Finite Group Databasebeta

← Group #129798

Character table — Group #129798

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444488888888
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
χ51111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-222-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ19222222222222-2-2-2-222222222-2-2-2-222-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-2-222-2-222000000000000000000000000
χ21222-2-22-2-222-2-222-2-222-2-20000002-2000000000000000000002−22−22−22−2
χ22222-2-22-2-222-2-222-2-222-2-20000002-200000000000000000000−22−22−22−22
χ23222-2-22-2-222-2-222-2-2-2-222000000-22000000000000000000002−22−2−22−22
χ24222-2-22-2-222-2-222-2-2-2-222000000-2200000000000000000000−22−222−22−2
χ25222-2-22-2-222-2-2-2-22222-2-2000000-2200000000000000000000i2−i2−i2i2i2−i2−i2i2
χ26222-2-22-2-222-2-2-2-22222-2-2000000-2200000000000000000000−i2i2i2−i2−i2i2i2−i2
χ27222-2-22-2-222-2-2-2-222-2-2220000002-200000000000000000000i2−i2−i2i2−i2i2i2−i2
χ28222-2-22-2-222-2-2-2-222-2-2220000002-200000000000000000000−i2i2i2−i2i2−i2−i2i2
χ29222-2-22-2-2-2-22200002-22-22i2i−2i−2i00002i−2i00000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ30222-2-22-2-2-2-22200002-22-22i2i−2i−2i00002i−2i0000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ31222-2-22-2-2-2-22200002-22-2−2i−2i2i2i0000−2i2i00000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ32222-2-22-2-2-2-22200002-22-2−2i−2i2i2i0000−2i2i0000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ33222-2-22-2-2-2-2220000-22-222i2i−2i−2i0000−2i2i00000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ34222-2-22-2-2-2-2220000-22-222i2i−2i−2i0000−2i2i0000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ35222-2-22-2-2-2-2220000-22-22−2i−2i2i2i00002i−2i00000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ36222-2-22-2-2-2-2220000-22-22−2i−2i2i2i00002i−2i0000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ372-2-2-2-22222-2-222-22-200002-22-22-2000000002-2002-20000000000000000
χ382-2-2-2-22222-2-222-22-200002-22-22-200000000-2200-220000000000000000
χ392-2-2-2-22222-2-222-22-20000-22-22-220000002-2002-2000000000000000000
χ402-2-2-2-22222-2-222-22-20000-22-22-22000000-2200-22000000000000000000
χ412-2-2-2-22222-2-22-22-2200002-22-2-220000002-200-22000000000000000000
χ422-2-2-2-22222-2-22-22-2200002-22-2-22000000-22002-2000000000000000000
χ432-2-2-2-22222-2-22-22-220000-22-222-2000000002-200-220000000000000000
χ442-2-2-2-22222-2-22-22-220000-22-222-200000000-22002-20000000000000000
χ4544444444-4-4-4-400004-4-44000000000000000000000000000000000000
χ4644444444-4-4-4-40000-444-4000000000000000000000000000000000000
χ474-4-4444-4-44-44-44-4-440000000000000000000000000000000000000000
χ484-4-4444-4-44-44-4-444-40000000000000000000000000000000000000000
χ494-4-4444-4-4-44-44000000004i−4i−4i4i00000000000000000000000000000000
χ504-4-4444-4-4-44-4400000000−4i4i4i−4i00000000000000000000000000000000
χ514-4-4-4-4444-444-40000000000000000004-4000000000000000000000000
χ524-4-4-4-4444-444-4000000000000000000-44000000000000000000000000
χ5388-88-8-88-8000000000000000000000000000000000000000000000000
χ5488-8-88-8-88000000000000000000000000000000000000000000000000
χ558-888-8-8-88000000000000000000000000000000000000000000000000
χ568-88-88-88-8000000000000000000000000000000000000000000000000

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