Finite Group Databasebeta

← Group #342149

Character table — Group #342149

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444244444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1111-1-11-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11-1-11111-1-1-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-111-1-111-1-11111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11111-1-1-1-111-1-1-1-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-111-1-11111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-111111-1-1-1-1-1-1-1-1111-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111111-1-1-111-1-1-1-111-1-1-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1111111-1-111-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1111111-1-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11-1-1-1-1-1-11111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111111111-1-111-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1-1-1-1-111-1-1-1-11111
χ17222222222-2-22-2-222-2-2000000002222-2-2-2-2000000002200-2-2000-22000000000000000
χ18222222222-2-22-2-222-2-2000000002222-2-2-2-200000000-2-200220002-2000000000000000
χ19222222222-2-22-2-222-2-200000000-2-2-2-2222200000000220022000-2-2000000000000000
χ20222222222-2-22-2-222-2-200000000-2-2-2-2222200000000-2-200-2-200022000000000000000
χ2122222222-222-222-2-2-2-22222-2-2-2-2000000000000000000220022-200-200000000000000
χ2222222222-222-222-2-2-2-22222-2-2-2-2000000000000000000-2-200-2-2200200000000000000
χ2322222222-222-222-2-2-2-2-2-2-2-222220000000000000000002200-2-2200-200000000000000
χ2422222222-222-222-2-2-2-2-2-2-2-22222000000000000000000-2-20022-200200000000000000
χ2522-22-22-2-202-202-200002i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i22222−2−2−2−2002-2002i−2i0000000000002−2i2−i200
χ2622-22-22-2-202-202-200002i2i−2i−2i0000i2i2−i2−i2i2i2−i2−i22222−2−2−2−200-2200−2i2i000000000000−22−i2i200
χ2722-22-22-2-202-202-200002i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i2−2−2−2−22222002-2002i−2i000000000000−22−i2i200
χ2822-22-22-2-202-202-200002i2i−2i−2i0000−i2−i2i2i2−i2−i2i2i2−2−2−2−2222200-2200−2i2i0000000000002−2i2−i200
χ2922-22-22-2-202-202-20000−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i2−2−2−2−22222002-200−2i2i000000000000−22i2−i200
χ3022-22-22-2-202-202-20000−2i−2i2i2i0000i2i2−i2−i2i2i2−i2−i2−2−2−2−2222200-22002i−2i0000000000002−2−i2i200
χ3122-22-22-2-202-202-20000−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i22222−2−2−2−2002-200−2i2i0000000000002−2−i2i200
χ3222-22-22-2-202-202-20000−2i−2i2i2i0000−i2−i2i2i2−i2−i2i2i22222−2−2−2−200-22002i−2i000000000000−22i2−i200
χ332-2-222-2-22222-2-2-22-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000002i−2i2-20000000000
χ342-2-222-2-22222-2-2-22-22-200000000000000002i2i−2i−2i2i2i−2i−2i000000000000−2i2i-220000000000
χ352-2-222-2-22222-2-2-22-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000002i−2i-220000000000
χ362-2-222-2-22222-2-2-22-22-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000000−2i2i2-20000000000
χ372-2-2-2-2222-200-20022002−22−222−2−200002-22-22−22−22−22−22-2002-200000000002−22−2000000
χ382-2-2-2-2222-200-20022002−22−222−2−200002-22-22−22−22−22−2-2200-220000000000−22−22000000
χ392-2-2-2-2222-200-20022002−22−222−2−20000-22-22−22−22−22−222-200-2200000000002−2−22000000
χ402-2-2-2-2222-200-20022002−22−222−2−20000-22-22−22−22−22−22-22002-20000000000−222−2000000
χ412-2-2-2-2222-200-2002200−22−22−2−22200002-22-2−22−22−22−222-2002-20000000000−22−22000000
χ422-2-2-2-2222-200-2002200−22−22−2−22200002-22-2−22−22−22−22-2200-2200000000002−22−2000000
χ432-2-2-2-2222-200-2002200−22−22−2−2220000-22-222−22−22−22−22-200-220000000000−222−2000000
χ442-2-2-2-2222-200-2002200−22−22−2−2220000-22-222−22−22−22−2-22002-200000000002−2−22000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-4-44400-400-4400000000004i−4i4i−4i00000000000000000000000000000000000000
χ47444-4-4-4-44400-400-440000000000−4i4i−4i4i00000000000000000000000000000000000000
χ48444-4-4-4-44-4004004-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ49444-4-4-4-44-4004004-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ5044-44-44-4-40-440-440000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ5144-44-44-4-40-440-44000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ5244-4-44-44-4000000000000002i2−2i22i2−2i222−22−222200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5344-4-44-44-4000000000000002i2−2i22i2−2i2−222222−220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5444-4-44-44-400000000000000−2i22i2−2i22i222−22−22220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5544-4-44-44-400000000000000−2i22i2−2i22i2−222222−2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ564-444-4-44-404-40-44000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ574-444-4-44-404-40-4400000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ584-444-4-44-40-4404-4000000004i−4i−4i4i000000000000000000000000000000000000000000
χ594-444-4-44-40-4404-400000000−4i4i4i−4i000000000000000000000000000000000000000000
χ604-44-444-4-400000000002i2−2i2−2i22i2000000002i2−2i2−2i22i22-22-2-22-2200000000000000000000000000
χ614-44-444-4-400000000002i2−2i2−2i22i200000000−2i22i22i2−2i2-22-222-22-200000000000000000000000000
χ624-44-444-4-40000000000−2i22i22i2−2i2000000002i2−2i2−2i22i2-22-222-22-200000000000000000000000000
χ634-44-444-4-40000000000−2i22i22i2−2i200000000−2i22i22i2−2i22-22-2-22-2200000000000000000000000000
χ644-4-444-4-444-4-4-4444-4-4400000000000000000000000000000000000000000000000000
χ654-4-444-4-44-4444-4-4-44-4400000000000000000000000000000000000000000000000000
χ664-4-444-4-44-4-4-4444-444-400000000000000000000000000000000000000000000000000
χ674-4-4-4-4444400400-4-40022−2222−22−22−222222000000000000000000000000000000000000000000
χ684-4-4-4-4444400400-4-400−2222−22222222−22−22000000000000000000000000000000000000000000

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