Finite Group Databasebeta

← Group #174098

Character table — Group #174098

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444422444444442244488888888888888882444444444888844
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1111111
χ51111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-11111-1-1
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ911111111-1-1-1-1-1-111-1-1111111-1-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-111-1-1111111-1-1-11111-1-1-1-11111-1-1-1-1-111-1-11-1-111-1-111-11
χ1111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-1-111-11
χ1211111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11111-1-1-1-11111-111-1-11-1-11111-1-11-1
χ1311111111-1-1-1-1-1-111-1-11111-1-1-1111111-1-1-1-1-1-1-1-111111-1-111-1-1-111-1-1111-1
χ1411111111-1-1-1-1-1-111-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-11
χ1511111111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-111111111-1-1-1-11-1-111-1-1-11111-1-1-11
χ1611111111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1111-1-1-1-1111-1
χ17222222222222222-2-2-2-2-22-200-20000000000000000000000002-22-2000000
χ18222222222222222-2-2-2-2-22-200-2000000000000000000000000-22-22000000
χ19222222222222-2-2-22-2-2-2-2-22222-2-200000000000000000-202000000000000
χ20222222222222-2-2-22-2-2-2-2-22-2-22220000000000000000020-2000000000000
χ21222222222222-2-2-2-22222-2-200-20000000000000000002020-2-20000000000
χ22222222222222-2-2-2-22222-2-200-2000000000000000000-20-20220000000000
χ2322222222-2-2-2-222-2222-2-2-2222-22200000000000000000-20-2000000000000
χ2422222222-2-2-2-222-2222-2-2-22-2-2-2-2-200000000000000000202000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-200200000000000000000020-20-220000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2002000000000000000000-20202-20000000000
χ2722222222-2-2-2-2-2-22-222-2-22-20020000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-22-222-2-22-2002000000000000000000000000-222-2000000
χ292-22-2-2-22200002-20-22-200022-202-222−2−222−2−222−2−222−2−20000000000000000
χ302-22-2-2-22200002-20-22-200022-202-2−2−222−2−222−2−222−2−2220000000000000000
χ312-22-2-2-22200002-20-22-20002-220-2222−2−222−2−2−2−222−2−2220000000000000000
χ322-22-2-2-22200002-20-22-20002-220-22−2−222−2−22222−2−222−2−20000000000000000
χ332-22-2-2-2220000-220-2-2200022-20-2222−2−2−2−22222−2−2−2−2220000000000000000
χ342-22-2-2-2220000-220-2-2200022-20-22−2−22222−2−2−2−22222−2−20000000000000000
χ352-22-2-2-2220000-220-2-220002-2202-222−2−2−2−222−2−22222−2−20000000000000000
χ362-22-2-2-2220000-220-2-220002-2202-2−2−22222−2−222−2−2−2−2220000000000000000
χ37444-4-44-4-444-4-4000000000000000000000002-22-22-22-20000000000000000
χ38444-4-44-4-444-4-400000000000000000000000-22-22-22-220000000000000000
χ39444-4-44-4-4-4-444000000000000000000000002-22-2-22-220000000000000000
χ40444-4-44-4-4-4-44400000000000000000000000-22-222-22-20000000000000000
χ4144-44-4-44-44i−4i4i−4i000000000000000000000000000000000000000002-22i−2i00
χ4244-44-4-44-44i−4i4i−4i00000000000000000000000000000000000000000-22−2i2i00
χ4344-44-4-44-4−4i4i−4i4i000000000000000000000000000000000000000002-2−2i2i00
χ4444-44-4-44-4−4i4i−4i4i00000000000000000000000000000000000000000-222i−2i00
χ4544-4-44-4-444i−4i−4i4i0000000000000002i−2i2i−2i2-22-2000000000000000000000000
χ4644-4-44-4-444i−4i−4i4i000000000000000−2i2i−2i2i-22-22000000000000000000000000
χ4744-4-44-4-44−4i4i4i−4i0000000000000002i−2i2i−2i-22-22000000000000000000000000
χ4844-4-44-4-44−4i4i4i−4i000000000000000−2i2i−2i2i2-22-2000000000000000000000000
χ494-4444-4-4-400000000004-400000000000000022−22−222200000000000000000000
χ504-4444-4-4-400000000004-4000000000000000−222222−2200000000000000000000
χ514-4444-4-4-40000000000-44000000000000000000022−22−22220000000000000000
χ524-4444-4-4-40000000000-440000000000000000000−222222−220000000000000000
χ534-44-4-4-44400004-404-44000-40000000000000000000000000000000000000
χ544-44-4-4-4440000-44044-4000-40000000000000000000000000000000000000
χ554-4-44-44-44000000400000-40000002i2−2i2−2i22i20000000000000000000000000000
χ564-4-44-44-44000000400000-4000000−2i22i22i2−2i20000000000000000000000000000
χ574-4-44-44-44000000-4000004000000000022−22−2222000000000000000000000000
χ584-4-44-44-44000000-40000040000000000−222222−22000000000000000000000000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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