Finite Group Databasebeta

← Group #94293

Character table — Group #94293

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444448888881616161616161616161616161616161616161616161616161616
order12442224442222444424444444444444448888888888888888
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
χ5111111111111-1-11-1-11-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111-1-11-1-11-1-1-1-1-1-111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111-1-11-1-11-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111-1-11-1-11-1-1-1-1-1-111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i
χ911-1-1111-1-1-11111-1-1-1-11-111-1-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-1111-1-1-11111-1-1-1-11-111-1-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-1111-1-1-11111-1-1-1-11-111-1-11-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-1111-1-1-11111-1-1-1-11-111-1-11-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-1111-1-1-111-1-1-111-1-11-1-1111-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ1411-1-1111-1-1-111-1-1-111-1-11-1-1111-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ1511-1-1111-1-1-111-1-1-111-1-11-1-1111-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ1611-1-1111-1-1-111-1-1-111-1-11-1-1111-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ1722222222222222222222-2-2-2-2-2-2000000000000000000000000
χ18222222222222-2-22-2-22-2-22222-2-2000000000000000000000000
χ1922222-2-22-2-22-200200-2002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ2022222-2-22-2-22-200200-2002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ2122222-2-22-2-22-200200-200−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ2222222-2-22-2-22-200200-200−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ2322222-2-22-2-2-2222-2222-2-200000000000000000000002−22−22−22−2
χ2422222-2-22-2-2-2222-2222-2-20000000000000000000000−22−22−22−22
χ2522222-2-22-2-2-22-2-2-2-2-22220000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ2622222-2-22-2-2-22-2-2-2-2-22220000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ2722-2-2222-2-2-22222-2-2-2-22-2-2-222-22000000000000000000000000
χ2822-2-2222-2-2-222-2-2-222-2-2222-2-2-22000000000000000000000000
χ2922-2-22-2-2-2222-200-2002002i−2i−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ3022-2-22-2-2-2222-200-2002002i−2i−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ3122-2-22-2-2-2222-200-200200−2i2i2i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ3222-2-22-2-2-2222-200-200200−2i2i2i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ3322-2-22-2-2-222-22222-2-2-2-220000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ3422-2-22-2-2-222-22222-2-2-2-220000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ3522-2-22-2-2-222-22-2-2222-22-200000000000000000000002−2−22−222−2
χ3622-2-22-2-2-222-22-2-2222-22-20000000000000000000000−222−22−2−22
χ374444444444-4-400-400-400000000000000000000000000000000
χ384444-44-4-44-400000000000000000000000000002-22-200000000
χ394444-44-4-44-40000000000000000000000000000-22-2200000000
χ404444-4-44-4-440000000000000000000000002-22-2000000000000
χ414444-4-44-4-44000000000000000000000000-22-22000000000000
χ4244-4-4444-4-4-4-4-400400400000000000000000000000000000000
χ4344-4-4-44-44-4400000000000000000000000000002i−2i−2i2i00000000
χ4444-4-4-44-44-440000000000000000000000000000−2i2i2i−2i00000000
χ4544-4-4-4-4444-40000000000000000000000002i−2i−2i2i000000000000
χ4644-4-4-4-4444-4000000000000000000000000−2i2i2i−2i000000000000
χ478-88i−8i000000004-404i−4i000000000000000000000000000000000
χ488-88i−8i00000000-440−4i4i000000000000000000000000000000000
χ498-8−8i8i000000004-40−4i4i000000000000000000000000000000000
χ508-8−8i8i00000000-4404i−4i000000000000000000000000000000000

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