Finite Group Databasebeta

← Group #136124

Character table — Group #136124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12222222222244442222444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111
χ51111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1
χ911-1-111-1-111-1-11-1-1111-1-11-1ii−i−iii−i−iii−i−i1-1i−ii−i1-1i−i11-1-1ii−i−i11-1-1
χ1011-1-111-1-111-1-11-1-1111-1-11-1ii−i−iii−i−iii−i−i1-1−ii−ii1-1i−i-1-111−i−iii-1-111
χ1111-1-111-1-111-1-11-1-1111-1-11-1−i−iii−i−iii−i−iii1-1i−ii−i1-1−ii-1-111ii−i−i-1-111
χ1211-1-111-1-111-1-11-1-1111-1-11-1−i−iii−i−iii−i−iii1-1−ii−ii1-1−ii11-1-1−i−iii11-1-1
χ1311-1-111-1-111-1-11-1-11-1-1111-1ii−i−i−i−iiiii−i−i1-1i−ii−i-11−ii11-1-1−i−iii-1-111
χ1411-1-111-1-111-1-11-1-11-1-1111-1ii−i−i−i−iiiii−i−i1-1−ii−ii-11−ii-1-111ii−i−i11-1-1
χ1511-1-111-1-111-1-11-1-11-1-1111-1−i−iiiii−i−i−i−iii1-1i−ii−i-11i−i-1-111−i−iii11-1-1
χ1611-1-111-1-111-1-11-1-11-1-1111-1−i−iiiii−i−i−i−iii1-1−ii−ii-11i−i11-1-1ii−i−i-1-111
χ1722222222222222220000-2-222220000-2-2-2-2-2-200000000000000000000
χ1822222222222222220000-2-2-2-2-2-200002222-2-200000000000000000000
χ19222222222222-2-2-2-20000-220000222200002-2000000-2-2000000000000
χ20222222222222-2-2-2-20000-220000-2-2-2-200002-200000022000000000000
χ21222222222222-2-2-2-222222-2000000000000-220000-2-200000000000000
χ22222222222222-2-2-2-2-2-2-2-22-2000000000000-2200002200000000000000
χ2322-2-222-2-222-2-22-2-220000-222i2i−2i−2i0000−2i−2i2i2i-2200000000000000000000
χ2422-2-222-2-222-2-22-2-220000-22−2i−2i2i2i00002i2i−2i−2i-2200000000000000000000
χ2522-2-222-2-222-2-2-222-20000-2-200002i2i−2i−2i000022000000−2i2i000000000000
χ2622-2-222-2-222-2-2-222-20000-2-20000−2i−2i2i2i0000220000002i−2i000000000000
χ2722-2-222-2-222-2-2-222-222-2-222000000000000-2-20000-2200000000000000
χ2822-2-222-2-222-2-2-222-2-2-22222000000000000-2-200002-200000000000000
χ292-2222-2-2-2-222-2-22-220000002i−2i2i−2i0000000000000000000000i2−i2i2−i22−22−2
χ302-2222-2-2-2-222-2-22-220000002i−2i2i−2i0000000000000000000000−i2i2−i2i2−22−22
χ312-2222-2-2-2-222-2-22-22000000−2i2i−2i2i0000000000000000000000i2−i2i2−i2−22−22
χ322-2222-2-2-2-222-2-22-22000000−2i2i−2i2i0000000000000000000000−i2i2−i2i22−22−2
χ332-2-2-22-222-22-22-2-2220000002-2-2200000000000000000000002−2−222−2−22
χ342-2-2-22-222-22-22-2-2220000002-2-220000000000000000000000−222−2−222−2
χ352-2-2-22-222-22-22-2-222000000-222-200000000000000000000002−2−22−222−2
χ362-2-2-22-222-22-22-2-222000000-222-20000000000000000000000−222−22−2−22
χ3744444444-4-4-4-400000000000000000000000022-2-20000000000000000
χ3844444444-4-4-4-4000000000000000000000000-2-2220000000000000000
χ3944-4-444-4-4-4-4440000000000000000000000002i−2i−2i2i0000000000000000
χ4044-4-444-4-4-4-444000000000000000000000000−2i2i2i−2i0000000000000000
χ414-4444-4-4-44-4-44000000000000000000000000000000002-22-200000000
χ424-4444-4-4-44-4-4400000000000000000000000000000000-22-2200000000
χ434-4444-4-4-4-444-44-44-40000000000000000000000000000000000000000
χ444-44-4-444-4000000002-22-20000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ454-44-4-444-4000000002-22-2000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ464-44-4-444-400000000-22-220000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ474-44-4-444-400000000-22-22000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ484-4-44-44-44000000002-2-220000002-2-222-2-220000000000000000000000
χ494-4-44-44-44000000002-2-22000000-222-2-222-20000000000000000000000
χ504-4-44-44-4400000000-222-20000002-2-22-222-20000000000000000000000
χ514-4-44-44-4400000000-222-2000000-222-22-2-220000000000000000000000
χ524-4-4-44-4444-44-4000000000000000000000000000000002-2-2200000000
χ534-4-4-44-4444-44-400000000000000000000000000000000-222-200000000
χ544-4-4-44-444-44-4444-4-40000000000000000000000000000000000000000
χ55888-8-8-8-88000000000000000000000000000000000000000000000000
χ5688-88-8-88-8000000000000000000000000000000000000000000000000

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