Finite Group Databasebeta

← Group #344191

Character table — Group #344191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-11-1-1-1-1-111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1111-1-1-11-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1111111-1-1-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1111-1-11111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-1-1-1-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-111-1-1-11111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-11-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1111111-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-111-1111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1111111-111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111
χ17222222222-2-2222-2-2-2-22222-2-2-2-20000000000000000002200-2-22000-20000000000000
χ18222222222-2-2222-2-2-2-22222-2-2-2-2000000000000000000-2-20022-200020000000000000
χ19222222222-2-2222-2-2-2-2-2-2-2-22222000000000000000000220022-2000-20000000000000
χ20222222222-2-2222-2-2-2-2-2-2-2-22222000000000000000000-2-200-2-2200020000000000000
χ2122222222-222-2-2-222-2-2000000002222-2-2-2-200000000220022000-200000-20000000000
χ2222222222-222-2-2-222-2-2000000002222-2-2-2-200000000-2-200-2-200020000020000000000
χ2322222222-222-2-2-222-2-200000000-2-2-2-22222000000002200-2-2000200000-20000000000
χ2422222222-222-2-2-222-2-200000000-2-2-2-2222200000000-2-20022000-20000020000000000
χ2522-2-2-2-22202-20002-200i2i2−i2−i2i2i2−i2−i22i2i−2i−2i00002222−2−2−2−22i−2i002-200000000002−2i2−i2000000
χ2622-2-2-2-22202-20002-200i2i2−i2−i2i2i2−i2−i22i2i−2i−2i00002222−2−2−2−2−2i2i00-220000000000−22−i2i2000000
χ2722-2-2-2-22202-20002-200i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i0000−2−2−2−222222i−2i00-2200000000002−2−i2i2000000
χ2822-2-2-2-22202-20002-200i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i0000−2−2−2−22222−2i2i002-20000000000−22i2−i2000000
χ2922-2-2-2-22202-20002-200−i2−i2i2i2−i2−i2i2i22i2i−2i−2i0000−2−2−2−222222i−2i002-20000000000−22−i2i2000000
χ3022-2-2-2-22202-20002-200−i2−i2i2i2−i2−i2i2i22i2i−2i−2i0000−2−2−2−22222−2i2i00-2200000000002−2i2−i2000000
χ3122-2-2-2-22202-20002-200−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i00002222−2−2−2−22i−2i00-220000000000−22i2−i2000000
χ3222-2-2-2-22202-20002-200−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i00002222−2−2−2−2−2i2i002-200000000002−2−i2i2000000
χ332-22-22-22-22-2-2-22-2222-200000000000000002i2i−2i−2i2i2i−2i−2i00000000002-202i−2i00000000000
χ342-22-22-22-22-2-2-22-2222-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000-220−2i2i00000000000
χ352-22-22-22-22-2-2-22-2222-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000002-20−2i2i00000000000
χ362-22-22-22-22-2-2-22-2222-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000-2202i−2i00000000000
χ372-2-222-2-22200-2-22000000002-22-2i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2002-2002-2000000000000i2−i2i2−i200
χ382-2-222-2-22200-2-22000000002-22-2i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i200-2200-22000000000000−i2i2−i2i200
χ392-2-222-2-22200-2-22000000002-22-2−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i2002-2002-2000000000000−i2i2−i2i200
χ402-2-222-2-22200-2-22000000002-22-2−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i200-2200-22000000000000i2−i2i2−i200
χ412-2-222-2-22200-2-2200000000-22-22i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i2002-200-22000000000000i2−i2−i2i200
χ422-2-222-2-22200-2-2200000000-22-22i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i200-22002-2000000000000−i2i2i2−i200
χ432-2-222-2-22200-2-2200000000-22-22−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i2002-200-22000000000000−i2i2i2−i200
χ442-2-222-2-22200-2-2200000000-22-22−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i200-22002-2000000000000i2−i2−i2i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-4000000000022−2222−220000000022−2222−222-2-22-222-200000000000000000000000000
χ474444-4-4-4-4000000000022−2222−2200000000−2222−2222-222-22-2-2200000000000000000000000000
χ484444-4-4-4-40000000000−2222−22220000000022−2222−22-222-22-2-2200000000000000000000000000
χ494444-4-4-4-40000000000−2222−222200000000−2222−22222-2-22-222-200000000000000000000000000
χ5044-4-444-4-44004-4-40000000000000000000022−22−222222−22−222200000000000000000000000000
χ5144-4-444-4-44004-4-400000000000000000000−222222−22−222222−2200000000000000000000000000
χ5244-4-444-4-4-400-44400004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5344-4-444-4-4-400-4440000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ5444-4-4-4-4440-44000-44002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ5544-4-4-4-4440-44000-4400−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ564-44-44-44-4444-44-4-4-4-4400000000000000000000000000000000000000000000000000
χ574-44-44-44-4-4444-44-4-44-400000000000000000000000000000000000000000000000000
χ584-44-44-44-4-4-4-44-4444-4400000000000000000000000000000000000000000000000000
χ594-44-4-44-44000000000000002i2−2i2−2i22i222−22−22220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ604-44-4-44-44000000000000002i2−2i2−2i22i2−222222−2200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ614-44-4-44-4400000000000000−2i22i22i2−2i222−22−222200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ624-44-4-44-4400000000000000−2i22i22i2−2i2−222222−220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ634-4-444-4-44-40044-40000000000002i2−2i22i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ644-4-444-4-44-40044-4000000000000−2i22i2−2i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ654-4-44-444-404-4000-44000000000000004i−4i−4i4i0000000000000000000000000000000000
χ664-4-44-444-404-4000-4400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ674-4-44-444-40-440004-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ684-4-44-444-40-440004-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000

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