Finite Group Databasebeta

← Group #138271

Character table — Group #138271

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244442222444444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ61111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-222-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-222222222-2-222-2-200000000000000000000000000000000
χ21222-2-2-2-222-22-2000000000022-2-22i2i−2i−2i002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ22222-2-2-2-222-22-2000000000022-2-22i2i−2i−2i002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ23222-2-2-2-222-22-2000000000022-2-2−2i−2i2i2i00−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ24222-2-2-2-222-22-2000000000022-2-2−2i−2i2i2i00−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ25222-2-2-2-222-22-20000000000-2-2222i2i−2i−2i00−2i2i001+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i0000000000000000
χ26222-2-2-2-222-22-20000000000-2-2222i2i−2i−2i00−2i2i00−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i0000000000000000
χ27222-2-2-2-222-22-20000000000-2-222−2i−2i2i2i002i−2i001−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i0000000000000000
χ28222-2-2-2-222-22-20000000000-2-222−2i−2i2i2i002i−2i00−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i0000000000000000
χ292-2-222-2-2222-2-222-2-200002-200002i−2i2i−2i00002i−2i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i0000000000000000
χ302-2-222-2-2222-2-222-2-200002-200002i−2i2i−2i00002i−2i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i0000000000000000
χ312-2-222-2-2222-2-222-2-200002-20000−2i2i−2i2i0000−2i2i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000000000000000
χ322-2-222-2-2222-2-222-2-200002-20000−2i2i−2i2i0000−2i2i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000000000000000
χ332-2-222-2-2222-2-2-2-2220000-2200002i−2i2i−2i0000−2i2i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i0000000000000000
χ342-2-222-2-2222-2-2-2-2220000-2200002i−2i2i−2i0000−2i2i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i0000000000000000
χ352-2-222-2-2222-2-2-2-2220000-220000−2i2i−2i2i00002i−2i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i0000000000000000
χ362-2-222-2-2222-2-2-2-2220000-220000−2i2i−2i2i00002i−2i−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i0000000000000000
χ372-2-222-2-22-2-22222-2-222-2-2-222-22-20000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ382-2-222-2-22-2-22222-2-222-2-2-222-22-20000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ392-2-222-2-22-2-22222-2-2-2-222-22-22-2200000000000000000000000000000000002−22−2−22−22
χ402-2-222-2-22-2-22222-2-2-2-222-22-22-220000000000000000000000000000000000−22−222−22−2
χ412-2-222-2-22-2-222-2-22222-2-22-2-22-220000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ422-2-222-2-22-2-222-2-22222-2-22-2-22-220000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ432-2-222-2-22-2-222-2-222-2-2222-22-22-200000000000000000000000000000000002−2−22−222−2
χ442-2-222-2-22-2-222-2-222-2-2222-22-22-20000000000000000000000000000000000−222−22−2−22
χ452-2-2-2-22222-2-2200002-22-20000002-2-222-2000000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ462-2-2-2-22222-2-2200002-22-20000002-2-222-200000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ472-2-2-2-22222-2-2200002-22-2000000-222-2-2200002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ482-2-2-2-22222-2-2200002-22-2000000-222-2-220000−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ492-2-2-2-22222-2-220000-22-220000002-2-22-2200002-2-2200002-2-2200000000000000000000
χ502-2-2-2-22222-2-220000-22-220000002-2-22-220000-222-20000-222-200000000000000000000
χ512-2-2-2-22222-2-220000-22-22000000-222-22-2000000002-2-2200002-2-220000000000000000
χ522-2-2-2-22222-2-220000-22-22000000-222-22-200000000-222-20000-222-20000000000000000
χ5344444444-4-4-4-444440000-4-40000000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ55444-4-4-4-44-44-4400004-4-44000000000000000000000000000000000000000000000000
χ56444-4-4-4-44-44-440000-444-4000000000000000000000000000000000000000000000000
χ5744-4-444-4-400004i−4i4i−4i00000000000000000000000000000000000000002-22i−2i00000000
χ5844-4-444-4-400004i−4i4i−4i0000000000000000000000000000000000000000-22−2i2i00000000
χ5944-4-444-4-40000−4i4i−4i4i00000000000000000000000000000000000000002-2−2i2i00000000
χ6044-4-444-4-40000−4i4i−4i4i0000000000000000000000000000000000000000-222i−2i00000000
χ614-44-44-44-400004i−4i−4i4i0000000000000000000000000000000000002-22i−2i000000000000
χ624-44-44-44-400004i−4i−4i4i000000000000000000000000000000000000-22−2i2i000000000000
χ634-44-44-44-40000−4i4i4i−4i0000000000000000000000000000000000002-2−2i2i000000000000
χ644-44-44-44-40000−4i4i4i−4i000000000000000000000000000000000000-222i−2i000000000000
χ654-4-4-4-4444-444-400000000004-4-44000000000000000000000000000000000000000000
χ664-4-4-4-4444-444-40000000000-444-4000000000000000000000000000000000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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