Finite Group Databasebeta

← Group #270024

Character table — Group #270024

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-11-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-1
χ71111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1111-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-11111-1-11
χ911111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-11
χ1011111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-111111111-1-11-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-11111-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11-1-1111-1-1-1-1111
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-111-11111-1-1-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-111-1-11-1-111-1-1-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-111-1-1111
χ17222222222-2-2222-2-2-20000-222222222-2-20000-2-200000000000000-2000000000000
χ18222222222-2-2222-2-2-20000-22222-2-2-2-2220000-2-2000000000000002000000000000
χ19222222222-2-2222-2-2-20000-2-2-2-2-222-2-22200002200000000000000-2000000000000
χ20222222222-2-2222-2-2-20000-2-2-2-2-2-2-222-2-2000022000000000000002000000000000
χ2122222222-222-2-2-222-22222-2000000000022-2-200000022-2-200000000000-20000000
χ2222222222-222-2-2-222-22222-20000000000-2-2-2-2000000-2-2220000000000020000000
χ2322222222-222-2-2-222-2-2-2-2-2-200000000002222000000-2-22200000000000-20000000
χ2422222222-222-2-2-222-2-2-2-2-2-20000000000-2-22200000022-2-20000000000020000000
χ252-222-2-2-2202-20002-202i2i−2i−2i0i2i2−i2−i20000002i−2i00i2−i222−2−22-200i2i2−i2−i2000000002−200000
χ262-222-2-2-2202-20002-202i2i−2i−2i0i2i2−i2−i2000000−2i2i00i2−i222−2−2-2200−i2−i2i2i200000000−2200000
χ272-222-2-2-2202-20002-202i2i−2i−2i0−i2−i2i2i20000002i−2i00−i2i2−2−2222-200−i2−i2i2i200000000−2200000
χ282-222-2-2-2202-20002-202i2i−2i−2i0−i2−i2i2i2000000−2i2i00−i2i2−2−222-2200i2i2−i2−i2000000002−200000
χ292-222-2-2-2202-20002-20−2i−2i2i2i0i2i2−i2−i20000002i−2i00i2−i2−2−222-2200−i2−i2i2i2000000002−200000
χ302-222-2-2-2202-20002-20−2i−2i2i2i0i2i2−i2−i2000000−2i2i00i2−i2−2−2222-200i2i2−i2−i200000000−2200000
χ312-222-2-2-2202-20002-20−2i−2i2i2i0−i2−i2i2i20000002i−2i00−i2i222−2−2-2200i2i2−i2−i200000000−2200000
χ322-222-2-2-2202-20002-20−2i−2i2i2i0−i2−i2i2i2000000−2i2i00−i2i222−2−22-200−i2−i2i2i2000000002−200000
χ332-2-2-2-2222222-22-2-2-220000-20000002-22-20000002i−2i2i−2i000000000002i−2i0000000000
χ342-2-2-2-2222222-22-2-2-220000-20000002-22-2000000−2i2i−2i2i00000000000−2i2i0000000000
χ352-2-2-2-2222222-22-2-2-220000-2000000-22-220000002i−2i2i−2i00000000000−2i2i0000000000
χ362-2-2-2-2222222-22-2-2-220000-2000000-22-22000000−2i2i−2i2i000000000002i−2i0000000000
χ372-2-2-2-22222-2-2-22-222-22-22-220000002-2-22002-200000000000000000002-200000000
χ382-2-2-2-22222-2-2-22-222-22-22-22000000-222-2002-20000000000000000000-2200000000
χ392-2-2-2-22222-2-2-22-222-2-22-2220000002-2-2200-220000000000000000000-2200000000
χ402-2-2-2-22222-2-2-22-222-2-22-222000000-222-200-2200000000000000000002-200000000
χ412-2-2-2-2222-2-2-22-222222-22-2-2000000000000-22000000000000002-200000000002-20
χ422-2-2-2-2222-2-2-22-222222-22-2-2000000000000-2200000000000000-220000000000-220
χ432-2-2-2-2222-2-2-22-22222-22-22-20000000000002-2000000000000002-20000000000-220
χ442-2-2-2-2222-2-2-22-22222-22-22-20000000000002-200000000000000-2200000000002-20
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-44-4-44004-4-4000000004-44-4000000000000000000000000000000000000000
χ47444-4-44-4-44004-4-400000000-44-44000000000000000000000000000000000000000
χ48444-4-44-4-4-400-444000000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ49444-4-44-4-4-400-44400000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ5044-4-44-4-4404-4000-4400000000000000000000002i2−2i2−2i22i200000000000000000000000
χ5144-4-44-4-4404-4000-440000000000000000000000−2i22i22i2−2i200000000000000000000000
χ5244-4-44-4-440-440004-404i−4i−4i4i00000000000000000000000000000000000000000000
χ5344-4-44-4-440-440004-40−4i4i4i−4i00000000000000000000000000000000000000000000
χ544-444-4-4-440-44000-440000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ554-444-4-4-440-44000-44000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ564-44-44-44-4000000000000002i2−2i2−2i22i20000000000000000002i2−2i22-2-22000000000000000
χ574-44-44-44-4000000000000002i2−2i2−2i22i2000000000000000000−2i22i2-222-2000000000000000
χ584-44-44-44-400000000000000−2i22i22i2−2i20000000000000000002i2−2i2-222-2000000000000000
χ594-44-44-44-400000000000000−2i22i22i2−2i2000000000000000000−2i22i22-2-22000000000000000
χ604-4-4444-4-4400-4-440000000000004i−4i0000000000000000000000000000000000000
χ614-4-4444-4-4400-4-44000000000000−4i4i0000000000000000000000000000000000000
χ624-4-4444-4-4-40044-400000000000000000000000000000000000000000000002i2−2i2000
χ634-4-4444-4-4-40044-40000000000000000000000000000000000000000000000−2i22i2000
χ644-4-4-4-4444-4444-44-4-4-4000040000000000000000000000000000000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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