Finite Group Databasebeta

← Group #136196

Character table — Group #136196

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order122222222222444444444488888888448888161616161616161616161616161616164444444444444444
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
χ51111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911-11-11-1-11-1-111-11-1ii−i−i1-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−ii−i1-1i−i1-1ii−i−i11-1-1
χ1011-11-11-1-11-1-111-11-1ii−i−i1-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i−ii-11−ii-11−i−iii-1-111
χ1111-11-11-1-11-1-111-11-1ii−i−i1-111-1-111-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiiii−i1-1i−i1-1−i−iii-1-111
χ1211-11-11-1-11-1-111-11-1ii−i−i1-111-1-111-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiii−ii-11−ii-11ii−i−i11-1-1
χ1311-11-11-1-11-1-111-11-1−i−iii1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiiii−i-11i−i-11ii−i−i-1-111
χ1411-11-11-1-11-1-111-11-1−i−iii1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii−ii1-1−ii1-1−i−iii11-1-1
χ1511-11-11-1-11-1-111-11-1−i−iii1-111-1-111-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−ii−i-11i−i-11−i−iii11-1-1
χ1611-11-11-1-11-1-111-11-1−i−iii1-111-1-111-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−i−ii1-1−ii1-1ii−i−i-1-111
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
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
χ21222222222222-2-2-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-222220000-2-222-2-2-2-2220000000000000000000000002200-2-200000000
χ2422222222-2-2-2-222220000-2-222-2-2-2-222000000000000000000000000-2-2002200000000
χ2522222222-2-2-2-222220000-2-2-2-22222-2-200000000000000000000002200-2-20000000000
χ2622222222-2-2-2-222220000-2-2-2-22222-2-20000000000000000000000-2-200220000000000
χ27222-2-2-2-22-22-2200002-22-2002−22−22−22−2002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ28222-2-2-2-22-22-2200002-22-2002−22−22−22−2002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ29222-2-2-2-22-22-2200002-22-200−22−22−22−2200−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ30222-2-2-2-22-22-2200002-22-200−22−22−22−2200−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ31222-2-2-2-22-22-220000-22-22002−22−22−22−200−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ32222-2-2-2-22-22-220000-22-22002−22−22−22−200−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ33222-2-2-2-22-22-220000-22-2200−22−22−22−22002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ34222-2-2-2-22-22-220000-22-2200−22−22−22−22002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ3522-22-22-2-22-2-222-22-22i2i−2i−2i2-2-2-222-2-2222i−2i−2i−2i2i2i00000000000000000000000000000000
χ3622-22-22-2-22-2-222-22-2−2i−2i2i2i2-2-2-222-2-222−2i2i2i2i−2i−2i00000000000000000000000000000000
χ3722-22-22-2-22-2-22-22-222i2i−2i−2i-2200000000−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ3822-22-22-2-22-2-22-22-222i2i−2i−2i-2200000000−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ3922-22-22-2-22-2-22-22-22−2i−2i2i2i-22000000002i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ4022-22-22-2-22-2-22-22-22−2i−2i2i2i-22000000002i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ4122-22-22-2-2-222-22-22-20000-222222-2-2-2-20000000000000000000000002-200-2200000000
χ4222-22-22-2-2-222-22-22-20000-222222-2-2-2-2000000000000000000000000-22002-200000000
χ4322-22-22-2-2-222-22-22-20000-22-2-2-2-2222200000000000000000000002i−2i00−2i2i0000000000
χ4422-22-22-2-2-222-22-22-20000-22-2-2-2-222220000000000000000000000−2i2i002i−2i0000000000
χ4522-2-22-22-2-2-22200002i−2i−2i2i002−2−222−2−2200i2−i2−i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ4622-2-22-22-2-2-22200002i−2i−2i2i002−2−222−2−2200i2−i2−i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ4722-2-22-22-2-2-22200002i−2i−2i2i00−222−2−222−200−i2i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ4822-2-22-22-2-2-22200002i−2i−2i2i00−222−2−222−200−i2i2i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ4922-2-22-22-2-2-2220000−2i2i2i−2i002−2−222−2−2200−i2i2i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ5022-2-22-22-2-2-2220000−2i2i2i−2i002−2−222−2−2200−i2i2i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ5122-2-22-22-2-2-2220000−2i2i2i−2i00−222−2−222−200i2−i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ5222-2-22-22-2-2-2220000−2i2i2i−2i00−222−2−222−200i2−i2−i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-4-4-4-444-44-4000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ55444-4-4-4-444-44-40000000000−222222−2222−22−222200000000000000000000000000000000000000
χ5644-44-44-4-4-444-4-44-4400004-40000000000000000000000000000000000000000000000
χ5744-4-44-44-444-4-4000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ5844-4-44-44-444-4-40000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ594-44-4-444-400004-4-440000000000000000000000000000000000000000000000002i−2i2i−2i
χ604-44-4-444-400004-4-44000000000000000000000000000000000000000000000000−2i2i−2i2i
χ614-44-4-444-40000-444-4000000000000000000000000000000000000000000002i−2i2i−2i0000
χ624-44-4-444-40000-444-400000000000000000000000000000000000000000000−2i2i−2i2i0000
χ634-4-4-444-44000044-4-40000000000000000000000000000000000000000000000002i−2i−2i2i
χ644-4-4-444-44000044-4-4000000000000000000000000000000000000000000000000−2i2i2i−2i
χ654-4-4-444-440000-4-444000000000000000000000000000000000000000000002-2-220000
χ664-4-4-444-440000-4-44400000000000000000000000000000000000000000000-222-20000
χ678-8888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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