Finite Group Databasebeta

← Group #310587

Character table — Group #310587

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-11111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-111-1-111-1
χ71111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11
χ911111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11
χ1011111111111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111111-1-11-1-111-1-1-1-1111
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1111111-1-1-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-111111-1-1-1-111-1-1-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111
χ17222222222-222-2-2-22-22222-200000000-2-2002222-2-20000000000000-200000000000
χ18222222222-222-2-2-22-22222-200000000-2-200-2-2-2-2220000000000000200000000000
χ19222222222-222-2-2-22-2-2-2-2-2-200000000220022-2-2220000000000000-200000000000
χ20222222222-222-2-2-22-2-2-2-2-2-2000000002200-2-222-2-20000000000000200000000000
χ2122222222-22-2-2222-2-20000-2222222-2-200220000000000-2-20000-200000000000000
χ2222222222-22-2-2222-2-20000-22222-2-22200-2-20000000000-2-20000200000000000000
χ2322222222-22-2-2222-2-20000-2-2-2-2-2222200-2-20000000000220000-200000000000000
χ2422222222-22-2-2222-2-20000-2-2-2-2-2-2-2-2-200220000000000220000200000000000000
χ252-222-22-2-2-202-2000202i2i−2i−2i022−2−2000000002i−2i2-200i2i2−i2−i22−222−2−200000000i2−i200000
χ262-222-22-2-2-202-2000202i2i−2i−2i022−2−200000000−2i2i-2200i2i2−i2−i22−2−2−22200000000−i2i200000
χ272-222-22-2-2-202-2000202i2i−2i−2i0−2−222000000002i−2i2-200−i2−i2i2i2−22−2−22200000000−i2i200000
χ282-222-22-2-2-202-2000202i2i−2i−2i0−2−22200000000−2i2i-2200−i2−i2i2i2−2222−2−200000000i2−i200000
χ292-222-22-2-2-202-200020−2i−2i2i2i022−2−2000000002i−2i-2200−i2−i2i2i22−2−2−22200000000i2−i200000
χ302-222-22-2-2-202-200020−2i−2i2i2i022−2−200000000−2i2i2-200−i2−i2i2i22−222−2−200000000−i2i200000
χ312-222-22-2-2-202-200020−2i−2i2i2i0−2−222000000002i−2i-2200i2i2−i2−i2−2222−2−200000000−i2i200000
χ322-222-22-2-2-202-200020−2i−2i2i2i0−2−22200000000−2i2i2-200i2i2−i2−i2−22−2−22200000000i2−i200000
χ332-2-222-2-2222-2-2-22-2220000-20000002i−2i002i−2i0000002-22-200000000002i−2i000000000
χ342-2-222-2-2222-2-2-22-2220000-20000002i−2i002i−2i000000-22-220000000000−2i2i000000000
χ352-2-222-2-2222-2-2-22-2220000-2000000−2i2i00−2i2i0000002-22-20000000000−2i2i000000000
χ362-2-222-2-2222-2-2-22-2220000-2000000−2i2i00−2i2i000000-22-2200000000002i−2i000000000
χ372-2-222-2-22-2222-22-2-2-22i−2i2i−2i20000002i−2i2i−2i−2i2i00000000000000000000002-20000000
χ382-2-222-2-22-2222-22-2-2-22i−2i2i−2i2000000−2i2i2i−2i2i−2i0000000000000000000000-220000000
χ392-2-222-2-22-2222-22-2-2-2−2i2i−2i2i20000002i−2i−2i2i−2i2i0000000000000000000000-220000000
χ402-2-222-2-22-2222-22-2-2-2−2i2i−2i2i2000000−2i2i−2i2i2i−2i00000000000000000000002-20000000
χ412-2-222-2-22-2-2222-22-222i−2i2i−2i-200000000−2i2i00000000000000000002-20000000002i−2i0
χ422-2-222-2-22-2-2222-22-222i−2i2i−2i-200000000−2i2i0000000000000000000-22000000000−2i2i0
χ432-2-222-2-22-2-2222-22-22−2i2i−2i2i-2000000002i−2i00000000000000000002-2000000000−2i2i0
χ442-2-222-2-22-2-2222-22-22−2i2i−2i2i-2000000002i−2i0000000000000000000-220000000002i−2i0
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-4-4404004-4-4000000000000000000000000000000022−2222−22000000000000000
χ47444-4-4-4-4404004-4-40000000000000000000000000000000−2222−2222000000000000000
χ48444-4-4-4-440-400-44400000004i−4i4i−4i000000000000000000000000000000000000000
χ49444-4-4-4-440-400-4440000000−4i4i−4i4i000000000000000000000000000000000000000
χ5044-44-4-44-4404-4000-404-4-4400000000000000000000000000000000000000000000
χ5144-44-4-44-4404-4000-40-444-400000000000000000000000000000000000000000000
χ5244-44-4-44-4-40-4400040000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5344-44-4-44-4-40-440004000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ544-444-44-4-440-44000-40000002222−22−22000000000000000000−22220000000000000000000
χ554-444-44-4-440-44000-4000000−22−22222200000000000000000022−220000000000000000000
χ564-44-44-44-4000000000000002i2−2i2−2i22i20000000000002i2−2i20000002-2-22000000000000000
χ574-44-44-44-4000000000000002i2−2i2−2i22i2000000000000−2i22i2000000-222-2000000000000000
χ584-44-44-44-400000000000000−2i22i22i2−2i20000000000002i2−2i2000000-222-2000000000000000
χ594-44-44-44-400000000000000−2i22i22i2−2i2000000000000−2i22i20000002-2-22000000000000000
χ604-4-444-4-444-4-4-44-444-4000040000000000000000000000000000000000000000000
χ614-4-4-4-44440400-4-4400000000000000000000000000000000000000000000022−22000
χ624-4-4-4-44440400-4-44000000000000000000000000000000000000000000000−2222000
χ634-4-4-4-44440-40044-4000000000004-40000000000000000000000000000000000000
χ644-4-4-4-44440-40044-400000000000-440000000000000000000000000000000000000
χ6588-8-888-8-8000000000000000000000000000000000000000000000000000000000

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