Finite Group Databasebeta

← Group #174465

Character table — Group #174465

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444442244488888888888888882444444444888824
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-11-1-1-1-11-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1111111
χ51111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1-111-1-1-1-1-111
χ61111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-11-111-1-1-111111-1-1
χ71111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-111-11111-1-1
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-11-111-1-1-11-1-1-1-111
χ911111111-1-1-1-1-1-11-1-11111111-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-11-1111-1-11-1
χ1011111111-1-1-1-1-1-11-1-11111111-1-1-11111-1-1-1-11111-1-1-1-1-11-1111-1-11-1-1-111-11
χ1111111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-11-11-1-111-11
χ1211111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-11-111-1-11-1
χ1311111111-1-1-1-1-1-11-1-111111-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-1111-1
χ1411111111-1-1-1-1-1-11-1-111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-11-11111-1-1-11
χ1511111111-1-1-1-1-1-11-1-111111-1-1-111-1-1-1-111111111-1-1-1-11-1-1-11111-1-111-1-1-11
χ1611111111-1-1-1-1-1-11-1-111111-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-11-111-1-1111-1
χ17222222222222222-2-2-2-2-2-2200-200000000000000000000202-2000-2000000
χ18222222222222222-2-2-2-2-2-2200-200000000000000000000-20-220002000000
χ19222222222222-2-2-222-2-222-200-2000000000000000000200-2000-220000000
χ20222222222222-2-2-222-2-222-200-2000000000000000000-20020002-20000000
χ21222222222222-2-2-2-2-222-2-2-2222-2-200000000000000000-200002000000000
χ22222222222222-2-2-2-2-222-2-2-2-2-22220000000000000000020000-2000000000
χ2322222222-2-2-2-222-22222-2-2-222-22200000000000000000-20000-2000000000
χ2422222222-2-2-2-222-22222-2-2-2-2-2-2-2-200000000000000000200002000000000
χ2522222222-2-2-2-222-2-2-2-2-222-20020000000000000000002002000-2-20000000
χ2622222222-2-2-2-222-2-2-2-2-222-2002000000000000000000-200-2000220000000
χ2722222222-2-2-2-2-2-2222-2-2-2-220020000000000000000000020-22000-2000000
χ2822222222-2-2-2-2-2-2222-2-2-2-2200200000000000000000000-202-20002000000
χ29222-2-2-22-200002i−2i02i−2i2-20002-202i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i20000000000000000
χ30222-2-2-22-200002i−2i02i−2i2-20002-202i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i20000000000000000
χ31222-2-2-22-200002i−2i02i−2i2-2000-220−2i2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000000000
χ32222-2-2-22-200002i−2i02i−2i2-2000-220−2i2i−2−222−i2−i2i2i222−2−2i2i2−i2−i20000000000000000
χ33222-2-2-22-20000−2i2i0−2i2i2-20002-20−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i20000000000000000
χ34222-2-2-22-20000−2i2i0−2i2i2-20002-20−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i20000000000000000
χ35222-2-2-22-20000−2i2i0−2i2i2-2000-2202i−2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000000000
χ36222-2-2-22-20000−2i2i0−2i2i2-2000-2202i−2i−2−222i2i2−i2−i222−2−2−i2−i2i2i20000000000000000
χ37444-4-4-44-400004i−4i0−4i4i-440000000000000000000000000000000000000000
χ38444-4-4-44-40000−4i4i04i−4i-440000000000000000000000000000000000000000
χ3944-44-4-4-44000000000004-40000000000000000002i2−2i22i2−2i20000000000000000
χ4044-44-4-4-44000000000004-4000000000000000000−2i22i2−2i22i20000000000000000
χ4144-44-4-4-4400000000000-44000000000000002i2−2i22i2−2i200000000000000000000
χ4244-44-4-4-4400000000000-4400000000000000−2i22i2−2i22i200000000000000000000
χ4344-4-444-4-44i4i−4i−4i000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ4444-4-444-4-44i4i−4i−4i00000000000000000000000−2i2i2i−2i-222-20000000000000000
χ4544-4-444-4-4−4i−4i4i4i000000000000000000000002i−2i−2i2i-222-20000000000000000
χ4644-4-444-4-4−4i−4i4i4i00000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ474-4444-4-4-44i−4i4i−4i000000000000000000000000000000000000000002-22i−2i00
χ484-4444-4-4-44i−4i4i−4i00000000000000000000000000000000000000000-22−2i2i00
χ494-4444-4-4-4−4i4i−4i4i000000000000000000000000000000000000000002-2−2i2i00
χ504-4444-4-4-4−4i4i−4i4i00000000000000000000000000000000000000000-222i−2i00
χ514-4-44-444-40000004000000-40000000002i2−2i22i2−2i2000000000000000000000000
χ524-4-44-444-40000004000000-4000000000−2i22i2−2i22i2000000000000000000000000
χ534-4-44-444-4000000-400000040000022−2222−220000000000000000000000000000
χ544-4-44-444-4000000-4000000400000−2222−22220000000000000000000000000000
χ554-4-4-44-4444-4-440000000000000002-2-222-2-22000000000000000000000000
χ564-4-4-44-4444-4-44000000000000000-222-2-222-2000000000000000000000000
χ574-4-4-44-444-444-40000000000000002-2-22-222-2000000000000000000000000
χ584-4-4-44-444-444-4000000000000000-222-22-2-22000000000000000000000000
χ598-88-8-88-88000000000000000000000000000000000000000000000000000

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