Finite Group Databasebeta

← Group #166327

Character table — Group #166327

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444444444444442222444448888888822444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ51111111111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ71111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1-111-1-11111-1-1-1-1111-11-11-11-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-11-11-11-11-111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-111-11-111-1-11-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-11-111-1-111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1111111-1-111-111-1-11111-1-1-1-1-1-11-1-11-11-111111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1-11111111-1-11-11-11-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1111111-1-1-1-1-1-1-111-1-111-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111111-1-111-1-1-111-1-1-1-1111111-111-1-111-1-1-111-1-1-1-111
χ1722222222222222-2-22-2-2-2-220000-222220000000000-2-20000000000000000
χ1822222222222222-2-22-2-2-2-220000-2-2-2-2-20000000000220000000000000000
χ19222222222222-2-222-222-2-2-222-2-2-2000000000000000000-22000000000000
χ20222222222222-2-222-222-2-2-2-2-222-20000000000000000002-2000000000000
χ21222222222222-2-2-2-2-2-2-222-20000200000000000000002-200-220000000000
χ22222222222222-2-2-2-2-2-2-222-2000020000000000000000-22002-20000000000
χ2322222222-2-2-2-22222-2-2-222-20000-200000000000000002200-2-20000000000
χ2422222222-2-2-2-22222-2-2-222-20000-20000000000000000-2-200220000000000
χ2522222222-2-2-2-222-2-2-222-2-2-222222000000000000000000-2-2000000000000
χ2622222222-2-2-2-222-2-2-222-2-2-2-2-2-2-2200000000000000000022000000000000
χ2722222222-2-2-2-2-2-2222-2-2-2-220000222-2-20000000000-220000000000000000
χ2822222222-2-2-2-2-2-2222-2-2-2-2200002-2-22200000000002-20000000000000000
χ2922-2-2-2-22222-2-22-200-200002000002-22-222−2−222−2−20000000000002−22−20000
χ3022-2-2-2-22222-2-22-200-200002000002-22-2−2−222−2−222000000000000−22−220000
χ3122-2-2-2-22222-2-22-200-20000200000-22-2222−2−222−2−2000000000000−22−220000
χ3222-2-2-2-22222-2-22-200-20000200000-22-22−2−222−2−2220000000000002−22−20000
χ3322-2-2-2-222-2-222-2200-200002000002-2-2222−2−2−2−2220000000000002−2−220000
χ3422-2-2-2-222-2-222-2200-200002000002-2-22−2−22222−2−2000000000000−222−20000
χ3522-2-2-2-222-2-222-2200-20000200000-222-222−2−2−2−222000000000000−222−20000
χ3622-2-2-2-222-2-222-2200-20000200000-222-2−2−22222−2−20000000000002−2−220000
χ374444-4-4-4-40000000004-4000004-4000000000000000000000000000000000
χ384444-4-4-4-40000000004-400000-44000000000000000000000000000000000
χ394444-4-4-4-4000000000-440004-400000000000000000000000000000000000
χ404444-4-4-4-4000000000-44000-4400000000000000000000000000000000000
χ4144-4-4-4-44444-4-4-440040000-40000000000000000000000000000000000000
χ4244-4-4-4-444-4-4444-40040000-40000000000000000000000000000000000000
χ434-44-44-44-44i−4i4i−4i00000000000000000000000000000000000000000002-22i−2i
χ444-44-44-44-44i−4i4i−4i0000000000000000000000000000000000000000000-22−2i2i
χ454-44-44-44-4−4i4i−4i4i00000000000000000000000000000000000000000002-2−2i2i
χ464-44-44-44-4−4i4i−4i4i0000000000000000000000000000000000000000000-222i−2i
χ474-44-4-44-44000000000004-40000000000000022−2222−2200000000000000000000
χ484-44-4-44-44000000000004-400000000000000−2222−222200000000000000000000
χ494-44-4-44-4400000000000-44000000000022−2222−22000000000000000000000000
χ504-44-4-44-4400000000000-440000000000−2222−2222000000000000000000000000
χ514-4-444-4-440000004-40000000000000002-2-222-2-2200000000000000000000
χ524-4-444-4-440000004-4000000000000000-222-2-222-200000000000000000000
χ534-4-444-4-44000000-440000000000000002-2-22-222-200000000000000000000
χ544-4-444-4-44000000-44000000000000000-222-22-2-2200000000000000000000
χ554-4-44-444-44i−4i−4i4i0000000000000000000000000002-2000000002i−2i00000000
χ564-4-44-444-44i−4i−4i4i000000000000000000000000000-2200000000−2i2i00000000
χ574-4-44-444-4−4i4i4i−4i0000000000000000000000000002-200000000−2i2i00000000
χ584-4-44-444-4−4i4i4i−4i000000000000000000000000000-22000000002i−2i00000000
χ5988-8-888-8-8000000000000000000000000000000000000000000000000000

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