Finite Group Databasebeta

← Group #342207

Character table — Group #342207

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1111-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-11-1-1111-1-111-1-1-1-1-11
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11111-1-11-1-1-1-111-1-11-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-11111-1-1111-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-111-1-11111-11
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-111111-1-1-1-1-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11111111-1-1-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-111-1-1-11111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11-1-111111-1-1-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-11-1-1-1-1-11-1-111-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-11-1-1-1-1-111-1-111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1111111-11111-1-1-1-1-1-1
χ17222222222-2-22-2-222-2-2000000002222-2-2-2-20000000000002222-2-20000000000000000
χ18222222222-2-22-2-222-2-2000000002222-2-2-2-2000000000000-2-2-2-2220000000000000000
χ19222222222-2-22-2-222-2-200000000-2-2-2-2222200000000000022-2-2-220000000000000000
χ20222222222-2-22-2-222-2-200000000-2-2-2-22222000000000000-2-2222-20000000000000000
χ2122222222-222-222-2-2-2-22222-2-2-2-200000000000000002222000000-20000-20000000000
χ2222222222-222-222-2-2-2-22222-2-2-2-20000000000000000-2-2-2-20000002000020000000000
χ2322222222-222-222-2-2-2-2-2-2-2-22222000000000000000022-2-200000020000-20000000000
χ2422222222-222-222-2-2-2-2-2-2-2-222220000000000000000-2-222000000-2000020000000000
χ2522-2-22-2-22200-200-2200i2i2−i2−i2i2i2−i2−i22i2i−2i−2i00002222−2−2−2−200002i−2i2-200000000002−2i2−i20000
χ2622-2-22-2-22200-200-2200i2i2−i2−i2i2i2−i2−i22i2i−2i−2i00002222−2−2−2−20000−2i2i-220000000000−22−i2i20000
χ2722-2-22-2-22200-200-2200i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i0000−2−2−2−2222200002i−2i-2200000000002−2−i2i20000
χ2822-2-22-2-22200-200-2200i2i2−i2−i2i2i2−i2−i2−2i−2i2i2i0000−2−2−2−222220000−2i2i2-20000000000−22i2−i20000
χ2922-2-22-2-22200-200-2200−i2−i2i2i2−i2−i2i2i22i2i−2i−2i0000−2−2−2−2222200002i−2i2-20000000000−22−i2i20000
χ3022-2-22-2-22200-200-2200−i2−i2i2i2−i2−i2i2i22i2i−2i−2i0000−2−2−2−222220000−2i2i-2200000000002−2i2−i20000
χ3122-2-22-2-22200-200-2200−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i00002222−2−2−2−200002i−2i-220000000000−22i2−i20000
χ3222-2-22-2-22200-200-2200−i2−i2i2i2−i2−i2i2i2−2i−2i2i2i00002222−2−2−2−20000−2i2i2-200000000002−2−i2i20000
χ3322-2-2-222-202-202-200002i−2i2i−2i0000i2−i2i2−i2i2i2−i2−i222−2−222−2−22-22i−2i000000000000i2−i200002−200
χ3422-2-2-222-202-202-200002i−2i2i−2i0000i2−i2i2−i2i2i2−i2−i222−2−222−2−2-22−2i2i000000000000−i2i20000−2200
χ3522-2-2-222-202-202-200002i−2i2i−2i0000−i2i2−i2i2−i2−i2i2i2−2−222−2−2222-22i−2i000000000000−i2i20000−2200
χ3622-2-2-222-202-202-200002i−2i2i−2i0000−i2i2−i2i2−i2−i2i2i2−2−222−2−222-22−2i2i000000000000i2−i200002−200
χ3722-2-2-222-202-202-20000−2i2i−2i2i0000i2−i2i2−i2i2i2−i2−i2−2−222−2−2222-2−2i2i000000000000i2−i20000−2200
χ3822-2-2-222-202-202-20000−2i2i−2i2i0000i2−i2i2−i2i2i2−i2−i2−2−222−2−222-222i−2i000000000000−i2i200002−200
χ3922-2-2-222-202-202-20000−2i2i−2i2i0000−i2i2−i2i2−i2−i2i2i222−2−222−2−22-2−2i2i000000000000−i2i200002−200
χ4022-2-2-222-202-202-20000−2i2i−2i2i0000−i2i2−i2i2−i2−i2i2i222−2−222−2−2-222i−2i000000000000i2−i20000−2200
χ412-2-22-2-222222-2-2-22-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000002i−2i2-200000000000
χ422-2-22-2-222222-2-2-22-22-200000000000000002i−2i2i−2i2i−2i2i−2i00000000000−2i2i-2200000000000
χ432-2-22-2-222222-2-2-22-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000002i−2i-2200000000000
χ442-2-22-2-222222-2-2-22-22-20000000000000000−2i2i−2i2i−2i2i−2i2i00000000000−2i2i2-200000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ464444-4-4-4-4000000000022−22−2222000022−22−2222000022-2-2-2-22200000000000000000000000000
χ474444-4-4-4-4000000000022−22−22220000−222222−220000-2-22222-2-200000000000000000000000000
χ484444-4-4-4-40000000000−222222−22000022−22−22220000-2-22222-2-200000000000000000000000000
χ494444-4-4-4-40000000000−222222−220000−222222−22000022-2-2-2-22200000000000000000000000000
χ5044-4-44-4-44-4004004-4002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ5144-4-44-4-44-4004004-400−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ5244-4-4-444-40-440-440000000000002i2−2i22i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ5344-4-4-444-40-440-44000000000000−2i22i2−2i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ544-44-44-44-404-40-44000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ554-44-44-44-404-40-4400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ564-44-44-44-40-4404-4000000004i−4i4i−4i000000000000000000000000000000000000000000
χ574-44-44-44-40-4404-400000000−4i4i−4i4i000000000000000000000000000000000000000000
χ584-44-4-44-44400400-4-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ594-44-4-44-44400400-4-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ604-44-4-44-44-400-40044000000000000004-44-40000000000000000000000000000000000
χ614-44-4-44-44-400-4004400000000000000-44-440000000000000000000000000000000000
χ624-4-4444-4-40000000000000022−22−222200002i2−2i2−2i22i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ634-4-4444-4-40000000000000022−22−22220000−2i22i22i2−2i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ644-4-4444-4-400000000000000−222222−2200002i2−2i2−2i22i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ654-4-4444-4-400000000000000−222222−220000−2i22i22i2−2i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ664-4-44-4-4444-4-4-4444-4-4400000000000000000000000000000000000000000000000000
χ674-4-44-4-444-4444-4-4-44-4400000000000000000000000000000000000000000000000000
χ684-4-44-4-444-4-4-4444-444-400000000000000000000000000000000000000000000000000

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