Finite Group Databasebeta

← Group #168682

Character table — Group #168682

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222222244444444444444444444444888888884444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ911111111-1-1-1-111-1-1-1-1111111-1-111-1-1-111-1-11111-1-1-1-11-11-11-111-1-111-1-11-1
χ1011111111-1-1-1-111-1-1-1-1111111-1-111-1-1-111-1-1-1-1-1-111111-11-11-1-1-111-1-111-11
χ1111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1111111-1-1-1-1-111-1-1111-1-1-1-111-11
χ1211111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-111-1-1-1-11111-111-1-11-1-11111-1-11-1
χ1311111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1111111-1-1-1-1-11-111-1-1-111-1-1111-1
χ1411111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-111-1-1-1-11111-11-111-111-1-111-1-1-11
χ1511111111-1-1-1-111-1-1-1-11111-1-111-1-111-111-1-11111-1-1-1-11-1-11-11-1-11111-1-1-11
χ1611111111-1-1-1-111-1-1-1-11111-1-111-1-111-111-1-1-1-1-1-111111-1-11-1111-1-1-1-1111-1
χ172222222222222-222-2-2-2-22-200000000-2222200000000-2-200000000000000
χ182222222222222-222-2-2-2-22-200000000-2-2-2-2-2000000002200000000000000
χ19222222222222-22-2-222-2-2-2222220000-200000000000000-2-2000000000000
χ20222222222222-22-2-222-2-2-22-2-2-2-20000-20000000000000022000000000000
χ21222222222222-2-2-2-2-2-222-2-20000222220000000000000000-2-20000000000
χ22222222222222-2-2-2-2-2-222-2-20000-2-2-2-220000000000000000220000000000
χ2322222222-2-2-2-22-2-2-222-2-22-200000000222-2-200000000-2200000000000000
χ2422222222-2-2-2-22-2-2-222-2-22-2000000002-2-222000000002-200000000000000
χ2522222222-2-2-2-2-2222-2-2-2-2-2222-2-20000200000000000000-22000000000000
χ2622222222-2-2-2-2-2222-2-2-2-2-22-2-22200002000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2222222-2-2000022-2-2-20000000000000000-220000000000
χ2822222222-2-2-2-2-2-2222222-2-20000-2-222-200000000000000002-20000000000
χ29222-2-22-2-222-2-20-2002-200022-22-2000000000i2i2−i2−i2i2i2−i2−i2000000i2−i2i2−i2000000
χ30222-2-22-2-222-2-20-2002-200022-22-2000000000−i2−i2i2i2−i2−i2i2i2000000−i2i2−i2i2000000
χ31222-2-22-2-222-2-20-2002-20002-22-22000000000i2i2−i2−i2i2i2−i2−i2000000−i2i2−i2i2000000
χ32222-2-22-2-222-2-20-2002-20002-22-22000000000−i2−i2i2i2−i2−i2i2i2000000i2−i2i2−i2000000
χ33222-2-22-2-2-2-2220-200-2200022-2-22000000000i2i2−i2−i2−i2−i2i2i2000000i2−i2−i2i2000000
χ34222-2-22-2-2-2-2220-200-2200022-2-22000000000−i2−i2i2i2i2i2−i2−i2000000−i2i2i2−i2000000
χ35222-2-22-2-2-2-2220-200-220002-222-2000000000i2i2−i2−i2−i2−i2i2i2000000−i2i2i2−i2000000
χ36222-2-22-2-2-2-2220-200-220002-222-2000000000−i2−i2i2i2i2i2−i2−i2000000i2−i2−i2i2000000
χ3722-22-2-22-22-22-2-202-20000200000000002i−2i2i−2i2−22−22−22−20000000000i2−i2i2−i200
χ3822-22-2-22-22-22-2-202-20000200000000002i−2i2i−2i−22−22−22−220000000000−i2i2−i2i200
χ3922-22-2-22-22-22-2-202-2000020000000000−2i2i−2i2i2−22−22−22−20000000000−i2i2−i2i200
χ4022-22-2-22-22-22-2-202-2000020000000000−2i2i−2i2i−22−22−22−220000000000i2−i2i2−i200
χ4122-22-2-22-2-22-22-20-220000200000000002i−2i−2i2i2−22−2−22−220000000000i2−i2−i2i200
χ4222-22-2-22-2-22-22-20-220000200000000002i−2i−2i2i−22−222−22−20000000000−i2i2i2−i200
χ4322-22-2-22-2-22-22-20-22000020000000000−2i2i2i−2i2−22−2−22−220000000000−i2i2i2−i200
χ4422-22-2-22-2-22-22-20-22000020000000000−2i2i2i−2i−22−222−22−20000000000i2−i2−i2i200
χ45444-4-44-4-444-4-40400-44000-40000000000000000000000000000000000000
χ46444-4-44-4-4-4-44404004-4000-40000000000000000000000000000000000000
χ4744-44-4-44-44-44-440-440000-400000000000000000000000000000000000000
χ4844-44-4-44-4-44-44404-40000-400000000000000000000000000000000000000
χ4944-4-44-4-444-4-44000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ5044-4-44-4-444-4-4400000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ5144-4-44-4-44-444-4000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ5244-4-44-4-44-444-400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ534-444-4-4-4400000000004-4000000004i−4i00000000000000000000000000000
χ544-444-4-4-4400000000004-400000000−4i4i00000000000000000000000000000
χ554-444-4-4-440000000000-440000004i−4i0000000000000000000000000000000
χ564-444-4-4-440000000000-44000000−4i4i0000000000000000000000000000000
χ578-88-88-88-8000000000000000000000000000000000000000000000000000
χ588-8-8888-8-8000000000000000000000000000000000000000000000000000
χ598-8-8-8-8888000000000000000000000000000000000000000000000000000

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