Finite Group Databasebeta

← Group #336291

Character table — Group #336291

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888244444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11
χ3111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-11-1-1-111-1-1-1-1-1-111-1
χ4111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111111-1-1-11111-1-111-1-1-1
χ51111111111111111111111-1-111111111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1
χ71111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-11111-111-1-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-11111-1-1-1-1-1111-1-1
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-11111-111
χ12111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-11111-1-11-11
χ13111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-11-1-1-1-1111-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1111-1-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-111-111111-1-11-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-111-11-1-11111-11-1
χ172222222222-2-2-222-2-2-222222200000000-2-20000000000-2000-22000000000
χ182222222222-2-2-222-2-2-22222-2-200000000-2-2000000000020002-2000000000
χ192222222222-2-2-222-2-2-2-2-2-2-222000000002200000000002000-2-2000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2-2-200000000220000000000-200022000000000
χ2122222222-2-2222-2-22-2-20000002222-2-222000000-2-200000-20000000000000
χ2222222222-2-2222-2-22-2-200000022-2-222-2-20000002200000-20000000000000
χ2322222222-2-2222-2-22-2-2000000-2-222-2-2-2-2000000220000020000000000000
χ2422222222-2-2222-2-22-2-2000000-2-2-2-22222000000-2-20000020000000000000
χ252-22-2-2-22222-22-2-2-22-2200000000000000002i2i−2i−2i000000002i−2i0000002-2000
χ262-22-2-2-22222-22-2-2-22-2200000000000000002i2i−2i−2i00000000−2i2i000000-22000
χ272-22-2-2-22222-22-2-2-22-220000000000000000−2i−2i2i2i000000002i−2i000000-22000
χ282-22-2-2-22222-22-2-2-22-220000000000000000−2i−2i2i2i00000000−2i2i0000002-2000
χ292-2-222-22-20022-200-20022−2−2002i−2i002-2002−22−22−22i−2ii2i2−i2−i200000000i2−i200000
χ302-2-222-22-20022-200-20022−2−2002i−2i00-22002−2−22−22−2i2i−i2−i2i2i200000000i2−i200000
χ312-2-222-22-20022-200-20022−2−200−2i2i002-2002−22−22−2−2i2i−i2−i2i2i200000000−i2i200000
χ322-2-222-22-20022-200-20022−2−200−2i2i00-22002−2−22−222i−2ii2i2−i2−i200000000−i2i200000
χ332-2-222-22-20022-200-200−2−222002i−2i002-200−22−22−222i−2i−i2−i2i2i200000000−i2i200000
χ342-2-222-22-20022-200-200−2−222002i−2i00-2200−222−22−2−2i2ii2i2−i2−i200000000−i2i200000
χ352-2-222-22-20022-200-200−2−22200−2i2i002-200−22−22−22−2i2ii2i2−i2−i200000000i2−i200000
χ362-2-222-22-20022-200-200−2−22200−2i2i00-2200−222−22−22i−2i−i2−i2i2i200000000i2−i200000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ384444-4-4-4-44-40004-40000000000000000000000000000000000022−220000000
χ394444-4-4-4-44-40004-400000000000000000000000000000000000−22220000000
χ404444-4-4-4-4-44000-4400000004-400000000000000000000000000000000000
χ414444-4-4-4-4-44000-440000000-4400000000000000000000000000000000000
χ4244-4-44-4-4400000000002i2−2i22i2−2i2000000002i2−2i2000000002-22-2000000000000000
χ4344-4-44-4-4400000000002i2−2i22i2−2i200000000−2i22i200000000-22-22000000000000000
χ4444-4-44-4-440000000000−2i22i2−2i22i2000000002i2−2i200000000-22-22000000000000000
χ4544-4-44-4-440000000000−2i22i2−2i22i200000000−2i22i2000000002-22-2000000000000000
χ4644-4-4-444-4004-4-400400000000004i−4i0000000000000000000000000000000
χ4744-4-4-444-4004-4-40040000000000−4i4i0000000000000000000000000000000
χ4844-4-4-444-400-44400-40000000000000000002i2−2i2−2i22i2000000000000000000000
χ4944-4-4-444-400-44400-4000000000000000000−2i22i22i2−2i2000000000000000000000
χ504-44-444-4-44-4000-440004i−4i−4i4i0000000000000000000000000000000000000
χ514-44-444-4-44-4000-44000−4i4i4i−4i0000000000000000000000000000000000000
χ524-44-444-4-4-440004-400000000000000000000000002i2−2i2−2i22i2000000000000000
χ534-44-444-4-4-440004-40000000000000000000000000−2i22i22i2−2i2000000000000000
χ544-44-4-4-444444-44-4-4-44-400000000000000000000000000000000000000000
χ554-44-4-4-444-4-44-4444-4-4400000000000000000000000000000000000000000
χ564-44-4-4-444-4-4-44-44444-400000000000000000000000000000000000000000
χ574-4-444-44-400-4-44004002222−22−220000000000−22220000000000000000000000000
χ584-4-444-44-400-4-4400400−22−222222000000000022−220000000000000000000000000
χ598-8-88-88-88000000000000000000000000000000000000000000000000000

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