Finite Group Databasebeta

← Group #342145

Character table — Group #342145

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-11-1-1-1-111-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11-1-1-1-1-1-1-111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111111-1-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-11111-1-1111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-111111-1-111-1-1-1-1-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-11111111-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1-1-11-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-111-1-111-1-11111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-111111-1111-1-1-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-11-1-11-111-1-111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-1-1-1-1-1-11-1-111-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111111-1111-1-1-11111-1-1-1-1
χ17222222222-222-2-2-22-2-22222-2-2-2-2000000000000000022220000-200-200000000000000
χ18222222222-222-2-2-22-2-22222-2-2-2-20000000000000000-2-2-2-20000200200000000000000
χ19222222222-222-2-2-22-2-2-2-2-2-22222000000000000000022-2-20000200-200000000000000
χ20222222222-222-2-2-22-2-2-2-2-2-222220000000000000000-2-2220000-200200000000000000
χ2122222222-22-2-2222-2-2-2000000002222-2-2-2-200000000000022-2-20000002-20000000000
χ2222222222-22-2-2222-2-2-2000000002222-2-2-2-2000000000000-2-222000000-220000000000
χ2322222222-22-2-2222-2-2-200000000-2-2-2-222220000000000002222000000-2-20000000000
χ2422222222-22-2-2222-2-2-200000000-2-2-2-22222000000000000-2-2-2-2000000220000000000
χ2522-222-2-2-2-202-20002002i2i−2i−2i000022−2−222−2−2i2i2i2i2−i2−i2−i2−i22-22i−2i000000000000i2−i22−2000000
χ2622-222-2-2-2-202-20002002i2i−2i−2i000022−2−222−2−2i2i2i2i2−i2−i2−i2−i2-22−2i2i000000000000−i2i2−22000000
χ2722-222-2-2-2-202-20002002i2i−2i−2i0000−2−222−2−222−i2−i2−i2−i2i2i2i2i22-22i−2i000000000000−i2i2−22000000
χ2822-222-2-2-2-202-20002002i2i−2i−2i0000−2−222−2−222−i2−i2−i2−i2i2i2i2i2-22−2i2i000000000000i2−i22−2000000
χ2922-222-2-2-2-202-2000200−2i−2i2i2i000022−2−222−2−2−i2−i2−i2−i2i2i2i2i22-2−2i2i000000000000−i2i22−2000000
χ3022-222-2-2-2-202-2000200−2i−2i2i2i000022−2−222−2−2−i2−i2−i2−i2i2i2i2i2-222i−2i000000000000i2−i2−22000000
χ3122-222-2-2-2-202-2000200−2i−2i2i2i0000−2−222−2−222i2i2i2i2−i2−i2−i2−i22-2−2i2i000000000000i2−i2−22000000
χ3222-222-2-2-2-202-2000200−2i−2i2i2i0000−2−222−2−222i2i2i2i2−i2−i2−i2−i2-222i−2i000000000000−i2i22−2000000
χ332-2-22-2-222-2222-22-2-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000002-202i−2i000000000000
χ342-2-22-2-222-2222-22-2-22-200000000000000002i2i−2i−2i2i2i−2i−2i000000000-220−2i2i000000000000
χ352-2-22-2-222-2222-22-2-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000002-20−2i2i000000000000
χ362-2-22-2-222-2222-22-2-22-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000-2202i−2i000000000000
χ372-2-2-2222-202002-2-20002−22−222−2−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200002-22i−2i0000000000002−2i2−i200
χ382-2-2-2222-202002-2-20002−22−222−2−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000-22−2i2i000000000000−22−i2i200
χ392-2-2-2222-202002-2-20002−22−222−2−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200002-2−2i2i0000000000002−2−i2i200
χ402-2-2-2222-202002-2-20002−22−222−2−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000-222i−2i000000000000−22i2−i200
χ412-2-2-2222-202002-2-2000−22−22−2−22200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200002-22i−2i000000000000−22−i2i200
χ422-2-2-2222-202002-2-2000−22−22−2−22200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000-22−2i2i0000000000002−2i2−i200
χ432-2-2-2222-202002-2-2000−22−22−2−2220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200002-2−2i2i000000000000−22i2−i200
χ442-2-2-2222-202002-2-2000−22−22−2−2220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000-222i−2i0000000000002−2−i2i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-40400-4-44000000000000000000022−22−222222−22−222200000000000000000000000000
χ47444-4-4-44-40400-4-440000000000000000000−222222−22−222222−2200000000000000000000000000
χ48444-4-4-44-40-40044-4000000000004-44-400000000000000000000000000000000000000
χ49444-4-4-44-40-40044-400000000000-44-4400000000000000000000000000000000000000
χ5044-444-4-4-440-44000-400000000002222−22−22−22−2222220000000000000000000000000000000000
χ5144-444-4-4-440-44000-40000000000−22−2222222222−22−220000000000000000000000000000000000
χ5244-4-4-44-44000000000000002i2−2i22i2−2i222−22−222200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5344-4-4-44-44000000000000002i2−2i22i2−2i2−222222−220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5444-4-4-44-4400000000000000−2i22i2−2i22i222−22−22220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5544-4-4-44-4400000000000000−2i22i2−2i22i2−222222−2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ564-444-44-4-4404-4000-40000000000000000002222−22−22−22−22222200000000000000000000000000
χ574-444-44-4-4404-4000-4000000000000000000−22−2222222222−22−2200000000000000000000000000
χ584-444-44-4-4-40-4400040000004i−4i−4i4i000000000000000000000000000000000000000000
χ594-444-44-4-4-40-440004000000−4i4i4i−4i000000000000000000000000000000000000000000
χ604-44-44-4-4400000000002i2−2i2−2i22i2000000002i2−2i2−2i22i2-22-222-22-200000000000000000000000000
χ614-44-44-4-4400000000002i2−2i2−2i22i200000000−2i22i22i2−2i22-22-2-22-2200000000000000000000000000
χ624-44-44-4-440000000000−2i22i22i2−2i2000000002i2−2i2−2i22i22-22-2-22-2200000000000000000000000000
χ634-44-44-4-440000000000−2i22i22i2−2i200000000−2i22i22i2−2i2-22-222-22-200000000000000000000000000
χ644-4-44-4-44444-4-4-44-44-4400000000000000000000000000000000000000000000000000
χ654-4-44-4-4444-4-4-44-4444-400000000000000000000000000000000000000000000000000
χ664-4-44-4-444-4-4444-44-4-4400000000000000000000000000000000000000000000000000
χ674-4-4-4444-40-400-44400022−2222−22−22−222222000000000000000000000000000000000000000000
χ684-4-4-4444-40-400-444000−2222−22222222−22−22000000000000000000000000000000000000000000

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