Finite Group Databasebeta

← Group #166716

Character table — Group #166716

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444444444444444444444448888888822444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111-1-111111111-1-1-1-11-1-111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111
χ51111111111111111111111-1-1111-1-111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-11-1-1-1-11-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-11-1-1-1-111111111-1111-1-11-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1111-1-1-1-1111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-11-111111-1-1-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-1-1-11111-1-1-11-1111-1-11111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-11111-1-111-111-1-11111-1-1-1-11-1-111-11-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111-1-1-1-11111-1-111-111-1-1-1-1-1-111111-1-111-11-111-1-1-1-11111-1-1
χ1511111111-1-1-1-111-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-111-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-111-111-1-111-1-111-1-1-1-111
χ172222222222222-222-2-2-22-2-20022-2002200000000-20000-200000000000000
χ182222222222222-222-2-2-22-2-200-2-2-200-2-20000000020000200000000000000
χ19222222222222-22-2-222-2-22-22200-2-2-200000000000000200-2000000000000
χ20222222222222-22-2-222-2-22-2-2-200-22200000000000000-2002000000000000
χ21222222222222-2-2-2-2-2-22-2-220000200000000000002-2-20020000000000000
χ22222222222222-2-2-2-2-2-22-2-22000020000000000000-22200-20000000000000
χ2322222222-2-2-2-22-2-2-222-22-2-20022200-2-200000000-20000200000000000000
χ2422222222-2-2-2-22-2-2-222-22-2-200-2-2200220000000020000-200000000000000
χ2522222222-2-2-2-2-2222-2-2-2-22-2220022200000000000000-200-2000000000000
χ2622222222-2-2-2-2-2222-2-2-2-22-2-2-2002-2-2000000000000002002000000000000
χ2722222222-2-2-2-2-2-222222-2-220000-200000000000002-2200-20000000000000
χ2822222222-2-2-2-2-2-222222-2-220000-20000000000000-22-20020000000000000
χ29222-22-2-2-222-2-2-202-2000200002i−2i0002i−2i22−2−222−2−2000000000000i2−i2i2−i20000
χ30222-22-2-2-222-2-2-202-2000200002i−2i0002i−2i−2−222−2−222000000000000−i2i2−i2i20000
χ31222-22-2-2-222-2-2-202-200020000−2i2i000−2i2i22−2−222−2−2000000000000−i2i2−i2i20000
χ32222-22-2-2-222-2-2-202-200020000−2i2i000−2i2i−2−222−2−222000000000000i2−i2i2−i20000
χ33222-22-2-2-2-2-222-20-22000200002i−2i000−2i2i22−2−2−2−222000000000000i2−i2−i2i20000
χ34222-22-2-2-2-2-222-20-22000200002i−2i000−2i2i−2−22222−2−2000000000000−i2i2i2−i20000
χ35222-22-2-2-2-2-222-20-2200020000−2i2i0002i−2i22−2−2−2−222000000000000−i2i2i2−i20000
χ36222-22-2-2-2-2-222-20-2200020000−2i2i0002i−2i−2−22222−2−2000000000000i2−i2−i2i20000
χ37444-44-4-4-444-4-440-44000-4000000000000000000000000000000000000000
χ38444-44-4-4-4-4-444404-4000-4000000000000000000000000000000000000000
χ3944-44-44-4-4000004000000-404-400000000000000000000000000000000000
χ4044-44-44-4-4000004000000-40-4400000000000000000000000000000000000
χ4144-44-44-4-400000-400000040000004i−4i000000000000000000000000000000
χ4244-44-44-4-400000-40000004000000−4i4i000000000000000000000000000000
χ434-444-4-4-444i−4i4i−4i000000000000000000000000000000000002i−2i2-200000000
χ444-444-4-4-444i−4i4i−4i00000000000000000000000000000000000−2i2i-2200000000
χ454-444-4-4-44−4i4i−4i4i000000000000000000000000000000000002i−2i-2200000000
χ464-444-4-4-44−4i4i−4i4i00000000000000000000000000000000000−2i2i2-200000000
χ474-44-4-444-44i−4i−4i4i00000000000000000000000000000000000000000002-22i−2i
χ484-44-4-444-44i−4i−4i4i0000000000000000000000000000000000000000000-22−2i2i
χ494-44-4-444-4−4i4i4i−4i00000000000000000000000000000000000000000002-2−2i2i
χ504-44-4-444-4−4i4i4i−4i0000000000000000000000000000000000000000000-222i−2i
χ514-4-444-44-4000000004i−4i00000000000002-22-22i−2i2i−2i00000000000000000000
χ524-4-444-44-4000000004i−4i0000000000000-22-22−2i2i−2i2i00000000000000000000
χ534-4-444-44-400000000−4i4i00000000000002-22-2−2i2i−2i2i00000000000000000000
χ544-4-444-44-400000000−4i4i0000000000000-22-222i−2i2i−2i00000000000000000000
χ554-4-4-444-440000000000400-400000000000002i2−2i2−2i22i200000000000000000000
χ564-4-4-444-440000000000400-40000000000000−2i22i22i2−2i200000000000000000000
χ574-4-4-444-440000000000-400400000000022−22−2222000000000000000000000000
χ584-4-4-444-440000000000-4004000000000−222222−22000000000000000000000000
χ5988-8-8-8-888000000000000000000000000000000000000000000000000000

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