002i−2i-22i−2i02-22i−2i0000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000
χ232-2-222-20000200002i−2i-22i−2i0-22−2i2i2ζ2ζ−2ζ−2ζ000000002ζ32ζ3−2ζ3−2ζ3000000000000
χ242-2-222-20000200002i−2i-22i−2i0-22−2i2i−2ζ−2ζ2ζ2ζ00000000−2ζ3−2ζ32ζ32ζ3000000000000
χ252-2-222-2000020000−2i2i-2−2i2i02-2−2i2i00002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000
χ262-2-222-2000020000−2i2i-2−2i2i02-2−2i2i0000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000
χ272-2-222-2000020000−2i2i-2−2i2i0-222i−2i2ζ32ζ3−2ζ3−2ζ3000000002ζ2ζ−2ζ−2ζ000000000000
χ282-2-222-2000020000−2i2i-2−2i2i0-222i−2i−2ζ3−2ζ32ζ32ζ300000000−2ζ−2ζ2ζ2ζ000000000000
χ294444444444-4000000-400-400000000000000000000000000000000
χ30444444-4-4-4-4-4000000-400400000000000000000000000000000000
χ314444-4-444-4-400000000000000000000000000000002200-2-2000000
χ324444-4-444-4-40000000000000000000000000000000-2-20022000000
χ334444-4-4-4-44400000000000000000000000000000002-200-22000000
χ344444-4-4-4-4440000000000000000000000000000000-22002-2000000
χ3544-4-4004-400022-2-2220-2-2000002−22−22−22−22−22−22−22−2000000000000
χ3644-4-4004-400022-2-2220-2-200000−22−22−22−22−22−22−22−22000000000000
χ3744-4-4004-4000-2-222-2-202200000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3844-4-4004-4000-2-222-2-202200000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3944-4-400-4400022-2-2-2-202200000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4044-4-400-4400022-2-2-2-202200000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4144-4-400-44000-2-222220-2-2000002−22−2−22−22−22−222−22−2000000000000
χ4244-4-400-44000-2-222220-2-200000−22−222−22−22−22−2−22−22000000000000
χ434-44-400004i−4i02-22-22i−2i0−2i2i000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ444-44-400004i−4i02-22-22i−2i0−2i2i00000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ454-44-400004i−4i0-22-22−2i2i02i−2i000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ464-44-400004i−4i0-22-22−2i2i02i−2i00000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ474-44-40000−4i4i02-22-2−2i2i02i−2i000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ484-44-40000−4i4i02-22-2−2i2i02i−2i00000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ494-44-40000−4i4i0-22-222i−2i0−2i2i000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ504-44-40000−4i4i0-22-222i−2i0−2i2i00000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ514-4-444-40000-44-4-4400400000000000000000000000000000000000
χ524-4-444-40000-4-444-400400000000000000000000000000000000000
χ538-8-88-8800000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.