Finite Group Databasebeta

← Group #174196

Character table — Group #174196

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444488888888888888882444444444888844
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ511111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-111111-1-1
χ611111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11-1-1-11-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-11-1-1-11111-1-1
χ911111111-1-1-1-1111-1-1-1-1111-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1-11-1111-1-11-1
χ1011111111-1-1-1-1111-1-1-1-1111-111-1-11111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1-111-11
χ1111111111-1-1-1-1111-1-1-1-1111-111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-11-11-1-111-11
χ1211111111-1-1-1-1111-1-1-1-1111-111-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-111-1-11-1
χ1311111111-1-1-1-1111-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-11-11-11111-1-1-11
χ1411111111-1-1-1-1111-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111-1111-11-1-11-1-1-1111-1
χ1511111111-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-111111111-1-1-1-11-1-1-11-11-111-1-1111-1
χ1611111111-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-111111111-1-1-1-1-1111-11-1-11-111-1-1-11
χ172222222222222-2-222-2-22-2-2-20000000000000000000022000-2000-2000000
χ182222222222222-2-222-2-22-2-2-200000000000000000000-2-200020002000000
χ19222222222222-22-2-2-2-2-2-22-2222-2-200000000000000000000000-220000000
χ20222222222222-22-2-2-2-2-2-22-22-2-222000000000000000000000002-20000000
χ21222222222222-2-22-2-222-2-22-200000000000000000000002-220-2000000000
χ22222222222222-2-22-2-222-2-22-20000000000000000000000-22-202000000000
χ2322222222-2-2-2-22-2-2-2-2222-2-22000000000000000000002-20002000-2000000
χ2422222222-2-2-2-22-2-2-2-2222-2-2200000000000000000000-22000-20002000000
χ2522222222-2-2-2-2-22-22222-22-2-2222200000000000000000000000-2-20000000
χ2622222222-2-2-2-2-22-22222-22-2-2-2-2-2-200000000000000000000000220000000
χ2722222222-2-2-2-2-2-2222-2-2-2-22200000000000000000000002-2-202000000000
χ2822222222-2-2-2-2-2-2222-2-2-2-2220000000000000000000000-2220-2000000000
χ2922-2-2-22-2200000202-22-20-2002i−2i2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ3022-2-2-22-2200000202-22-20-2002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ3122-2-2-22-2200000202-22-20-200−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ3222-2-2-22-2200000202-22-20-200−2i2i−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ3322-2-2-22-220000020-22-220-2002i−2i−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ3422-2-2-22-220000020-22-220-2002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ3522-2-2-22-220000020-22-220-200−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ3622-2-2-22-220000020-22-220-200−2i2i2i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ374444-4-4-4-444-4-4000000000000000000000000000000000000000002-22-200
χ384444-4-4-4-444-4-400000000000000000000000000000000000000000-22-2200
χ394444-4-4-4-4-4-444000000000000000000000000000000000000000002-2-2200
χ404444-4-4-4-4-4-44400000000000000000000000000000000000000000-222-200
χ4144-4-4-44-4400000-404-4-440400000000000000000000000000000000000000
χ4244-4-4-44-4400000-40-444-40400000000000000000000000000000000000000
χ434-44-444-4-400004000000-4000000022−2222−220000000000000000000000000000
χ444-44-444-4-400004000000-40000000−2222−22220000000000000000000000000000
χ454-44-444-4-40000-40000004000000000002i2−2i22i2−2i2000000000000000000000000
χ464-44-444-4-40000-4000000400000000000−2i22i2−2i22i2000000000000000000000000
χ474-44-4-4-4440000004000000-400000000000002i2−2i22i2−2i200000000000000000000
χ484-44-4-4-4440000004000000-40000000000000−2i22i2−2i22i200000000000000000000
χ494-44-4-4-444000000-400000040000000000000000022−2222−220000000000000000
χ504-44-4-4-444000000-4000000400000000000000000−2222−22220000000000000000
χ514-4-444-4-444i−4i4i−4i000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ524-4-444-4-444i−4i4i−4i00000000000000000000000−2i2i2i−2i-222-20000000000000000
χ534-4-444-4-44−4i4i−4i4i000000000000000000000002i−2i−2i2i-222-20000000000000000
χ544-4-444-4-44−4i4i−4i4i00000000000000000000000−2i2i2i−2i2-2-220000000000000000
χ554-4-44-444-44i−4i−4i4i0000000000000002i−2i−2i2i2-2-22000000000000000000000000
χ564-4-44-444-44i−4i−4i4i000000000000000−2i2i2i−2i-222-2000000000000000000000000
χ574-4-44-444-4−4i4i4i−4i0000000000000002i−2i−2i2i-222-2000000000000000000000000
χ584-4-44-444-4−4i4i4i−4i000000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ5988-8-88-88-8000000000000000000000000000000000000000000000000000

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