Finite Group Databasebeta

← Group #174461

Character table — Group #174461

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
χ51111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1-111-11111-1-1
χ61111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-11-111-1-1-11-1-1-1-111
χ71111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-111-1-1-1-1-111
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-11-111-1-1-111111-1-1
χ911111111-1-1-1-1-1-11-1-11111111-1-1-11111-1-1-1-11111-1-1-1-11-1111-11-1-1-111-1-11-1
χ1011111111-1-1-1-1-1-11-1-11111111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-111-11
χ1111111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-11111-1-1-1-111111-1111-11-1-1-1-1-111-11
χ1211111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11111111-1-11-1
χ1311111111-1-1-1-1-1-11-1-111111-1-1-1111111-1-1-1-1-1-1-1-1111111-11-11-1-1-1111-1-1-11
χ1411111111-1-1-1-1-1-11-1-111111-1-1-1111111-1-1-1-1-1-1-1-11111-111-11-1-111-1-1-1111-1
χ1511111111-1-1-1-1-1-11-1-111111-1-1-111-1-1-1-111111111-1-1-1-111-11-11-1-1-11-1-1111-1
χ1611111111-1-1-1-1-1-11-1-111111-1-1-111-1-1-1-111111111-1-1-1-1-111-11-1-111-111-1-1-11
χ1722222222222222-2-2-2-2-222-200-20000000000000000000020-22000-2000000
χ1822222222222222-2-2-2-2-222-200-200000000000000000000-202-20002000000
χ19222222222222-2-2222-2-2-2-2200-2000000000000000000200-20002-20000000
χ20222222222222-2-2222-2-2-2-2200-2000000000000000000-2002000-220000000
χ21222222222222-2-2-2-2-222-2-2-2222-2-20000000000000000020000-2000000000
χ22222222222222-2-2-2-2-222-2-2-2-2-222200000000000000000-200002000000000
χ2322222222-2-2-2-2222-2-2-2-2-2-22002000000000000000000200-2000-220000000
χ2422222222-2-2-2-2222-2-2-2-2-2-22002000000000000000000-20020002-20000000
χ2522222222-2-2-2-222-22222-2-2-222-22200000000000000000-20000-2000000000
χ2622222222-2-2-2-222-22222-2-2-2-2-2-2-2-200000000000000000200002000000000
χ2722222222-2-2-2-2-2-2-222-2-222-20020000000000000000000020-2-20002000000
χ2822222222-2-2-2-2-2-2-222-2-222-200200000000000000000000-2022000-2000000
χ292-2222-2-2-200002i−2i02i−2i2-20002-202i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i20000000000000000
χ302-2222-2-2-200002i−2i02i−2i2-20002-202i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i20000000000000000
χ312-2222-2-2-200002i−2i02i−2i2-2000-220−2i2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000000000
χ322-2222-2-2-200002i−2i02i−2i2-2000-220−2i2i−2−222−i2−i2i2i222−2−2i2i2−i2−i20000000000000000
χ332-2222-2-2-20000−2i2i0−2i2i2-20002-20−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i20000000000000000
χ342-2222-2-2-20000−2i2i0−2i2i2-20002-20−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i20000000000000000
χ352-2222-2-2-20000−2i2i0−2i2i2-2000-2202i−2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000000000
χ362-2222-2-2-20000−2i2i0−2i2i2-2000-2202i−2i−2−222i2i2−i2−i222−2−2−i2−i2i2i20000000000000000
χ37444-4-4-44-444-4-40000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ38444-4-4-44-444-4-4000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ39444-4-4-44-4-4-4440000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ40444-4-4-44-4-4-444000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4144-44-4-4-444i−4i4i−4i000000000000000000000000000000000000000002-22i−2i00
χ4244-44-4-4-444i−4i4i−4i00000000000000000000000000000000000000000-22−2i2i00
χ4344-44-4-4-44−4i4i−4i4i000000000000000000000000000000000000000002-2−2i2i00
χ4444-44-4-4-44−4i4i−4i4i00000000000000000000000000000000000000000-222i−2i00
χ4544-4-444-4-44i−4i−4i4i000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ4644-4-444-4-44i−4i−4i4i00000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ4744-4-444-4-4−4i4i4i−4i000000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ4844-4-444-4-4−4i4i4i−4i00000000000000000000000-22-222i−2i2i−2i0000000000000000
χ494-4444-4-4-400004i−4i0−4i4i-440000000000000000000000000000000000000000
χ504-4444-4-4-40000−4i4i04i−4i-440000000000000000000000000000000000000000
χ514-44-4-44-440000004000000-4000002i2−2i2−2i22i20000000000000000000000000000
χ524-44-4-44-440000004000000-400000−2i22i22i2−2i20000000000000000000000000000
χ534-44-4-44-44000000-4000000400000000022−22−2222000000000000000000000000
χ544-44-4-44-44000000-40000004000000000−222222−22000000000000000000000000
χ554-4-4-44-444000000000004-40000000000000022−22−222200000000000000000000
χ564-4-4-44-444000000000004-400000000000000−222222−2200000000000000000000
χ574-4-4-44-44400000000000-4400000000000000000022−22−22220000000000000000
χ584-4-4-44-44400000000000-44000000000000000000−222222−220000000000000000
χ598-8-88-888-8000000000000000000000000000000000000000000000000000

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