Finite Group Databasebeta

← Group #149961

Character table — Group #149961

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444888888888888888888888161616161616323232323232
order12222244444444444444224448888888888888888222444888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111
χ511111111111-1-1-1-1-1-11-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-111111-1-1ii−i−i
χ611111111111-1-1-1-1-1-11-1-1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-11-1-111−i−iii
χ711111111111-1-1-1-1-1-11-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-111111-1-1−i−iii
χ811111111111-1-1-1-1-1-11-1-1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-11-1-111ii−i−i
χ9111111-1-1-1-111111-1-11-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-11-1i−ii−i
χ10111111-1-1-1-111111-1-11-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11−ii−ii
χ11111111-1-1-1-111111-1-11-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-1−ii−ii
χ12111111-1-1-1-111111-1-11-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11i−ii−i
χ13111111-1-1-1-11-1-1-1-11111111-1111111-1-1-1-1-1-1-1-11111-11-1-11-1-111-1-11
χ14111111-1-1-1-11-1-1-1-11111111-1111111-1-1-1-1-1-1-1-11111-1-11-1-111-1-111-1
χ15111111-1-1-1-11-1-1-1-11111111-111-1-1-1-111111111-1-1-1-1-11-1-11-1-11-111-1
χ16111111-1-1-1-11-1-1-1-11111111-111-1-1-1-111111111-1-1-1-1-1-11-1-111-11-1-11
χ1722222222222222222222-2-22-2-20000000000000000-200-200000000
χ1822222222222-2-2-2-2-2-22-2-2-2-22220000000000000000200-200000000
χ19222222-2-2-2-222222-2-22-2-2-2-2-2220000000000000000-200200000000
χ20222222-2-2-2-22-2-2-2-222222-2-2-2-2-20000000000000000200200000000
χ212-22-22-20000200002i−2i-22i−2i2-202i−2i00002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000
χ222-22-22-20000200002i−2i-22i−2i2-202i−2i0000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000
χ232-22-22-20000200002i−2i-22i−2i-220−2i2i2ζ2ζ−2ζ−2ζ000000002ζ32ζ3−2ζ3−2ζ3000000000000
χ242-22-22-20000200002i−2i-22i−2i-220−2i2i−2ζ−2ζ2ζ2ζ00000000−2ζ3−2ζ32ζ32ζ3000000000000
χ252-22-22-2000020000−2i2i-2−2i2i2-20−2i2i00002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000
χ262-22-22-2000020000−2i2i-2−2i2i2-20−2i2i0000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000
χ272-22-22-2000020000−2i2i-2−2i2i-2202i−2i2ζ32ζ3−2ζ3−2ζ3000000002ζ2ζ−2ζ−2ζ000000000000
χ282-22-22-2000020000−2i2i-2−2i2i-2202i−2i−2ζ3−2ζ32ζ32ζ300000000−2ζ−2ζ2ζ2ζ000000000000
χ294444444444-4000000-40000-4000000000000000000000000000000
χ30444444-4-4-4-4-4000000-400004000000000000000000000000000000
χ314444-4-444-4-400000000000000000000000000000000220-2-2000000
χ324444-4-444-4-400000000000000000000000000000000-2-2022000000
χ334444-4-4-4-444000000000000000000000000000000002-20-22000000
χ344444-4-4-4-44400000000000000000000000000000000-2202-2000000
χ3544-4-400004i−4i022-2-22i−2i0−2i2i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ3644-4-400004i−4i022-2-22i−2i0−2i2i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ3744-4-400004i−4i0-2-222−2i2i02i−2i000001+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i000000000000
χ3844-4-400004i−4i0-2-222−2i2i02i−2i00000−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i000000000000
χ3944-4-40000−4i4i022-2-2−2i2i02i−2i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ4044-4-40000−4i4i022-2-2−2i2i02i−2i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ4144-4-40000−4i4i0-2-2222i−2i0−2i2i000001−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i000000000000
χ4244-4-40000−4i4i0-2-2222i−2i0−2i2i00000−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i000000000000
χ434-44-44-40000-44-44-400400000000000000000000000000000000000
χ444-44-44-40000-4-44-4400400000000000000000000000000000000000
χ454-4-44004-40002-2-22220-2-200000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ464-4-44004-40002-2-22220-2-200000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ474-4-44004-4000-222-2-2-2022000002−2−222−2−22−222−2−222−2000000000000
χ484-4-44004-4000-222-2-2-202200000−222−2−222−22−2−222−2−22000000000000
χ494-4-4400-440002-2-22-2-2022000002−2−22−222−22−2−22−222−2000000000000
χ504-4-4400-440002-2-22-2-202200000−222−22−2−22−222−22−2−22000000000000
χ514-4-4400-44000-222-2220-2-200000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ524-4-4400-44000-222-2220-2-200000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ538-88-8-8800000000000000000000000000000000000000000000000

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