Finite Group Databasebeta

← Group #274191

Character table — Group #274191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888882444488888888888822448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ511111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-11
χ611111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-11
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ11111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1
χ12111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-11111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-11111-1-1-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-111-1-1-1-11111-11
χ17222222222-2-222-2-22-2-22222-2-2-2-222-2-22200000000-222-2-200000000000000000000000000
χ18222222222-2-222-2-22-2-22222-2-2-2-2-2-222-2-2000000002-2-22200000000000000000000000000
χ19222222222-2-222-2-22-2-2-2-2-2-2222222-2-22200000000-2-2-22200000000000000000000000000
χ20222222222-2-222-2-22-2-2-2-2-2-22222-2-222-2-200000000222-2-200000000000000000000000000
χ2122222222-222-2-222-2-2-2000000002222-2-222222222-20000-2-2-2-20000000000000000000000
χ2222222222-222-2-222-2-2-2000000002222-2-2-2-2-2-2-2-2-2-2-2000022220000000000000000000000
χ2322222222-222-2-222-2-2-200000000-2-2-2-2222222-2-2-2-220000-2-2220000000000000000000000
χ2422222222-222-2-222-2-2-200000000-2-2-2-222-2-2-2-222222000022-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2220000000022-2-2-2-2000000002000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2220000000022-2-2-2-200000000200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-22200000000-2-2222200000000-2000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-22200000000-2-2222200000000-200000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ292222-2-2-2-2200-2-200200000022-2-22i−2i002i−2ii2i2−i2−i222−2−20002i−2ii2−i22−2i2−i2i2−i22−22−200000000000000
χ302222-2-2-2-2200-2-200200000022-2-22i−2i002i−2i−i2−i2i2i2−2−2220002i−2i−i2i2−22−i2i2−i2i2−22−2200000000000000
χ312222-2-2-2-2200-2-200200000022-2-2−2i2i00−2i2ii2i2−i2−i2−2−222000−2i2ii2−i2−22i2−i2i2−i2−22−2200000000000000
χ322222-2-2-2-2200-2-200200000022-2-2−2i2i00−2i2i−i2−i2i2i222−2−2000−2i2i−i2i22−2−i2i2−i2i22−22−200000000000000
χ332222-2-2-2-2200-2-2002000000-2-2222i−2i002i−2ii2i2−i2−i222−2−2000−2i2ii2−i22−2−i2i2−i2i2−22−2200000000000000
χ342222-2-2-2-2200-2-2002000000-2-2222i−2i002i−2i−i2−i2i2i2−2−222000−2i2i−i2i2−22i2−i2i2−i22−22−200000000000000
χ352222-2-2-2-2200-2-2002000000-2-222−2i2i00−2i2ii2i2−i2−i2−2−2220002i−2ii2−i2−22−i2i2−i2i22−22−200000000000000
χ362222-2-2-2-2200-2-2002000000-2-222−2i2i00−2i2i−i2−i2i2i222−2−20002i−2i−i2i22−2i2−i2i2−i2−22−2200000000000000
χ372222-2-2-2-2-2002200-2002i2i−2i−2i00002i−2i00−2i2ii2i2−i2−i222−2−202-200−i2i2−222−2−22−i2i2i2−i200000000000000
χ382222-2-2-2-2-2002200-2002i2i−2i−2i00002i−2i00−2i2i−i2−i2i2i2−2−22202-200i2−i22−2−222−2i2−i2−i2i200000000000000
χ392222-2-2-2-2-2002200-2002i2i−2i−2i0000−2i2i002i−2ii2i2−i2−i2−2−2220-2200−i2i22−22−2−22i2−i2−i2i200000000000000
χ402222-2-2-2-2-2002200-2002i2i−2i−2i0000−2i2i002i−2i−i2−i2i2i222−2−20-2200i2−i2−22−222−2−i2i2i2−i200000000000000
χ412222-2-2-2-2-2002200-200−2i−2i2i2i00002i−2i00−2i2ii2i2−i2−i222−2−20-2200−i2i2−22−222−2i2−i2−i2i200000000000000
χ422222-2-2-2-2-2002200-200−2i−2i2i2i00002i−2i00−2i2i−i2−i2i2i2−2−2220-2200i2−i22−22−2−22−i2i2i2−i200000000000000
χ432222-2-2-2-2-2002200-200−2i−2i2i2i0000−2i2i002i−2ii2i2−i2−i2−2−22202-200−i2i22−2−222−2−i2i2i2−i200000000000000
χ442222-2-2-2-2-2002200-200−2i−2i2i2i0000−2i2i002i−2i−i2−i2i2i222−2−202-200i2−i2−222−2−22i2−i2−i2i200000000000000
χ4522-2-22-22-222-22-22-2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000002-22i−2i00000000
χ4622-2-22-22-222-22-22-2-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000-22−2i2i00000000
χ4722-2-22-22-222-22-22-2-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000002-2−2i2i00000000
χ4822-2-22-22-222-22-22-2-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000-222i−2i00000000
χ4922-2-22-22-22-222-2-22-2-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000002-20000002i−2i0000
χ5022-2-22-22-22-222-2-22-2-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000-22000000−2i2i0000
χ5122-2-22-22-22-222-2-22-2-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000002-2000000−2i2i0000
χ5222-2-22-22-22-222-2-22-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000-220000002i−2i0000
χ5344-4-44-44-4-44-4-444-44-4400000000000000000000000000000000000000000000000000000
χ5444-4-44-44-4-4-44-44-4444-400000000000000000000000000000000000000000000000000000
χ5544-4-4-44-44400-4400-40000004i−4i−4i4i000000000000000000000000000000000000000000000
χ5644-4-4-44-44400-4400-4000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ5744-4-4-44-44-4004-4004004-4-440000000000000000000000000000000000000000000000000
χ5844-4-4-44-44-4004-400400-444-40000000000000000000000000000000000000000000000000
χ594-44-444-4-4000000000000000000004i−4i002i2−2i22i2−2i222−2222−220000000000000000000000000000000
χ604-44-444-4-4000000000000000000004i−4i00−2i22i2−2i22i2−2222−22220000000000000000000000000000000
χ614-44-444-4-400000000000000000000−4i4i002i2−2i22i2−2i2−2222−22220000000000000000000000000000000
χ624-44-444-4-400000000000000000000−4i4i00−2i22i2−2i22i222−2222−220000000000000000000000000000000
χ634-44-4-4-44404-400-440000000000000000000004-4-440000000000000000000000000000000
χ644-44-4-4-44404-400-44000000000000000000000-444-40000000000000000000000000000000
χ654-44-4-4-4440-44004-4000000000000000004-4-4400000000000000000000000000000000000
χ664-44-4-4-4440-44004-400000000000000000-444-400000000000000000000000000000000000
χ674-4-44-444-404400-4-40000000000000000000000000000000000000000000000002i2−2i2000000
χ684-4-44-444-404400-4-4000000000000000000000000000000000000000000000000−2i22i2000000
χ694-4-44-444-40-4-40044000000000000000000000000000000000000000000000000000022−2200
χ704-4-44-444-40-4-400440000000000000000000000000000000000000000000000000000−222200
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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