Finite Group Databasebeta

← Group #94306

Character table — Group #94306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444448888881616161616161616161616161616161616161616161616161616
order1244222444222244442488888888888888888888881616161616161616
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111-1-1-11-11-1111-111-1-111-1-11-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ1011111-1-1-11-11-1111-111-1-111-1-11-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ1111111-1-1-11-11-1111-111-1-111-1-11-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ1211111-1-1-11-11-1111-111-1-111-1-11-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ1311111-1-1-11-11-1-1-11-1-1-111-1-1111-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ1411111-1-1-11-11-1-1-11-1-1-111-1-1111-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ1511111-1-1-11-11-1-1-11-1-1-111-1-1111-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ1611111-1-1-11-11-1-1-11-1-1-111-1-1111-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ1722222222222222222222-2-2-2-2-2-2000000000000000000000000
χ18222222222222-2-222-2-2-2-22222-2-2000000000000000000000000
χ1922222-2-2-22-22-2222-222-2-2-2-222-22000000000000000000000000
χ2022222-2-2-22-22-2-2-22-2-2-22222-2-2-22000000000000000000000000
χ2122-2-2222-2-2-22222-2-2-2-22-200000000000000000000002−22−22−22−2
χ2222-2-2222-2-2-22222-2-2-2-22-20000000000000000000000−22−22−22−22
χ2322-2-2222-2-2-222-2-2-2-222-220000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ2422-2-2222-2-2-222-2-2-2-222-220000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ2522-2-2222-2-2-2-2-2002200002i−2i2i−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ2622-2-2222-2-2-2-2-2002200002i−2i2i−2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ2722-2-2222-2-2-2-2-200220000−2i2i−2i2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ2822-2-2222-2-2-2-2-200220000−2i2i−2i2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ2922-2-22-2-22-222-222-22-2-2-220000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ3022-2-22-2-22-222-222-22-2-2-220000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ3122-2-22-2-22-222-2-2-2-22222-200000000000000000000002−2−22−222−2
χ3222-2-22-2-22-222-2-2-2-22222-20000000000000000000000−222−22−2−22
χ3322-2-22-2-22-22-22002-200002i−2i−2i2i00000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ3422-2-22-2-22-22-22002-200002i−2i−2i2i0000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ3522-2-22-2-22-22-22002-20000−2i2i2i−2i00000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ3622-2-22-2-22-22-22002-20000−2i2i2i−2i0000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ374444444444-4-400-4-40000000000000000000000000000000000
χ3844444-4-4-44-4-4400-440000000000000000000000000000000000
χ394444-44-44-4-4000000000000000000002i−2i2i−2i0000000000000000
χ404444-44-44-4-400000000000000000000−2i2i−2i2i0000000000000000
χ414444-4-44-4-44000000000000000000002-2-220000000000000000
χ424444-4-44-4-4400000000000000000000-222-20000000000000000
χ4344-4-4-44-4-44400000000000000002-22-200000000000000000000
χ4444-4-4-44-4-4440000000000000000-22-2200000000000000000000
χ4544-4-4-4-4444-400000000000000002i−2i−2i2i00000000000000000000
χ4644-4-4-4-4444-40000000000000000−2i2i2i−2i00000000000000000000
χ478-88i−8i000000004-4004i−4i00000000000000000000000000000000
χ488-88i−8i00000000-4400−4i4i00000000000000000000000000000000
χ498-8−8i8i000000004-400−4i4i00000000000000000000000000000000
χ508-8−8i8i00000000-44004i−4i00000000000000000000000000000000

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