Finite Group Databasebeta

← Group #336115

Character table — Group #336115

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888444444888888244
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1111111111111111-1-1-1-1-111-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11
χ4111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1
χ51111111111111111111111-1-1111111-1-1111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1
χ61111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1111-1-1-1-11111-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11-1-1111-1-111-1-11-1-1
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-111-111
χ11111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111111-1-1111-1-1-1-111-11-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-1-111-1-11-11
χ13111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-111-1-1111-11
χ14111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1111111-1-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-11-1-11111-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-11111-1-1111-1-1
χ172222222222-22-2-2-22-2-200002222-2-200-2-2000000220000-200000000000000
χ182222222222-22-2-2-22-2-2000022-2-2220022000000-2-20000-200000000000000
χ192222222222-22-2-2-22-2-20000-2-222-2-20022000000-2-20000200000000000000
χ202222222222-22-2-2-22-2-20000-2-2-2-22200-2-2000000220000200000000000000
χ2122222222-2-22-2222-2-2-222220000002200-2-2000000000002-2-200000000000
χ2222222222-2-22-2222-2-2-22222000000-2-200-2-200000000000-22200000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-200000022002200000000000-22-200000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2000000-2-20022000000000002-2200000000000
χ252222-2-2-2-22-20-200020022−2−22-2002i−2i002i−2i2−2i2i2−i2−i200i2i2−i2−i20000002−20000000
χ262222-2-2-2-22-20-200020022−2−22-200−2i2i00−2i2i2−2−i2−i2i2i200−i2−i2i2i20000002−20000000
χ272222-2-2-2-22-20-200020022−2−2-22002i−2i00−2i2i2−2i2i2−i2−i200−i2−i2i2i2000000−220000000
χ282222-2-2-2-22-20-200020022−2−2-2200−2i2i002i−2i2−2−i2−i2i2i200i2i2−i2−i2000000−220000000
χ292222-2-2-2-22-20-2000200−2−2222-2002i−2i002i−2i−22−i2−i2i2i200−i2−i2i2i2000000−220000000
χ302222-2-2-2-22-20-2000200−2−2222-200−2i2i00−2i2i−22i2i2−i2−i200i2i2−i2−i2000000−220000000
χ312222-2-2-2-22-20-2000200−2−222-22002i−2i00−2i2i−22−i2−i2i2i200i2i2−i2−i20000002−20000000
χ322222-2-2-2-22-20-2000200−2−222-2200−2i2i002i−2i−22i2i2−i2−i200−i2−i2i2i20000002−20000000
χ332-22-222-2-222-2-22-22-2-2200000000000000002-22-200000000002i−2i00002i−2i000
χ342-22-222-2-222-2-22-22-2-2200000000000000002-22-20000000000−2i2i0000−2i2i000
χ352-22-222-2-222-2-22-22-2-220000000000000000-22-2200000000002i−2i0000−2i2i000
χ362-22-222-2-222-2-22-22-2-220000000000000000-22-220000000000−2i2i00002i−2i000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ384444-4-4-4-4-4404000-4002222−22−220000000000−22220000000000000000000000000
χ394444-4-4-4-4-4404000-400−22−222222000000000022−220000000000000000000000000
χ4044-4-44-44-400000000002i2−2i22i2−2i200000000000000002i2−2i22-22-2000000000000000
χ4144-4-44-44-400000000002i2−2i22i2−2i20000000000000000−2i22i2-22-22000000000000000
χ4244-4-44-44-40000000000−2i22i2−2i22i200000000000000002i2−2i2-22-22000000000000000
χ4344-4-44-44-40000000000−2i22i2−2i22i20000000000000000−2i22i22-22-2000000000000000
χ4444-4-4-44-440040-4-440004i−4i−4i4i0000000000000000000000000000000000000
χ4544-4-4-44-440040-4-44000−4i4i4i−4i0000000000000000000000000000000000000
χ4644-4-4-44-4400-4044-400000000000000000000000002i2−2i2−2i22i2000000000000000
χ4744-4-4-44-4400-4044-40000000000000000000000000−2i22i22i2−2i2000000000000000
χ484-44-444-4-4444-4-44-4-44-400000000000000000000000000000000000000000
χ494-44-444-4-4-4-444-44-44-4400000000000000000000000000000000000000000
χ504-44-444-4-4-4-4-444-4444-400000000000000000000000000000000000000000
χ514-44-4-4-4444-404000-40000000000000000002i2−2i2−2i22i2000000000000000000000
χ524-44-4-4-4444-404000-4000000000000000000−2i22i22i2−2i2000000000000000000000
χ534-44-4-4-444-440-40004000000004-4000000000000000000000000000000000
χ544-44-4-4-444-440-4000400000000-44000000000000000000000000000000000
χ554-4-44-444-400404-4-400000000000004i−4i00000000000000000000000000000
χ564-4-44-444-400404-4-40000000000000−4i4i00000000000000000000000000000
χ574-4-44-444-400-40-444000000000000000000000000000000000000022−2200000
χ584-4-44-444-400-40-4440000000000000000000000000000000000000−222200000
χ598-8-888-8-88000000000000000000000000000000000000000000000000000

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