Finite Group Databasebeta

← Group #168708

Character table — Group #168708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444444444444888888882444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ51111111111111111111111-1-11111-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-1111-1-1-1-11111111-1-111-1-1-1-1-11111-1-1-1-11-11-11-111-1-111-1-11-1
χ1011111111-1-1-1-1111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-111111-11-11-1-1-111-1-111-11
χ1111111111-1-1-1-1111-1-1-1-111111-1-111-1-111-1-1-11111-1-1-1-1-111-1-1111-1-1-1-111-11
χ1211111111-1-1-1-1111-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-11111-111-1-11-1-11111-1-11-1
χ1311111111-1-1-1-1111-1-1-1-1111-1-111-1-1-1-111-1111111-1-1-1-11-1-11-11-1-11111-1-1-11
χ1411111111-1-1-1-1111-1-1-1-1111-1-111-1-1-1-111-111-1-1-1-111111-1-11-1111-1-1-1-1111-1
χ1511111111-1-1-1-1111-1-1-1-1111-1-1-1-11111-1-1-1111111-1-1-1-1-11-111-1-1-111-1-1111-1
χ1611111111-1-1-1-1111-1-1-1-1111-1-1-1-11111-1-1-111-1-1-1-11111-11-111-111-1-111-1-1-11
χ172222222222222-2-2-2-2-2-22-2-20000002222200000000000000-2-20000000000
χ182222222222222-2-2-2-2-2-22-2-2000000-2-2-2-2200000000000000220000000000
χ19222222222222-22-222-2-2-22-20022220000-20000000000-2-200000000000000
χ20222222222222-22-222-2-2-22-200-2-2-2-20000-200000000002200000000000000
χ21222222222222-2-22-2-222-2-222200000000-2220000000000-2-2000000000000
χ22222222222222-2-22-2-222-2-22-2-200000000-2-2-2000000000022000000000000
χ2322222222-2-2-2-22-2-222222-2-200000022-2-2-200000000000000-220000000000
χ2422222222-2-2-2-22-2-222222-2-2000000-2-222-2000000000000002-20000000000
χ2522222222-2-2-2-2-22-2-2-222-22-20022-2-2000020000000000-2200000000000000
χ2622222222-2-2-2-2-22-2-2-222-22-200-2-2220000200000000002-200000000000000
χ2722222222-2-2-2-2-2-2222-2-2-2-2222000000002-2-20000000000-22000000000000
χ2822222222-2-2-2-2-2-2222-2-2-2-22-2-20000000022200000000002-2000000000000
χ2922-222-2-2-222-2-200-2002-20022i−2i0000000002i−2i22−2−222−2−2000000i2−i2i2−i2000000
χ3022-222-2-2-222-2-200-2002-20022i−2i0000000002i−2i−2−222−2−222000000−i2i2−i2i2000000
χ3122-222-2-2-222-2-200-2002-2002−2i2i000000000−2i2i22−2−222−2−2000000−i2i2−i2i2000000
χ3222-222-2-2-222-2-200-2002-2002−2i2i000000000−2i2i−2−222−2−222000000i2−i2i2−i2000000
χ3322-222-2-2-2-2-22200-200-220022i−2i000000000−2i2i22−2−2−2−222000000i2−i2−i2i2000000
χ3422-222-2-2-2-2-22200-200-220022i−2i000000000−2i2i−2−22222−2−2000000−i2i2i2−i2000000
χ3522-222-2-2-2-2-22200-200-22002−2i2i0000000002i−2i22−2−2−2−222000000−i2i2i2−i2000000
χ3622-222-2-2-2-2-22200-200-22002−2i2i0000000002i−2i−2−22222−2−2000000i2−i2−i2i2000000
χ3722-2-2-222-22-22-20-202-200020002i−2i2i−2i0000000i2−i2i2−i2i2−i2i2−i200000000002−22−200
χ3822-2-2-222-22-22-20-202-200020002i−2i2i−2i0000000−i2i2−i2i2−i2i2−i2i20000000000−22−2200
χ3922-2-2-222-22-22-20-202-20002000−2i2i−2i2i0000000i2−i2i2−i2i2−i2i2−i20000000000−22−2200
χ4022-2-2-222-22-22-20-202-20002000−2i2i−2i2i0000000−i2i2−i2i2−i2i2−i2i200000000002−22−200
χ4122-2-2-222-2-22-220-20-2200020002i−2i−2i2i0000000i2−i2i2−i2−i2i2−i2i200000000002−2−2200
χ4222-2-2-222-2-22-220-20-2200020002i−2i−2i2i0000000−i2i2−i2i2i2−i2i2−i20000000000−222−200
χ4322-2-2-222-2-22-220-20-220002000−2i2i2i−2i0000000i2−i2i2−i2−i2i2−i2i20000000000−222−200
χ4422-2-2-222-2-22-220-20-220002000−2i2i2i−2i0000000−i2i2−i2i2i2−i2i2−i200000000002−2−2200
χ45444-4-4-4-444-4-44000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ46444-4-4-4-444-4-4400000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ47444-4-4-4-44-444-4000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ48444-4-4-4-44-444-400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ4944-444-4-4-444-4-400400-4400-40000000000000000000000000000000000000
χ5044-444-4-4-4-4-444004004-400-40000000000000000000000000000000000000
χ5144-4-4-444-44-44-4040-44000-400000000000000000000000000000000000000
χ5244-4-4-444-4-44-440404-4000-400000000000000000000000000000000000000
χ534-444-44-4-400004000000-4000000004-400000000000000000000000000000
χ544-444-44-4-400004000000-400000000-4400000000000000000000000000000
χ554-444-44-4-40000-4000000400000000004i−4i000000000000000000000000000
χ564-444-44-4-40000-400000040000000000−4i4i000000000000000000000000000
χ578-88-88-88-8000000000000000000000000000000000000000000000000000
χ588-8-88-8-888000000000000000000000000000000000000000000000000000
χ598-8-8-888-88000000000000000000000000000000000000000000000000000

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