Finite Group Databasebeta

← Group #253813

Character table — Group #253813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122224444444444488888888888888816161616161616161616161616161616163232
order12222244222244444444444444444444442244444444444888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11-1-111-1-1-1-111-11111-1-1-1-1-1-11111-1-1
χ4111111111111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ51111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-111-1-1111111-1-1-1-1-1-1
χ61111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ71111111111111-1-1-1-11111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ81111111111111-1-1-1-11111-1-1-1-1111-1-11111-1-11-1-1-1-1-1-111111111-1-1
χ911111111-1-1111111111-1-11111-1-1-11111111-1-11-1-1-1-1-111-1-111-1-11-1
χ1011111111-1-1111111111-1-11111-1-1-1111111-11-1-11-1-1-1-1-1-111-1-111-11
χ1111111111-1-1111111111-1-1-1-1-1-1-11111-1-1-1-11-111-1-1-111-1-11111-1-1-11
χ1211111111-1-1111111111-1-1-1-1-1-1-11111-1-1-1-1-111-11-1-11111-1-1-1-1111-1
χ1311111111-1-1111-1-1-1-111-1-11111-111-1-1-1-1-1-11-111-111-1-111-1-1-1-111-11
χ1411111111-1-1111-1-1-1-111-1-11111-111-1-1-1-1-1-1-111-1111-1-1-1-11111-1-11-1
χ1511111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-11-11111-1-111-1-1111-1
χ1611111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-11-1-11111111-1-111-1-1-11
χ172222222222-2-222222-2-22-20000-200-2-2000000000-22000000000000
χ182222222222-2-22-2-2-2-2-2-22-20000-200220000000002-2000000000000
χ1922222222-2-2-2-222222-2-2-220000200-2-20000000002-2000000000000
χ2022222222-2-2-2-22-2-2-2-2-2-2-22000020022000000000-22000000000000
χ21222222-2-22222-20000-2-2-2-222-2-220000000000000002-20000000000
χ22222222-2-22222-20000-2-2-2-2-2-2222000000000000000-220000000000
χ23222222-2-222-2-2-2000022-220000-2220022-2-200-20000000000000000
χ24222222-2-222-2-2-2000022-220000-2-2-200-2-2220020000000000000000
χ25222222-2-2-2-222-20000-2-22222-2-2-2000000000000000-220000000000
χ26222222-2-2-2-222-20000-2-222-2-222-20000000000000002-20000000000
χ27222222-2-2-2-2-2-2-20000222-2000022200-2-22200-20000000000000000
χ28222222-2-2-2-2-2-2-20000222-200002-2-20022-2-20020000000000000000
χ292222-2-2-2-2002-222i2i−2i−2i2-20000000002i−2i00000200-200000000002i−2i00
χ302222-2-2-2-2002-222i2i−2i−2i2-20000000002i−2i00000-20020000000000−2i2i00
χ312222-2-2-2-2002-22−2i−2i2i2i2-2000000000−2i2i00000200-20000000000−2i2i00
χ322222-2-2-2-2002-22−2i−2i2i2i2-2000000000−2i2i00000-200200000000002i−2i00
χ332222-2-2-2-200-2222i2i−2i−2i-22000000000−2i2i0000200-20000000002i−2i0000
χ342222-2-2-2-200-2222i2i−2i−2i-22000000000−2i2i0000-2002000000000−2i2i0000
χ352222-2-2-2-200-222−2i−2i2i2i-220000000002i−2i0000200-2000000000−2i2i0000
χ362222-2-2-2-200-222−2i−2i2i2i-220000000002i−2i0000-20020000000002i−2i0000
χ374444-4-444004-4-40000-440000000000000000000000000000000000
χ384444-4-44400-44-400004-40000000000000000000000000000000000
χ3944-4-4004i−4i000002+2i−2−2i2−2i−2+2i00002-22i−2i000002i−2i2-20000000000000000000
χ4044-4-4004i−4i000002+2i−2−2i2−2i−2+2i0000-22−2i2i00000−2i2i-220000000000000000000
χ4144-4-4004i−4i00000−2−2i2+2i−2+2i2−2i00002-22i−2i00000−2i2i-220000000000000000000
χ4244-4-4004i−4i00000−2−2i2+2i−2+2i2−2i0000-22−2i2i000002i−2i2-20000000000000000000
χ4344-4-400−4i4i000002−2i−2+2i2+2i−2−2i00002-2−2i2i00000−2i2i2-20000000000000000000
χ4444-4-400−4i4i000002−2i−2+2i2+2i−2−2i0000-222i−2i000002i−2i-220000000000000000000
χ4544-4-400−4i4i00000−2+2i2−2i−2−2i2+2i00002-2−2i2i000002i−2i-220000000000000000000
χ4644-4-400−4i4i00000−2+2i2−2i−2−2i2+2i0000-222i−2i00000−2i2i2-20000000000000000000
χ474-4-444-4004-40000000000000000000000000000000002i−2i2i−2i000000
χ484-4-444-4004-4000000000000000000000000000000000−2i2i−2i2i000000
χ494-4-444-400-440000000000000000000000000000000002i−2i−2i2i000000
χ504-4-444-400-44000000000000000000000000000000000−2i2i2i−2i000000
χ518-88-800000000000000000000004i−4i0000000000000000000000000
χ528-88-80000000000000000000000−4i4i0000000000000000000000000
χ538-8-88-8800000000000000000000000000000000000000000000000

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