Finite Group Databasebeta

← Group #308338

Character table — Group #308338

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-11111111111-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-11-1-111-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111-1-11-1-1-1-1-1-1111
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-111-1-11111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11
χ1011111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1
χ1111111111111111111-1-1-1-111111-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-11111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111111-1-1-111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111111-1-1111-1-1-1-111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-11111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-11111111-1-111-1
χ17222222222-2-22-222-2-20000-222220022-2-22200-2-200000000000000000-2000000000
χ18222222222-2-22-222-2-20000-2222200-2-222-2-200-2-2000000000000000002000000000
χ19222222222-2-22-222-2-20000-2-2-2-2-20022-2-2-2-20022000000000000000002000000000
χ20222222222-2-22-222-2-20000-2-2-2-2-200-2-22222002200000000000000000-2000000000
χ2122222222-222-22-2-22-22222-2000022000000-2-200220000-2-20000-200000000000000
χ2222222222-222-22-2-22-22222-20000-2-2000000-2-200-2-20000220000200000000000000
χ2322222222-222-22-2-22-2-2-2-2-2-20000220000002200-2-20000220000-200000000000000
χ2422222222-222-22-2-22-2-2-2-2-2-20000-2-20000002200220000-2-20000200000000000000
χ2522-2-2-222-202-20-200202i2i−2i−2i022−2−22-2000000002−22i−2ii2i2−i2−i200i2i2−i2−i2000000002−200000
χ2622-2-2-222-202-20-200202i2i−2i−2i022−2−2-22000000002−2−2i2ii2i2−i2−i200−i2−i2i2i200000000−2200000
χ2722-2-2-222-202-20-200202i2i−2i−2i0−2−2222-200000000−222i−2i−i2−i2i2i200−i2−i2i2i200000000−2200000
χ2822-2-2-222-202-20-200202i2i−2i−2i0−2−222-2200000000−22−2i2i−i2−i2i2i200i2i2−i2−i2000000002−200000
χ2922-2-2-222-202-20-20020−2i−2i2i2i022−2−22-2000000002−2−2i2i−i2−i2i2i200−i2−i2i2i2000000002−200000
χ3022-2-2-222-202-20-20020−2i−2i2i2i022−2−2-22000000002−22i−2i−i2−i2i2i200i2i2−i2−i200000000−2200000
χ3122-2-2-222-202-20-20020−2i−2i2i2i0−2−2222-200000000−22−2i2ii2i2−i2−i200i2i2−i2−i200000000−2200000
χ3222-2-2-222-202-20-20020−2i−2i2i2i0−2−222-2200000000−222i−2ii2i2−i2−i200−i2−i2i2i2000000002−200000
χ332-222-22-2-2222-2-22-2-220000-20000002-22-2000000002-22-200000002-2000000000000
χ342-222-22-2-2222-2-22-2-220000-20000002-22-200000000-22-220000000-22000000000000
χ352-222-22-2-2222-2-22-2-220000-2000000-22-22000000002-22-20000000-22000000000000
χ362-222-22-2-2222-2-22-2-220000-2000000-22-2200000000-22-2200000002-2000000000000
χ372-222-22-2-22-2-2-222-22-22i−2i2i−2i20000002-2-22002i−2i000000000000000002i−2i0000000000
χ382-222-22-2-22-2-2-222-22-22i−2i2i−2i2000000-222-2002i−2i00000000000000000−2i2i0000000000
χ392-222-22-2-22-2-2-222-22-2−2i2i−2i2i20000002-2-2200−2i2i00000000000000000−2i2i0000000000
χ402-222-22-2-22-2-2-222-22-2−2i2i−2i2i2000000-222-200−2i2i000000000000000002i−2i0000000000
χ412-222-22-2-2-2-2-222-22222i−2i2i−2i-2000000000000−2i2i000000000000000000002i−2i002-2000
χ422-222-22-2-2-2-2-222-22222i−2i2i−2i-2000000000000−2i2i00000000000000000000−2i2i00-22000
χ432-222-22-2-2-2-2-222-2222−2i2i−2i2i-20000000000002i−2i000000000000000000002i−2i00-22000
χ442-222-22-2-2-2-2-222-2222−2i2i−2i2i-20000000000002i−2i00000000000000000000−2i2i002-2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-4400-40-4400000004-44-4000000000000000000000000000000000000000
χ47444-44-4-4-4400-40-440000000-44-44000000000000000000000000000000000000000
χ48444-44-4-4-4-400404-4000000000000000000000000000000022−2222−22000000000000000
χ49444-44-4-4-4-400404-40000000000000000000000000000000−2222−2222000000000000000
χ5044-44-4-4-440000000000000022−22−22220000000000000000002i2−2i22i−2i−2i2i000000000000000
χ5144-44-4-4-440000000000000022−22−2222000000000000000000−2i22i2−2i2i2i−2i000000000000000
χ5244-44-4-4-4400000000000000−222222−220000000000000000002i2−2i2−2i2i2i−2i000000000000000
χ5344-44-4-4-4400000000000000−222222−22000000000000000000−2i22i22i−2i−2i2i000000000000000
χ5444-4-4-444-40-440400-40000002222−22−220000000000−2222000000000000000000000000000
χ5544-4-4-444-40-440400-4000000−22−222222000000000022−22000000000000000000000000000
χ564-444-44-4-4-4444-4-44-4-4000040000000000000000000000000000000000000000000
χ574-44-4-4-44440040-4-4000000000000000004i−4i0000000000000000000000000000000
χ584-44-4-4-44440040-4-400000000000000000−4i4i0000000000000000000000000000000
χ594-44-4-4-444-400-40440000000000000000000000000000000000000000000000022−220
χ604-44-4-4-444-400-404400000000000000000000000000000000000000000000000−22220
χ614-4-4-444-4404-40400-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ624-4-4-444-4404-40400-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ634-4-4-444-440-440-400404-4-4400000000000000000000000000000000000000000000
χ644-4-4-444-440-440-40040-444-400000000000000000000000000000000000000000000
χ658-8-888-88-8000000000000000000000000000000000000000000000000000000000

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