Finite Group Databasebeta

← Group #136362

Character table — Group #136362

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order1222224444888888884444888888888888888888882244444444448888161616161616161644
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ911-1-11-1-11-1111-1-1-1-111-1-1111-11-111111111-1-1-1-1-1-1-1-11-11-1ii−i−iii−i−ii−i1-111-1-1ii−i−ii−i
χ1011-1-11-1-11-1111-1-1-1-111-1-1111-11-111111111-1-1-1-1-1-1-1-11-11-1−i−iii−i−iii−ii1-111-1-1−i−iii−ii
χ1111-1-11-1-11-1111-1-1-1-111-1-1111-11-111111111-1-1-1-1-1-1-1-1-11-11ii−i−i−i−iiii−i-11-1-111ii−i−i−ii
χ1211-1-11-1-11-1111-1-1-1-111-1-1111-11-111111111-1-1-1-1-1-1-1-1-11-11−i−iiiii−i−i−ii-11-1-111−i−iiii−i
χ1311-1-11-1-11-1111-1-1-1-111-1-1111-11-1-1-1-1-1-1-1-1-1111111111-11-1ii−i−iii−i−ii−i1-1-1-111−i−iii−ii
χ1411-1-11-1-11-1111-1-1-1-111-1-1111-11-1-1-1-1-1-1-1-1-1111111111-11-1−i−iii−i−iii−ii1-1-1-111ii−i−ii−i
χ1511-1-11-1-11-1111-1-1-1-111-1-1111-11-1-1-1-1-1-1-1-1-111111111-11-11ii−i−i−i−iiii−i-1111-1-1−i−iiii−i
χ1611-1-11-1-11-1111-1-1-1-111-1-1111-11-1-1-1-1-1-1-1-1-111111111-11-11−i−iiiii−i−i−ii-1111-1-1ii−i−i−ii
χ17222222222222-2-222-2-2-2-2-2-222-2-2000000000000000022220000000000-2-20000000000
χ18222222222222-2-222-2-2-2-2-2-222-2-20000000000000000-2-2-2-20000000000220000000000
χ192222222222-2-222-2-222-2-2-2-2-2-2220000000000000000000022220000-2-2000000000000
χ202222222222-2-222-2-222-2-2-2-2-2-22200000000000000000000-2-2-2-2000022000000000000
χ212222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000002-22-200000000000000
χ222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000-22-2200000000000000
χ232222-2-22-2-2200-2-200-2-200000022i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200002-22-2000000000000i2−i2i2−i200
χ242222-2-22-2-2200-2-200-2-200000022i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000-22-22000000000000−i2i2−i2i200
χ252222-2-22-2-2200-2-200-2-200000022−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200002-22-2000000000000−i2i2−i2i200
χ262222-2-22-2-2200-2-200-2-200000022−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000-22-22000000000000i2−i2i2−i200
χ272222-2-2-222-2-2-200-2-20000002200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i222-2-2000000000000i2−i2i2−i2000000
χ282222-2-2-222-2-2-200-2-20000002200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-2-222000000000000−i2i2−i2i2000000
χ292222-2-2-222-2-2-200-2-20000002200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i222-2-2000000000000−i2i2−i2i2000000
χ302222-2-2-222-2-2-200-2-20000002200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-2-222000000000000i2−i2i2−i2000000
χ3122-2-22-2-22-222222-2-2-2-222-2-22-2-2200000000000000002-22-20000000000-220000000000
χ3222-2-22-2-22-222222-2-2-2-222-2-22-2-220000000000000000-22-2200000000002-20000000000
χ3322-2-22-2-22-22-2-22222-2-2-2-222-22-220000000000000000000000002i−2i−2i2i00000000000000
χ3422-2-22-2-22-22-2-22222-2-2-2-222-22-22000000000000000000000000−2i2i2i−2i00000000000000
χ3522-2-22-2-22-22-2-2-2-2222222-2-2-222-2000000000000000000002i2i−2i−2i0000−2i2i000000000000
χ3622-2-22-2-22-22-2-2-2-2222222-2-2-222-200000000000000000000−2i−2i2i2i00002i−2i000000000000
χ3722-2-2-2222-2-2-2-200220000002-200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22-2-22000000000000i2−i2−i2i2000000
χ3822-2-2-2222-2-2-2-200220000002-200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-222-2000000000000−i2i2i2−i2000000
χ3922-2-2-2222-2-2-2-200220000002-200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22-2-22000000000000−i2i2i2−i2000000
χ4022-2-2-2222-2-2-2-200220000002-200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-222-2000000000000i2−i2−i2i2000000
χ4122-2-2-22-2-222002200-2-20000002-2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200002i−2i−2i2i000000000000−222−200
χ4222-2-2-22-2-222002200-2-20000002-2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000−2i2i2i−2i0000000000002−2−2200
χ4322-2-2-22-2-222002200-2-20000002-2−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200002i−2i−2i2i0000000000002−2−2200
χ4422-2-2-22-2-222002200-2-20000002-2−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000−2i2i2i−2i000000000000−222−200
χ45444444-4-4-4-4000000000000000022-2-2-2-22222-2-2-2-22200000000000000000000000000
χ46444444-4-4-4-40000000000000000-2-22222-2-2-2-22222-2-200000000000000000000000000
χ474444-4-44-4-4400440044000000-4-4000000000000000000000000000000000000000000
χ484444-4-4-444-4440044000000-4-400000000000000000000000000000000000000000000
χ4944-4-44-44-44-4000000000000000022-2-2-2-222-2-22222-2-200000000000000000000000000
χ5044-4-44-44-44-40000000000000000-2-22222-2-222-2-2-2-22200000000000000000000000000
χ5144-4-4-4444-4-44400-4-4000000-4400000000000000000000000000000000000000000000
χ5244-4-4-44-4-44400-4-40044000000-44000000000000000000000000000000000000000000
χ534-44-40000002i2−2i22i2−2i22i2−2i22i2−2i22-22-200002−2ζ+2i−ζ3−ζ−2i+ζ3ζ−2i−ζ3−ζ+2i+ζ32−22−2ζ+2i−ζ3−ζ−2i+ζ3ζ−2i−ζ3−ζ+2i+ζ32−200000000000000000000000000
χ544-44-40000002i2−2i22i2−2i22i2−2i22i2−2i22-22-20000−22−ζ−2i+ζ3ζ+2i−ζ3−ζ+2i+ζ3ζ−2i−ζ3−22−22−ζ−2i+ζ3ζ+2i−ζ3−ζ+2i+ζ3ζ−2i−ζ3−2200000000000000000000000000
χ554-44-40000002i2−2i2−2i22i22i2−2i2−2i22i2-22-220000ζ+2i−ζ3−ζ−2i+ζ3−22−22ζ−2i−ζ3−ζ+2i+ζ3ζ+2i−ζ3−ζ−2i+ζ3−22−22ζ−2i−ζ3−ζ+2i+ζ300000000000000000000000000
χ564-44-40000002i2−2i2−2i22i22i2−2i2−2i22i2-22-220000−ζ−2i+ζ3ζ+2i−ζ32−22−2−ζ+2i+ζ3ζ−2i−ζ3−ζ−2i+ζ3ζ+2i−ζ32−22−2−ζ+2i+ζ3ζ−2i−ζ300000000000000000000000000
χ574-44-4000000−2i22i22i2−2i2−2i22i22i2−2i2-22-220000ζ−2i−ζ3−ζ+2i+ζ3−22−22ζ+2i−ζ3−ζ−2i+ζ3ζ−2i−ζ3−ζ+2i+ζ3−22−22ζ+2i−ζ3−ζ−2i+ζ300000000000000000000000000
χ584-44-4000000−2i22i22i2−2i2−2i22i22i2−2i2-22-220000−ζ+2i+ζ3ζ−2i−ζ32−22−2−ζ−2i+ζ3ζ+2i−ζ3−ζ+2i+ζ3ζ−2i−ζ32−22−2−ζ−2i+ζ3ζ+2i−ζ300000000000000000000000000
χ594-44-4000000−2i22i2−2i22i2−2i22i2−2i22i22-22-200002−2ζ−2i−ζ3−ζ+2i+ζ3ζ+2i−ζ3−ζ−2i+ζ32−22−2ζ−2i−ζ3−ζ+2i+ζ3ζ+2i−ζ3−ζ−2i+ζ32−200000000000000000000000000
χ604-44-4000000−2i22i2−2i22i2−2i22i2−2i22i22-22-20000−22−ζ+2i+ζ3ζ−2i−ζ3−ζ−2i+ζ3ζ+2i−ζ3−22−22−ζ+2i+ζ3ζ−2i−ζ3−ζ−2i+ζ3ζ+2i−ζ3−2200000000000000000000000000
χ614-4-440000002i2−2i22i2−2i2−2i22i2−2i22i22-2-220000ζ+2i−ζ3−ζ−2i+ζ3−22−22ζ−2i−ζ3−ζ+2i+ζ3−ζ−2i+ζ3ζ+2i−ζ32−22−2−ζ+2i+ζ3ζ−2i−ζ300000000000000000000000000
χ624-4-440000002i2−2i22i2−2i2−2i22i2−2i22i22-2-220000−ζ−2i+ζ3ζ+2i−ζ32−22−2−ζ+2i+ζ3ζ−2i−ζ3ζ+2i−ζ3−ζ−2i+ζ3−22−22ζ−2i−ζ3−ζ+2i+ζ300000000000000000000000000
χ634-4-440000002i2−2i2−2i22i2−2i22i22i2−2i2-222-200002−2ζ+2i−ζ3−ζ−2i+ζ3ζ−2i−ζ3−ζ+2i+ζ32−2−22−ζ−2i+ζ3ζ+2i−ζ3−ζ+2i+ζ3ζ−2i−ζ3−2200000000000000000000000000
χ644-4-440000002i2−2i2−2i22i2−2i22i22i2−2i2-222-20000−22−ζ−2i+ζ3ζ+2i−ζ3−ζ+2i+ζ3ζ−2i−ζ3−222−2ζ+2i−ζ3−ζ−2i+ζ3ζ−2i−ζ3−ζ+2i+ζ32−200000000000000000000000000
χ654-4-44000000−2i22i22i2−2i22i2−2i2−2i22i2-222-200002−2ζ−2i−ζ3−ζ+2i+ζ3ζ+2i−ζ3−ζ−2i+ζ32−2−22−ζ+2i+ζ3ζ−2i−ζ3−ζ−2i+ζ3ζ+2i−ζ3−2200000000000000000000000000
χ664-4-44000000−2i22i22i2−2i22i2−2i2−2i22i2-222-20000−22−ζ+2i+ζ3ζ−2i−ζ3−ζ−2i+ζ3ζ+2i−ζ3−222−2ζ−2i−ζ3−ζ+2i+ζ3ζ+2i−ζ3−ζ−2i+ζ32−200000000000000000000000000
χ674-4-44000000−2i22i2−2i22i22i2−2i22i2−2i22-2-220000ζ−2i−ζ3−ζ+2i+ζ3−22−22ζ+2i−ζ3−ζ−2i+ζ3−ζ+2i+ζ3ζ−2i−ζ32−22−2−ζ−2i+ζ3ζ+2i−ζ300000000000000000000000000
χ684-4-44000000−2i22i2−2i22i22i2−2i22i2−2i22-2-220000−ζ+2i+ζ3ζ−2i−ζ32−22−2−ζ−2i+ζ3ζ+2i−ζ3ζ−2i−ζ3−ζ+2i+ζ3−22−22ζ+2i−ζ3−ζ−2i+ζ300000000000000000000000000

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