Finite Group Databasebeta

← Group #32702

Character table — Group #32702

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size1111222222444444444444888888888888161616161616
order1244222444444488888888224488888888448888
χ11111111111111111111111111111111111111111
χ211111111111111111111111-11-111-1-1-1-1-1-11-11-1-1-1
χ31111111111111111111111-11-11-1-111-1-1-1-1-11-11-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ611111111111111-1-1-1-1-1-1-1-11-11-1-1-1111111-111-1-1-1
χ711111111111111-1-1-1-1-1-1-1-1-11-1111-1-111111-1-11-1-1
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ91111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-1-11-1
χ101111111111-1-1-1-11111-1-1-1-11-11-11111-1-111-1-1-11-11
χ111111111111-1-1-1-11111-1-1-1-1-11-11-1-1-1-1-1-111111-1-11
χ121111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11-1111-1
χ131111111111-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-1-11-1
χ141111111111-1-1-1-1-1-1-1-111111-11-1-1-1-1-111-1-111-11-11
χ151111111111-1-1-1-1-1-1-1-11111-11-11111111-1-1-1-11-1-11
χ161111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-11111-1
χ1722-2-22-2-222-2000000002i2i−2i−2i020-2002i−2i0000000000
χ1822-2-22-2-222-2000000002i2i−2i−2i0-20200−2i2i0000000000
χ1922-2-22-2-222-200000000−2i−2i2i2i020-200−2i2i0000000000
χ2022-2-22-2-222-200000000−2i−2i2i2i0-202002i−2i0000000000
χ2122-2-2-22-22-2200002i2i−2i−2i000020-202i−2i000000000000
χ2222-2-2-22-22-2200002i2i−2i−2i0000-2020−2i2i000000000000
χ2322-2-2-22-22-220000−2i−2i2i2i000020-20−2i2i000000000000
χ2422-2-2-22-22-220000−2i−2i2i2i0000-20202i−2i000000000000
χ2522-2-2-2-22-22222-2-200000000000000002i−2i2i−2i000000
χ2622-2-2-2-22-22222-2-20000000000000000−2i2i−2i2i000000
χ2722-2-2-2-22-222-2-22200000000000000002i−2i−2i2i000000
χ2822-2-2-2-22-222-2-2220000000000000000−2i2i2i−2i000000
χ2944444-4-4-4-44000000000000000000000000000000
χ304444-44-4-44-4000000000000000000000000000000
χ314444-4-444-4-4000000000000000000000000000000
χ3244-4-4444-4-4-4000000000000000000000000000000
χ334-44i−4i0000002-22i−2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000
χ344-44i−4i0000002-22i−2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000
χ354-44i−4i000000-22−2i2i2ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000
χ364-44i−4i000000-22−2i2i−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000
χ374-4−4i4i0000002-2−2i2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000
χ384-4−4i4i0000002-2−2i2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000
χ394-4−4i4i000000-222i−2i2ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000
χ404-4−4i4i000000-222i−2i−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000

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