Finite Group Databasebeta

← Group #310568

Character table — Group #310568

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888224444448888882
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-11111111111111111-1-1-1-1-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-1-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1111111-1-1-1
χ911111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11
χ1011111111111111111-1-1-1-1111111111-1-111-1-1111111-1-1-1-11111-1-11-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-111111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111111-1-11-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-11111-1-111-1
χ17222222222-22-2-222-2-20000-2222222-2-200-2-200-2-2000000000000002000000000000
χ18222222222-22-2-222-2-20000-22222-2-222002200-2-200000000000000-2000000000000
χ19222222222-22-2-222-2-20000-2-2-2-2-2222200-2-2002200000000000000-2000000000000
χ20222222222-22-2-222-2-20000-2-2-2-2-2-2-2-2-200220022000000000000002000000000000
χ2122222222-22-222-2-22-22222-200000000-2-200220022-2-20000000000000-2000000000
χ2222222222-22-222-2-22-22222-200000000-2-200-2-200-2-22200000000000002000000000
χ2322222222-22-222-2-22-2-2-2-2-2-20000000022002200-2-2220000000000000-2000000000
χ2422222222-22-222-2-22-2-2-2-2-2-2000000002200-2-20022-2-200000000000002000000000
χ252-222-2-22-222-2-2-22-2220000-200002i−2i00002i−2i0000000022-2-200000002i−2i0000000000
χ262-222-2-22-222-2-2-22-2220000-200002i−2i00002i−2i00000000-2-2220000000−2i2i0000000000
χ272-222-2-22-222-2-2-22-2220000-20000−2i2i0000−2i2i0000000022-2-20000000−2i2i0000000000
χ282-222-2-22-222-2-2-22-2220000-20000−2i2i0000−2i2i00000000-2-22200000002i−2i0000000000
χ292-222-2-22-22-2-2222-2-2-22i2i−2i−2i200002i−2i002i−2i−2i2i00000000000000002-20000000000000
χ302-222-2-22-22-2-2222-2-2-22i2i−2i−2i20000−2i2i002i−2i2i−2i0000000000000000-220000000000000
χ312-222-2-22-22-2-2222-2-2-2−2i−2i2i2i200002i−2i00−2i2i−2i2i0000000000000000-220000000000000
χ322-222-2-22-22-2-2222-2-2-2−2i−2i2i2i20000−2i2i00−2i2i2i−2i00000000000000002-20000000000000
χ332-222-2-22-2-2-2222-22-222i2i−2i−2i-200000000−2i2i0000000000000000000000002-2002i−2i000
χ342-222-2-22-2-2-2222-22-222i2i−2i−2i-200000000−2i2i000000000000000000000000-2200−2i2i000
χ352-222-2-22-2-2-2222-22-22−2i−2i2i2i-2000000002i−2i0000000000000000000000002-200−2i2i000
χ362-222-2-22-2-2-2222-22-22−2i−2i2i2i-2000000002i−2i000000000000000000000000-22002i−2i000
χ372-2-2-2222-20202-200-202i−2i2i−2i022−2−2000000002i−2i2−22-200i2−i2i2−i222−2−200000000i2−i200000
χ382-2-2-2222-20202-200-202i−2i2i−2i022−2−200000000−2i2i2−2-2200i2−i2i2−i2−2−22200000000−i2i200000
χ392-2-2-2222-20202-200-202i−2i2i−2i0−2−222000000002i−2i−222-200−i2i2−i2i2−2−22200000000−i2i200000
χ402-2-2-2222-20202-200-202i−2i2i−2i0−2−22200000000−2i2i−22-2200−i2i2−i2i222−2−200000000i2−i200000
χ412-2-2-2222-20202-200-20−2i2i−2i2i022−2−2000000002i−2i2−2-2200−i2i2−i2i2−2−22200000000i2−i200000
χ422-2-2-2222-20202-200-20−2i2i−2i2i022−2−200000000−2i2i2−22-200−i2i2−i2i222−2−200000000−i2i200000
χ432-2-2-2222-20202-200-20−2i2i−2i2i0−2−222000000002i−2i−22-2200i2−i2i2−i222−2−200000000−i2i200000
χ442-2-2-2222-20202-200-20−2i2i−2i2i0−2−22200000000−2i2i−222-200i2−i2i2−i2−2−22200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-4000000000000002i2−2i22i2−2i2000000000000002i2−2i200002-22-2000000000000000
χ47444-44-4-4-4000000000000002i2−2i22i2−2i200000000000000−2i22i20000-22-22000000000000000
χ48444-44-4-4-400000000000000−2i22i2−2i22i2000000000000002i2−2i20000-22-22000000000000000
χ49444-44-4-4-400000000000000−2i22i2−2i22i200000000000000−2i22i200002-22-2000000000000000
χ5044-44-44-4-440-400-4400000000000004i−4i00000000000000000000000000000000000
χ5144-44-44-4-440-400-440000000000000−4i4i00000000000000000000000000000000000
χ5244-44-44-4-4-404004-4000000000000000000000000000000000000000000000002i2−2i20
χ5344-44-44-4-4-404004-400000000000000000000000000000000000000000000000−2i22i20
χ5444-4-4-4-444040-4400-4000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ5544-4-4-4-444040-4400-400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5644-4-4-4-4440-404-400404-4-4400000000000000000000000000000000000000000000
χ5744-4-4-4-4440-404-40040-444-400000000000000000000000000000000000000000000
χ584-444-4-44-4-444-4-4-444-4000040000000000000000000000000000000000000000000
χ594-4-444-4-4440400-4-400000004i−4i−4i4i000000000000000000000000000000000000000
χ604-4-444-4-4440400-4-40000000−4i4i4i−4i000000000000000000000000000000000000000
χ614-4-444-4-44-40-40044000000000000000000000000000000022−22−2222000000000000000
χ624-4-444-4-44-40-400440000000000000000000000000000000−222222−22000000000000000
χ634-4-4-4444-40-40-440040000002222−22−220000000000−2222000000000000000000000000000
χ644-4-4-4444-40-40-44004000000−22−222222000000000022−22000000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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