Finite Group Databasebeta

← Group #97178

Character table — Group #97178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222222244444444444444888888882244444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1111111111-11-11-1-1-11-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-11-11-11-1-1-11-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-11-11111-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-1-1-11111-1-1iiii−i−i−i−i1111-1-1-11-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1-1-111-1111ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−iiiii1111-1-1-11-1-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1-1-111-1111−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−i1-11-1-111-1-11−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−i-11-111-11-11-1−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii1-11-1-111-1-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii-11-111-11-11-1ii−i−iii−i−i−i−iii
χ17222222222222222-2-2-2-22-2-222-2-2000000000000002-200000000000000
χ18222222222222222-2-2-2-22-2-2-2-22200000000000000-2200000000000000
χ19222222222222-2-2-222-2-2-22-2000000000000020-20-20002000000000000
χ20222222222222-2-2-222-2-2-22-20000000000000-20202000-2000000000000
χ21222222222222-2-2-2-2-222-2-2200000000000020-20-200020000000000000
χ22222222222222-2-2-2-2-222-2-22000000000000-20202000-20000000000000
χ2322222222-2-2-2-222-22222-2-2-2222200000000000000-2-200000000000000
χ2422222222-2-2-2-222-22222-2-2-2-2-2-2-2000000000000002200000000000000
χ2522222222-2-2-2-2-2-2222-2-22-2200000000000020-202000-20000000000000
χ2622222222-2-2-2-2-2-2222-2-22-22000000000000-2020-200020000000000000
χ2722222222-2-2-2-2-2-22-2-22222-2000000000000020-202000-2000000000000
χ2822222222-2-2-2-2-2-22-2-22222-20000000000000-2020-20002000000000000
χ292-222-2-22-200002-202i−2i2i−2i0002-22i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000001+i−1−i1−i−1+i00000000
χ302-222-2-22-200002-202i−2i2i−2i0002-22i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−1−i1+i−1+i1−i00000000
χ312-222-2-22-200002-202i−2i2i−2i000-22−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−1−i1+i−1+i1−i00000000
χ322-222-2-22-200002-202i−2i2i−2i000-22−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000001+i−1−i1−i−1+i00000000
χ332-222-2-22-200002-20−2i2i−2i2i0002-2−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000001−i−1+i1+i−1−i00000000
χ342-222-2-22-200002-20−2i2i−2i2i0002-2−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−1+i1−i−1−i1+i00000000
χ352-222-2-22-200002-20−2i2i−2i2i000-222i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−1+i1−i−1−i1+i00000000
χ362-222-2-22-200002-20−2i2i−2i2i000-222i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000001−i−1+i1+i−1−i00000000
χ3744-4-4-4-44444-4-4000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ3844-4-4-4-44444-4-400000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ3944-4-4-4-444-4-444000000000000002-22-2-22-220000000000000000000000
χ4044-4-4-4-444-4-44400000000000000-22-222-22-20000000000000000000000
χ414-444-4-44-40000-4404i−4i−4i4i0000000000000000000000000000000000000
χ424-444-4-44-40000-440−4i4i4i−4i0000000000000000000000000000000000000
χ434-44-44-4-444-44-40000000000000000000000000000000000002i−2i2i−2i0000
χ444-44-44-4-444-44-4000000000000000000000000000000000000−2i2i−2i2i0000
χ454-44-44-4-44-44-440000000000000000000000000000000000002-2-220000
χ464-44-44-4-44-44-44000000000000000000000000000000000000-222-20000
χ474-4-44-44-444-4-4400000000000000000000000000000000000000002-22-2
χ484-4-44-44-444-4-440000000000000000000000000000000000000000-22-22
χ494-4-44-44-44-444-400000000000000000000000000000000000000002i−2i−2i2i
χ504-4-44-44-44-444-40000000000000000000000000000000000000000−2i2i2i−2i
χ514-4-4-4444-400000040000-40000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ524-4-4-4444-400000040000-4000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ534-4-4-4444-4000000-4000040000002-2-22-222-20000000000000000000000
χ544-4-4-4444-4000000-400004000000-222-22-2-220000000000000000000000
χ55888-8-88-8-8000000000000000000000000000000000000000000000000
χ5688-888-8-8-8000000000000000000000000000000000000000000000000

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