Finite Group Databasebeta

← Group #130121

Character table — Group #130121

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122444444444488888888888888888816161616161616161616161632323232
order12222222444444444444444444888888884444444444448888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-111111111-11-1-111-1-1-1-1-1-111-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-111
χ5111111111111111111-1-111-1-11111111111-1-11-1-1-11-11111-1-1-1-1
χ6111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1111111111-1-11-1-1-11-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-11111111-1-1
χ9111111-1-111-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−i1-1-1-1-1111ii−i−ii−ii−i
χ10111111-1-111-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii1-1-1-1-1111−i−iii−ii−ii
χ11111111-1-111-1-1-1-1-1-11111-1-11111iiii−i−i−i−i-1-111-11-1-1−i−iiii−i−ii
χ12111111-1-111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii-1-111-11-1-1ii−i−i−iii−i
χ13111111-1-111-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−i-11-111-11-1ii−i−i−ii−ii
χ14111111-1-111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii-11-111-11-1−i−iiii−ii−i
χ15111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111iiii−i−i−i−i111-11-1-11−i−iii−iii−i
χ16111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111−i−i−i−iiiii111-11-1-11ii−i−ii−i−ii
χ1722222222222-2-2-2-22-2-2002200-2-200000000002000-2000000000
χ1822222222222-2-2-2-22-2-200-2-200220000000000-20002000000000
χ1922222222-2-2-222-2-2-22-20000220000000000200-2000-200000000
χ2022222222-2-2-222-2-2-22-20000-2-20000000000-2002000200000000
χ2122222222-2-2-2-2-222-2-2222000000000000000-2002-20000000000
χ2222222222-2-2-2-2-222-2-22-2-2000000000000000200-220000000000
χ23222222-2-222-22222-2-2-2002200220000000000-2000-2000000000
χ24222222-2-222-22222-2-2-200-2-200-2-2000000000020002000000000
χ25222222-2-2-2-2222-2-22-2222000000000000000200-2-20000000000
χ26222222-2-2-2-2222-2-22-22-2-2000000000000000-200220000000000
χ27222222-2-2-2-22-2-22222-20000220000000000-200-2000200000000
χ28222222-2-2-2-22-2-22222-20000-2-200000000002002000-200000000
χ292-2-222-2002-202i−2i2i−2i000002-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001+i−1−i1−i−1+i0000
χ302-2-222-2002-202i−2i2i−2i000002-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1−i1+i−1+i1−i0000
χ312-2-222-2002-202i−2i2i−2i00000-2200−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1−i1+i−1+i1−i0000
χ322-2-222-2002-202i−2i2i−2i00000-2200−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001+i−1−i1−i−1+i0000
χ332-2-222-2002-20−2i2i−2i2i000002-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001−i−1+i1+i−1−i0000
χ342-2-222-2002-20−2i2i−2i2i000002-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1+i1−i−1−i1+i0000
χ352-2-222-2002-20−2i2i−2i2i00000-22002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1+i1−i−1−i1+i0000
χ362-2-222-2002-20−2i2i−2i2i00000-22002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001−i−1+i1+i−1−i0000
χ374444-4-4000040000-400000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ384444-4-4000040000-40000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ394444-4-40000-40000400000000002-22-2-22-220000000000000000
χ404444-4-40000-4000040000000000-22-222-22-20000000000000000
χ414-4-444-400-4404i−4i−4i4i00000000000000000000000000000000000
χ424-4-444-400-440−4i4i4i−4i00000000000000000000000000000000000
χ434-4-44-444-40000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ444-4-44-444-4000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ454-4-44-44-440000000000000000002-2-22-222-20000000000000000
χ464-4-44-44-44000000000000000000-222-22-2-220000000000000000
χ4788-8-80000000000000000004-400000000000000000000000000
χ4888-8-8000000000000000000-4400000000000000000000000000
χ498-88-8000000000000004-4000000000000000000000000000000
χ508-88-800000000000000-44000000000000000000000000000000

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