Finite Group Databasebeta

← Group #337155

Character table — Group #337155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882222444488888888888888444444888888244
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111-11-1-1-1-1-1-1-1-11-11
χ3111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-1
χ51111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-11-1
χ61111111111111111111111-1-111-1-1-1-1111111-1-1-1-1111111-11-1-11111-1-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-11
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11111-111
χ11111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-111111-1-1111-1-1
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111-11-111-1-111-1-11-1-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-111-1-11111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1111-1-111-1-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1111-1-11111-1-11
χ172222222222-22-2-2-22-2-2222200220000-2-2000000000000-2-20200000000000
χ182222222222-22-2-2-22-2-2222200-2-20000-2-2000000000000220-200000000000
χ192222222222-22-2-2-22-2-2-2-2-2-20022000022000000000000-220-200000000000
χ202222222222-22-2-2-22-2-2-2-2-2-200-2-20000220000000000002-20200000000000
χ2122222222-2-22-2222-2-2-200002200-2-2220022-2-20000000000-2000000000000
χ2222222222-2-22-2222-2-2-200002200-2-2-2-200-2-22200000000002000000000000
χ2322222222-2-22-2222-2-2-20000-2-200222200-2-2220000000000-2000000000000
χ2422222222-2-22-2222-2-2-20000-2-20022-2-20022-2-200000000002000000000000
χ252222-2-2-2-2-2-2-2222-222-200000000000000000022-2-2000000002i−2i002i−2i00000
χ262222-2-2-2-2-2-2-2222-222-200000000000000000022-2-200000000−2i2i00−2i2i00000
χ272222-2-2-2-2-2-2-2222-222-2000000000000000000-2-222000000002i−2i00−2i2i00000
χ282222-2-2-2-2-2-2-2222-222-2000000000000000000-2-22200000000−2i2i002i−2i00000
χ292-22-22-22-200202-2-200022−2−22-200002i−2i2−22i−2i002−22−2i2i2−i2−i20000000000i2−i2000
χ302-22-22-22-200202-2-200022−2−22-20000−2i2i2−2−2i2i002−22−2−i2−i2i2i20000000000−i2i2000
χ312-22-22-22-200202-2-200022−2−2-2200002i−2i2−2−2i2i00−22−22−i2−i2i2i20000000000i2−i2000
χ322-22-22-22-200202-2-200022−2−2-220000−2i2i2−22i−2i00−22−22i2i2−i2−i20000000000−i2i2000
χ332-22-22-22-200202-2-2000−2−2222-200002i−2i−222i−2i00−22−22−i2−i2i2i20000000000−i2i2000
χ342-22-22-22-200202-2-2000−2−2222-20000−2i2i−22−2i2i00−22−22i2i2−i2−i20000000000i2−i2000
χ352-22-22-22-200202-2-2000−2−222-2200002i−2i−22−2i2i002−22−2i2i2−i2−i20000000000−i2i2000
χ362-22-22-22-200202-2-2000−2−222-220000−2i2i−222i−2i002−22−2−i2−i2i2i20000000000i2−i2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ384444-4-4-4-4444-4-4-44-44-400000000000000000000000000000000000000000
χ394444-4-4-4-444-4-444-4-4-4400000000000000000000000000000000000000000
χ404444-4-4-4-4-4-444-4-444-4400000000000000000000000000000000000000000
χ4144-4-444-4-400000000002i2−2i22i2−2i200000000000022−2200002i−2i2i−2i000000000000000
χ4244-4-444-4-400000000002i2−2i22i2−2i2000000000000−22220000−2i2i−2i2i000000000000000
χ4344-4-444-4-40000000000−2i22i2−2i22i200000000000022−220000−2i2i−2i2i000000000000000
χ4444-4-444-4-40000000000−2i22i2−2i22i2000000000000−222200002i−2i2i−2i000000000000000
χ454-44-44-44-400-40-4440002222−22−2200000000−2222000000000000000000000000000
χ464-44-44-44-400-40-444000−22−2222220000000022−22000000000000000000000000000
χ474-44-4-44-440040-44-4000000000004i−4i0000000000000000000000000000000
χ484-44-4-44-440040-44-400000000000−4i4i0000000000000000000000000000000
χ494-44-4-44-4400-404-4400000000000000000000022−22−22220000000000000000000
χ504-44-4-44-4400-404-44000000000000000000000−222222−220000000000000000000
χ514-4-444-4-444-404000-4004i−4i−4i4i0000000000000000000000000000000000000
χ524-4-444-4-444-404000-400−4i4i4i−4i0000000000000000000000000000000000000
χ534-4-444-4-44-440-4000400000000000000000000000022−22−2222000000000000000
χ544-4-444-4-44-440-40004000000000000000000000000−222222−22000000000000000
χ554-4-44-444-44-40-40004000000004-4000000000000000000000000000000000
χ564-4-44-444-44-40-4000400000000-44000000000000000000000000000000000
χ574-4-44-444-4-4404000-400000000000000000000000000000000002i2−2i20000000
χ584-4-44-444-4-4404000-40000000000000000000000000000000000−2i22i20000000
χ5988-8-8-8-888000000000000000000000000000000000000000000000000000

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