Finite Group Databasebeta

← Group #306151

Character table — Group #306151

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1111-1-1-111-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-111111-1-111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11-111-1-111-1-1111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-11-1-1-1-11111-1-1-11
χ17222222222-2-22-222-2-2-222220000-2-2-2-2000000000000000022220000-2-2000000000000
χ18222222222-2-22-222-2-2-222220000-2-2-2-20000000000000000-2-2-2-2000022000000000000
χ19222222222-2-22-222-2-2-2-2-2-2-200002222000000000000000022-2-20000-22000000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2000022220000000000000000-2-22200002-2000000000000
χ2122222222-222-22-2-22-2-2000022220000-2-2-2-20000000022-2-200002-20000000000000000
χ2222222222-222-22-2-22-2-2000022220000-2-2-2-200000000-2-2220000-220000000000000000
χ2322222222-222-22-2-22-2-20000-2-2-2-2000022220000000022-2-20000-220000000000000000
χ2422222222-222-22-2-22-2-20000-2-2-2-20000222200000000-2-22200002-20000000000000000
χ2522-222-2-2-2222-2-22-2-2-2200000000000000002222-2-2-2-22-22-20000000000002-200000000
χ2622-222-2-2-2222-2-22-2-2-2200000000000000002222-2-2-2-2-22-22000000000000-2200000000
χ2722-222-2-2-2222-2-22-2-2-220000000000000000-2-2-2-222222-22-2000000000000-2200000000
χ2822-222-2-2-2222-2-22-2-2-220000000000000000-2-2-2-22222-22-220000000000002-200000000
χ2922-222-2-2-2-2222-2-22-22-222-2-2000022-2-20000000000002-2-22000000000000002-2000000
χ3022-222-2-2-2-2222-2-22-22-222-2-2000022-2-2000000000000-222-200000000000000-22000000
χ3122-222-2-2-2-2222-2-22-22-2-2-2220000-2-2220000000000002-2-2200000000000000-22000000
χ3222-222-2-2-2-2222-2-22-22-2-2-2220000-2-222000000000000-222-2000000000000002-2000000
χ3322-222-2-2-2-2-2-222-222-2222-2-20000-2-22200000000000000000000002i−2i002i−2i0000000000
χ3422-222-2-2-2-2-2-222-222-2222-2-20000-2-2220000000000000000000000−2i2i00−2i2i0000000000
χ3522-222-2-2-2-2-2-222-222-22-2-222000022-2-200000000000000000000002i−2i00−2i2i0000000000
χ3622-222-2-2-2-2-2-222-222-22-2-222000022-2-20000000000000000000000−2i2i002i−2i0000000000
χ3722-2-2-2-22220020-2-20002-22-222−2−2000022−2−222−2−222−2−200002i−2i2i−2i000000000000i2−i2i2−i200
χ3822-2-2-2-22220020-2-20002-22-222−2−2000022−2−222−2−222−2−20000−2i2i−2i2i000000000000−i2i2−i2i200
χ3922-2-2-2-22220020-2-20002-22-2−2−2220000−2−222−2−222−2−22200002i−2i2i−2i000000000000−i2i2−i2i200
χ4022-2-2-2-22220020-2-20002-22-2−2−2220000−2−222−2−222−2−2220000−2i2i−2i2i000000000000i2−i2i2−i200
χ4122-2-2-2-22220020-2-2000-22-2222−2−2000022−2−2−2−222−2−22200002i−2i−2i2i000000000000i2−i2−i2i200
χ4222-2-2-2-22220020-2-2000-22-2222−2−2000022−2−2−2−222−2−2220000−2i2i2i−2i000000000000−i2i2i2−i200
χ4322-2-2-2-22220020-2-2000-22-22−2−2220000−2−22222−2−222−2−200002i−2i−2i2i000000000000−i2i2i2−i200
χ4422-2-2-2-22220020-2-2000-22-22−2−2220000−2−22222−2−222−2−20000−2i2i2i−2i000000000000i2−i2−i2i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-4400-40-4400000000000000000002222−22−22−22−22222200000000000000000000000000
χ47444-4-44-4-4400-40-440000000000000000000−22−2222222222−22−2200000000000000000000000000
χ48444-4-44-4-4-400404-40004-4-440000000000000000000000000000000000000000000000
χ49444-4-44-4-4-400404-4000-444-40000000000000000000000000000000000000000000000
χ5044-444-4-4-44-4-4-444-444-400000000000000000000000000000000000000000000000000
χ5144-4-4-4-444-400-404400000002222−22−220000−22−2222220000000000000000000000000000000000
χ5244-4-4-4-444-400-40440000000−22−22222200002222−22−220000000000000000000000000000000000
χ534-444-4-44-404-40400-40000004-44-4000000000000000000000000000000000000000000
χ544-444-4-44-404-40400-4000000-44-44000000000000000000000000000000000000000000
χ554-444-4-44-40-440-40040000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000
χ564-444-4-44-40-440-4004000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000
χ574-44-44-4-440000000000000000002i2−2i22i2−2i222−2222−222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ584-44-44-4-440000000000000000002i2−2i22i2−2i2−2222−2222−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ594-44-44-4-44000000000000000000−2i22i2−2i22i222−2222−22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ604-44-44-4-44000000000000000000−2i22i2−2i22i2−2222−22222i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ614-4-44-44-4404-40-4004000000000000004-4-440000000000000000000000000000000000
χ624-4-44-44-4404-40-400400000000000000-444-40000000000000000000000000000000000
χ634-4-44-44-440-440400-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ644-4-44-44-440-440400-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ654-4-4-4444-40000000000000022−22−22222i2−2i2−2i22i200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ664-4-4-4444-40000000000000022−22−2222−2i22i22i2−2i20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ674-4-4-4444-400000000000000−222222−222i2−2i2−2i22i20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ684-4-4-4444-400000000000000−222222−22−2i22i22i2−2i200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000

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