Finite Group Databasebeta

← Group #268174

Character table — Group #268174

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444422444444442244488888888888888882444444444888824
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1111111
χ51111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-11-11-1-11-11111-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-11-11-1-11-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-11-11-1-11-1-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-11-1-11-11-1-111111-1-1
χ911111111-1-1-1-1-1-11-1-1111111111-11111-1-1-1-11111-1-1-1-11-1-1-1-1-11-11111-1-11-1
χ1011111111-1-1-1-1-1-11-1-1111111111-11111-1-1-1-11111-1-1-1-1-11-1111-1-1-1-1-1-111-11
χ1111111111-1-1-1-1-1-11-1-1111111111-1-1-1-1-11111-1-1-1-111111-1-1-1-1-11-111-1-111-11
χ1211111111-1-1-1-1-1-11-1-1111111111-1-1-1-1-11111-1-1-1-11111-11-1111-1-1-1-111-1-11-1
χ1311111111-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-11-1-111-111-1-1-11
χ1411111111-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1111-11-1-1111-1
χ1511111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-11-1-111-1-1-1111-1
χ1611111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1111-1111-1-1-11
χ17222222222222222-2-2-2-2-22-20000-200000000000000000200-20200-2000000
χ18222222222222222-2-2-2-2-22-20000-200000000000000000-20020-2002000000
χ19222222222222-2-2-2222-2-2-220000-20000000000000000200-20200-20000000
χ20222222222222-2-2-2222-2-2-220000-20000000000000000-20020-20020000000
χ21222222222222-2-2-2-2-2-222-2-222-2-2200000000000000000020000-200000000
χ22222222222222-2-2-2-2-2-222-2-2-2-2222000000000000000000-20000200000000
χ2322222222-2-2-2-222-222-222-2-222-2-2-2000000000000000000-20000200000000
χ2422222222-2-2-2-222-222-222-2-2-2-222-200000000000000000020000-200000000
χ2522222222-2-2-2-222-2-2-22-2-2-2200002000000000000000020020-200-20000000
χ2622222222-2-2-2-222-2-2-22-2-2-22000020000000000000000-200-2020020000000
χ2722222222-2-2-2-2-2-2222-2-2-22-20000200000000000000000200-20-2002000000
χ2822222222-2-2-2-2-2-2222-2-2-22-20000200000000000000000-20020200-2000000
χ292-2-22-22-2200000020022-2-2-22-22-2000002i2i−2i−2i00002i2i−2i−2i0000000000000000
χ302-2-22-22-2200000020022-2-2-22-22-200000−2i−2i2i2i0000−2i−2i2i2i0000000000000000
χ312-2-22-22-2200000020022-2-2-2-22-22000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ322-2-22-22-2200000020022-2-2-2-22-2200000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ332-2-22-22-22000000-200-22-2222-2-22022-2-2000022-2-200000000000000000000
χ342-2-22-22-22000000-200-22-2222-2-220-2-2220000-2-22200000000000000000000
χ352-2-22-22-22000000-200-22-222-222-2022-2-20000-2-22200000000000000000000
χ362-2-22-22-22000000-200-22-222-222-20-2-222000022-2-200000000000000000000
χ37444-4-4-4-444i4i−4i−4i000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ38444-4-4-4-444i4i−4i−4i00000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ39444-4-4-4-44−4i−4i4i4i000000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ40444-4-4-4-44−4i−4i4i4i00000000000000000000000-22-222i−2i2i−2i0000000000000000
χ4144-44-4-44-44-44-40000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ4244-44-4-44-44-44-4000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ4344-44-4-44-4-44-440000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4444-44-4-44-4-44-44000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4544-4-444-4-44i−4i−4i4i000000000000000000000000000000000000000002-22i−2i00
χ4644-4-444-4-44i−4i−4i4i00000000000000000000000000000000000000000-22−2i2i00
χ4744-4-444-4-4−4i4i4i−4i000000000000000000000000000000000000000002-2−2i2i00
χ4844-4-444-4-4−4i4i4i−4i00000000000000000000000000000000000000000-222i−2i00
χ494-4444-4-4-400000004i−4i00000000002i−2i−2i2i2-2-22000000000000000000000000
χ504-4444-4-4-400000004i−4i0000000000−2i2i2i−2i-222-2000000000000000000000000
χ514-4444-4-4-40000000−4i4i00000000002i−2i−2i2i-222-2000000000000000000000000
χ524-4444-4-4-40000000−4i4i0000000000−2i2i2i−2i2-2-22000000000000000000000000
χ534-4-44-44-44000000400-4-44-440000000000000000000000000000000000000
χ544-4-44-44-44000000-4004-444-40000000000000000000000000000000000000
χ554-4-4-44-44400004-40000000000000000000002-2-222-2-220000000000000000
χ564-4-4-44-44400004-4000000000000000000000-222-2-222-20000000000000000
χ574-4-4-44-4440000-440000000000000000000002-2-22-222-20000000000000000
χ584-4-4-44-4440000-44000000000000000000000-222-22-2-220000000000000000
χ598-88-8-888-8000000000000000000000000000000000000000000000000000

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