Finite Group Databasebeta

← Group #150609

Character table — Group #150609

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222244444444488881616161616161616161616161616161616161632323232
order12222222244444444444422444448888888888888888
χ111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111-1-1111-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-11-1-1-1-11111-111iiii−i−i−i−i-1-1-1-1ii−i−i
χ6111111111111-1-1-1-11-1-1-1-11111-111−i−i−i−iiiii-1-1-1-1−i−iii
χ7111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1iiii−i−i−i−i1111−i−iii
χ8111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1−i−i−i−iiiii1111ii−i−i
χ911111-1-11-11-1-111111-1-1111-11-1-11-111-1-111-1-111-1-11-11-1
χ1011111-1-11-11-1-111111-1-1111-11-1-11-1-1-111-1-11111-1-1-11-11
χ1111111-1-11-11-1-111111-1-111-111-1-1-1111-1-111-1-1-1-111-11-11
χ1211111-1-11-11-1-111111-1-111-111-1-1-11-1-111-1-111-1-1111-11-1
χ1311111-1-11-11-1-1-1-1-1-1111-1-11-11-111-1ii−i−i−i−iii-1-111i−i−ii
χ1411111-1-11-11-1-1-1-1-1-1111-1-11-11-111-1−i−iiiii−i−i-1-111−iii−i
χ1511111-1-11-11-1-1-1-1-1-1111-1-1-111-11-11ii−i−i−i−iii11-1-1−iii−i
χ1611111-1-11-11-1-1-1-1-1-1111-1-1-111-11-11−i−iiiii−i−i11-1-1i−i−ii
χ172222222222222222222-2-200-2-2-2000000000000000000
χ18222222222222-2-2-2-22-2-22200-2-22000000000000000000
χ1922222-2-22-22-2-222222-2-2-2-200-222000000000000000000
χ2022222-2-22-22-2-2-2-2-2-22222200-22-2000000000000000000
χ21444444444-4-4-40000-4000000000000000000000000000
χ2244444-4-44-4-4440000-4000000000000000000000000000
χ234444-444-4-400000000000022000-2-20000000000000000
χ244444-444-4-4000000000000-2-2000220000000000000000
χ254444-4-4-4-440000000000002-2000-220000000000000000
χ264444-4-4-4-44000000000000-220002-20000000000000000
χ2744-4-404-4000002i2i−2i−2i02i−2i0000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ2844-4-404-4000002i2i−2i−2i02i−2i000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ2944-4-404-400000−2i−2i2i2i0−2i2i0000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ3044-4-404-400000−2i−2i2i2i0−2i2i000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ3144-4-40-44000002i2i−2i−2i0−2i2i0000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ3244-4-40-44000002i2i−2i−2i0−2i2i000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ3344-4-40-4400000−2i−2i2i2i02i−2i0000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ3444-4-40-4400000−2i−2i2i2i02i−2i000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ354-4-44400-4004-40000000000000000000000002i−2i2i−2i0000
χ364-4-44400-4004-4000000000000000000000000−2i2i−2i2i0000
χ374-4-44400-400-440000000000000000000000002i−2i−2i2i0000
χ384-4-44400-400-44000000000000000000000000−2i2i2i−2i0000
χ394-4-44-400404000000-4004i−4i00000000000000000000000
χ404-4-44-400404000000-400−4i4i00000000000000000000000
χ414-4-44-40040-4004-44-44000000000000000000000000000
χ424-4-44-40040-400-44-444000000000000000000000000000
χ438-88-8000000004i−4i−4i4i0000000000000000000000000000
χ448-88-800000000−4i4i4i−4i0000000000000000000000000000

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