Finite Group Databasebeta

← Group #129931

Character table — Group #129931

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order1222222222444444444488884488888822444444444444441616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-11111-1-111-1-1-1-11-1111-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111-1-111-1-1-1-11-1111-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-11111-1-111-1-1-1-1-11-1-1-11111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-11111-1-111-1-1-1-1-11-1-1-1111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-11-11-1-111-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-11-11-1-111-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-11-111-1-11ii−i−iii−i−i−i−iii−i−iii
χ12111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-11-111-1-11−i−iii−i−iiiii−i−iii−i−i
χ13111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-1-11ii−i−i−i−iiiii−i−i−i−iii
χ14111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-1-11−i−iiiii−i−i−i−iiiii−i−i
χ15111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11111-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11111-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-200002-200000000000000000000002−22−22−22−2
χ202222222222-2-2-2-2-2-222-2-200002-20000000000000000000000−22−22−22−22
χ212222222222-2-2-2-2-2-2-2-2220000-2200000000000000000000002−22−2−22−22
χ222222222222-2-2-2-2-2-2-2-2220000-220000000000000000000000−22−222−22−2
χ23222222-2-2-2-22222-2-222222222-2-2-2-2-2-222000000000000000000000000
χ24222222-2-2-2-22222-2-2-2-2-2-2222222-2-222-2-2000000000000000000000000
χ25222222-2-2-2-2-2-2-2-22222-2-20000-220000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ26222222-2-2-2-2-2-2-2-22222-2-20000-220000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ27222222-2-2-2-2-2-2-2-222-2-22200002-20000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ28222222-2-2-2-2-2-2-2-222-2-22200002-20000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ292222-2-22-22-2-2-2222-2000022-2-2002-20000020002-2-20000000000000000
χ302222-2-22-22-2-2-2222-2000022-2-2002-200000-2000-2220000000000000000
χ312222-2-22-22-2-2-2222-20000-2-22200-22000020-22-20000000000000000000
χ322222-2-22-22-2-2-2222-20000-2-22200-220000-202-220000000000000000000
χ332222-2-2-22-22-2-222-22000022-2-200-22000020-2-220000000000000000000
χ342222-2-2-22-22-2-222-22000022-2-200-220000-2022-20000000000000000000
χ352222-2-2-22-22-2-222-220000-2-222002-2000002000-22-20000000000000000
χ362222-2-2-22-22-2-222-220000-2-222002-200000-20002-220000000000000000
χ3722-2-22-200002-22-2002i−2i2i−2i2i−2i2i−2i0000002-2000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ3822-2-22-200002-22-2002i−2i2i−2i2i−2i2i−2i0000002-200000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ3922-2-22-200002-22-2002i−2i2i−2i−2i2i−2i2i000000-22000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ4022-2-22-200002-22-2002i−2i2i−2i−2i2i−2i2i000000-2200000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ4122-2-22-200002-22-200−2i2i−2i2i2i−2i2i−2i000000-22000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ4222-2-22-200002-22-200−2i2i−2i2i2i−2i2i−2i000000-2200000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ4322-2-22-200002-22-200−2i2i−2i2i−2i2i−2i2i0000002-2000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ4422-2-22-200002-22-200−2i2i−2i2i−2i2i−2i2i0000002-200000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ454444-4-44-44-444-4-4-440000000000000000000000000000000000000000
χ464444-4-4-44-4444-4-44-40000000000000000000000000000000000000000
χ4744-4-44-40000-44-44004i−4i−4i4i000000000000000000000000000000000000
χ4844-4-44-40000-44-4400−4i4i4i−4i000000000000000000000000000000000000
χ4944-4-4-4400004-4-44000000000000004i−4i00000000000000000000000000
χ5044-4-4-4400004-4-4400000000000000−4i4i00000000000000000000000000
χ5144-4-4-440000-444-40000004i−4i−4i4i00000000000000000000000000000000
χ5244-4-4-440000-444-4000000−4i4i4i−4i00000000000000000000000000000000
χ538-88-800080-80000000000000000000000000000000000000000000000
χ548-88-8000-8080000000000000000000000000000000000000000000000
χ558-8-880080-800000000000000000000000000000000000000000000000
χ568-8-8800-80800000000000000000000000000000000000000000000000

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