Finite Group Databasebeta

← Group #268693

Character table — Group #268693

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444448888888888888888888161616161616161616161616161616163232
order12224444442444442444444444488888888224444888888888848
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-11-111111-1-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-111-1-111111111-11-1-1-1-1-11-1-1-1-1
χ5111111111111111111-1-11-1-111111111-1-1-1-1-1-111-1-1-1-1111-1-1111-1-1
χ6111111111111111111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1-111-111-1-1
χ7111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-111-11111-1-1-1-1-111
χ8111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-1-1-1111-1-111
χ9111111111111-1-111-1-111-111111111111111-1-1-1-1-1-1111-1-1-1-11-1-1-11
χ10111111111111-1-111-1-111-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-11
χ11111111111111-1-111-1-111-111-1-1-1-111-1-111-1-1-1-111111-11-1-1-1-1-1111-1
χ12111111111111-1-111-1-111-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-11-111111111-1
χ13111111111111-1-111-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11-1-1111-1-11-1
χ14111111111111-1-111-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-111-1-1-1-1-11-1
χ15111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-111-1-111-111-11
χ16111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-1-111-1-1111-11
χ17222222-222-2-2-200-2200220-2-2000022002200000000-20-2000000000
χ18222222-222-2-2-200-2200220-2-20000-2-200-2-200000000202000000000
χ19222222-222-2-2-200-2200-2-202200002200-2-20000000020-2000000000
χ20222222-222-2-2-200-2200-2-20220000-2-2002200000000-202000000000
χ2122222-222-22-2-2222-22-200-200000000220000002-2000000000-20000
χ2222222-222-22-2-2222-22-200-200000000-2-2000000-2200000000020000
χ2322222-222-22-2-2-2-22-2-220020000000022000000-22000000000-20000
χ2422222-222-22-2-2-2-22-2-2200200000000-2-20000002-200000000020000
χ252222-222-222-2222-2-2-2200-2000000000000220000-220-20000000000
χ262222-222-222-2222-2-2-2200-2000000000000-2-200002-2020000000000
χ272222-222-222-22-2-2-2-22-20020000000000002200002-20-20000000000
χ282222-222-222-22-2-2-2-22-2002000000000000-2-20000-22020000000000
χ292222-2-22-2-222-222-22-2-22-222-20000000000002-20000000000000000
χ302222-2-22-2-222-222-22-2-2-222-22000000000000-220000000000000000
χ312222-2-22-2-222-2-2-2-22222-2-22-2000000000000-220000000000000000
χ322222-2-22-2-222-2-2-2-2222-22-2-220000000000002-20000000000000000
χ332222-2-2-2-2-2-2-220022002-20-220000000000000000000002i−2i2i−2i00000
χ342222-2-2-2-2-2-2-220022002-20-22000000000000000000000−2i2i−2i2i00000
χ352222-2-2-2-2-2-2-22002200-2202-20000000000000000000002i−2i−2i2i00000
χ362222-2-2-2-2-2-2-22002200-2202-2000000000000000000000−2i2i2i−2i00000
χ3744444-4-44-4-44400-4-40000000000000000000000000000000000000
χ384444-44-4-44-44-4004-40000000000000000000000000000000000000
χ3944-4-400-4004004i−4i0000000002i2i−2i−2i00000000000000000000002-200
χ4044-4-400-4004004i−4i000000000−2i−2i2i2i0000000000000000000000-2200
χ4144-4-400-400400−4i4i0000000002i2i−2i−2i0000000000000000000000-2200
χ4244-4-400-400400−4i4i000000000−2i−2i2i2i00000000000000000000002-200
χ434-44-4-40040000000000000002i−2i2i−2i22−222i2−2i20000000000000000000000
χ444-44-4-40040000000000000002i−2i2i−2i−2222−2i22i20000000000000000000000
χ454-44-4-4004000000000000000−2i2i−2i2i22−22−2i22i20000000000000000000000
χ464-44-4-4004000000000000000−2i2i−2i2i−22222i2−2i20000000000000000000000
χ474-4-440400-4000000000000002-2-2200002i2−2i22i2−2i2000000000000000000
χ484-4-440400-4000000000000002-2-220000−2i22i2−2i22i2000000000000000000
χ494-4-440400-400000000000000-222-200002i2−2i2−2i22i2000000000000000000
χ504-4-440400-400000000000000-222-20000−2i22i22i2−2i2000000000000000000
χ5188-8-800800-80000000000000000000000000000000000000000000
χ528-88-8800-8000000000000000000000000000000000000000000000
χ538-8-880-800800000000000000000000000000000000000000000000

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