Finite Group Databasebeta

← Group #93031

Character table — Group #93031

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order122222222222444422224488888888448888161616161616161616161616161616164444444444444444
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
χ51111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ61111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111-1-1-11-111-1-1-1-11111-1-11-1-1-1-1-111111-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111-1-1-11-111-1-1-1-11111-1-11-1-1-1-1-111111-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111-1-1-11-111-1-1-1-11111-1-11-1-1-1-1-111111-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111-1-1-11-111-1-1-1-11111-1-11-1-1-1-1-111111-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111-1-1-11-111-1-1-1-111-1-1111-11111-1-1-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1
χ14111-1-1-11-111-1-1-1-111-1-1111-11111-1-1-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-111
χ15111-1-1-11-111-1-1-1-111-1-1111-11111-1-1-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii11-1-1-1-111
χ16111-1-1-11-111-1-1-1-111-1-1111-11111-1-1-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-22222222222-2-2-2-2-2-200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-200000000-2-2000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-2-2-22222-2-200000000-2-20000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-200000000220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-200000000220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ2322222222-2-2-2-2-2-2-2-20000222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ2422222222-2-2-2-2-2-2-2-20000222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ2522222222-2-2-2-2-2-2-2-2000022−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ2622222222-2-2-2-2-2-2-2-2000022−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ27222-2-2-22-222-2-222-2-222-2-2-2200000000-22000022−2−2−2−22222−2−2−2−2220000000000000000
χ28222-2-2-22-222-2-222-2-222-2-2-2200000000-220000−2−22222−2−2−2−22222−2−20000000000000000
χ29222-2-2-22-222-2-222-2-2-2-222-22000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ30222-2-2-22-222-2-222-2-2-2-222-22000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ31222-2-2-22-222-2-2-2-22222-2-22-22222-2-2-2-22-2-2-22200000000000000000000000000000000
χ32222-2-2-22-222-2-2-2-222-2-2222-2-2-2-2-22222-22-2-22200000000000000000000000000000000
χ33222-2-2-22-2-2-22222-2-200002-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i
χ34222-2-2-22-2-2-22222-2-200002-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i
χ35222-2-2-22-2-2-22222-2-200002-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i
χ36222-2-2-22-2-2-22222-2-200002-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i
χ3722-222-2-2-22-22-200002-22-2002−22−22−22−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ3822-222-2-2-22-22-200002-22-2002−22−22−22−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ3922-222-2-2-22-22-200002-22-200−22−22−22−2200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ4022-222-2-2-22-22-200002-22-200−22−22−22−2200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ4122-222-2-2-22-22-20000-22-22002−22−22−22−200−22−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ4222-222-2-2-22-22-20000-22-22002−22−22−22−200−22−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ4322-222-2-2-22-22-20000-22-2200−22−22−22−22002−22−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000000000
χ4422-222-2-2-22-22-20000-22-2200−22−22−22−22002−22−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000000000
χ4522-2-2-22-222-2-2200002-2-22002−22−2−22−2200−222−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ4622-2-2-22-222-2-2200002-2-22002−22−2−22−2200−222−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ4722-2-2-22-222-2-2200002-2-2200−22−222−22−2002−2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ4822-2-2-22-222-2-2200002-2-2200−22−222−22−2002−2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ4922-2-2-22-222-2-220000-222-2002−22−2−22−22002−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000000000
χ5022-2-2-22-222-2-220000-222-2002−22−2−22−22002−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000000000
χ5122-2-2-22-222-2-220000-222-200−22−222−22−200−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ5222-2-2-22-222-2-220000-222-200−22−222−22−200−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ5344444444-4-4-4-444440000-4-40000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4-444-4-4440000-440000000000000000000000000000000000000000000000
χ5544-444-4-4-4-44-4400000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5644-444-4-4-4-44-440000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5744-4-4-44-44-444-400000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5844-4-4-44-44-444-40000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ594-4-44-444-400004-44-400000000000000000000000000000000000000002i−2i2i−2i00000000
χ604-4-44-444-400004-44-40000000000000000000000000000000000000000−2i2i−2i2i00000000
χ614-4-44-444-40000-44-440000000000000000000000000000000000002i−2i2i−2i000000000000
χ624-4-44-444-40000-44-44000000000000000000000000000000000000−2i2i−2i2i000000000000
χ634-4-4-44-44400004-4-440000000000000000000000000000000000002-2-22000000000000
χ644-4-4-44-44400004-4-44000000000000000000000000000000000000-222-2000000000000
χ654-4-4-44-4440000-444-400000000000000000000000000000000000000002-2-2200000000
χ664-4-4-44-4440000-444-40000000000000000000000000000000000000000-222-200000000
χ678-888-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.