Finite Group Databasebeta

← Group #307697

Character table — Group #307697

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1111-111-1-111-1-1-1-1-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-11111-1-11111-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1-111-1-1-1-1-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11-111-1-1-1-111-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-111-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-11-1-11111-1-1-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1111-1-111-1-111-1-1-11
χ172222222222-2-222-2-2-2-2000000002222-2-2-2-2000000000022-2-2002-20000000000000000
χ182222222222-2-222-2-2-2-2000000002222-2-2-2-20000000000-2-22200-220000000000000000
χ192222222222-2-222-2-2-2-200000000-2-2-2-22222000000000022-2-200-220000000000000000
χ202222222222-2-222-2-2-2-200000000-2-2-2-222220000000000-2-222002-20000000000000000
χ2122222222-2-222-2-222-2-22222-2-2-2-200000000000000002200002200-2-200000000000000
χ2222222222-2-222-2-222-2-22222-2-2-2-20000000000000000-2-20000-2-2002200000000000000
χ2322222222-2-222-2-222-2-2-2-2-2-222220000000000000000220000-2-200-2200000000000000
χ2422222222-2-222-2-222-2-2-2-2-2-222220000000000000000-2-2000022002-200000000000000
χ25222-2-2-2-22002-2002-20022-2-20000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i22-200002-200000000i2−i2i2−i2000000
χ26222-2-2-2-22002-2002-20022-2-20000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2-220000-2200000000−i2i2−i2i2000000
χ27222-2-2-2-22002-2002-20022-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22-200002-200000000−i2i2−i2i2000000
χ28222-2-2-2-22002-2002-20022-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2-220000-2200000000i2−i2i2−i2000000
χ29222-2-2-2-22002-2002-200-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i22-20000-2200000000i2−i2−i2i2000000
χ30222-2-2-2-22002-2002-200-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2-2200002-200000000−i2i2i2−i2000000
χ31222-2-2-2-22002-2002-200-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i22-20000-2200000000−i2i2i2−i2000000
χ32222-2-2-2-22002-2002-200-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2-2200002-200000000i2−i2−i2i2000000
χ332-2-2-222-222222-2-2-2-2-222-22-222-2-20000000000000000002i−2i2i−2i000000000000002i−2i0000
χ342-2-2-222-222222-2-2-2-2-222-22-222-2-2000000000000000000−2i2i−2i2i00000000000000−2i2i0000
χ352-2-2-222-222222-2-2-2-2-22-22-22-2-2220000000000000000002i−2i2i−2i00000000000000−2i2i0000
χ362-2-2-222-222222-2-2-2-2-22-22-22-2-222000000000000000000−2i2i−2i2i000000000000002i−2i0000
χ372-2-2-222-2222-2-2-2-2222-200000000000000002i2i−2i−2i2i2i−2i−2i002i−2i−2i2i00000000000000002-200
χ382-2-2-222-2222-2-2-2-2222-200000000000000002i2i−2i−2i2i2i−2i−2i00−2i2i2i−2i0000000000000000-2200
χ392-2-2-222-2222-2-2-2-2222-20000000000000000−2i−2i2i2i−2i−2i2i2i002i−2i−2i2i0000000000000000-2200
χ402-2-2-222-2222-2-2-2-2222-20000000000000000−2i−2i2i2i−2i−2i2i2i00−2i2i2i−2i00000000000000002-200
χ412-2-2-222-22-2-22222-2-22-22-22-2-2-22200000000000000000000000000002i−2i2i−2i0000000000
χ422-2-2-222-22-2-22222-2-22-22-22-2-2-2220000000000000000000000000000−2i2i−2i2i0000000000
χ432-2-2-222-22-2-22222-2-22-2-22-2222-2-200000000000000000000000000002i−2i−2i2i0000000000
χ442-2-2-222-22-2-22222-2-22-2-22-2222-2-20000000000000000000000000000−2i2i2i−2i0000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-4-4400-4400-4400000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ47444-4-4-4-4400-4400-440000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ4844-444-4-4-40000000000000022−2222−22000022−2222−222-22-22-22-200000000000000000000000000
χ4944-444-4-4-40000000000000022−2222−220000−2222−2222-22-22-22-2200000000000000000000000000
χ5044-444-4-4-400000000000000−2222−2222000022−2222−22-22-22-22-2200000000000000000000000000
χ5144-444-4-4-400000000000000−2222−22220000−2222−22222-22-22-22-200000000000000000000000000
χ5244-4-4-444-44-4004-400000000000000004i−4i−4i4i0000000000000000000000000000000000
χ5344-4-4-444-44-4004-40000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ5444-4-4-444-4-4400-44000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ5544-4-4-444-4-4400-4400000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ564-444-44-4-44-400-440000000000004-44-400000000000000000000000000000000000000
χ574-444-44-4-44-400-44000000000000-44-4400000000000000000000000000000000000000
χ584-444-44-4-4-44004-40000000000000000000022−22−2222−222222−2200000000000000000000000000
χ594-444-44-4-4-44004-400000000000000000000−222222−2222−22−222200000000000000000000000000
χ604-44-44-44-40000000000000022−22−22222i2−2i2−2i22i200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ614-44-44-44-40000000000000022−22−2222−2i22i22i2−2i20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ624-44-44-44-400000000000000−222222−222i2−2i2−2i22i20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ634-44-44-44-400000000000000−222222−22−2i22i22i2−2i200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ644-4-44-4-444004-400-44004-4-440000000000000000000000000000000000000000000000
χ654-4-44-4-444004-400-4400-444-40000000000000000000000000000000000000000000000
χ664-4-44-4-44400-44004-40000000000000000002222−22−22−22−22222200000000000000000000000000
χ674-4-44-4-44400-44004-4000000000000000000−22−2222222222−22−2200000000000000000000000000
χ684-4-4-444-44-4-4-4-44444-4400000000000000000000000000000000000000000000000000

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