Finite Group Databasebeta

← Group #97176

Character table — Group #97176

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222222244444444444444888888882444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11-1-1-11-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1111111111-11-1-111-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111111111-11-11-1-1-11-11-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-11111-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11-1111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-1-1-11111-1-1iiii−i−i−i−i111-1-1-1-111-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1-11-111-111ii−i−i−i−iii−i−iii
χ1111111111-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−iiiii111-1-1-1-111-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1-11-111-111−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−i1-1111-1-1-1-11−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-111-1-1-1-1-1-111-1-111iiii−i−i−i−i-11-1-11111-1-1−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii1-1111-1-1-1-11ii−i−i−i−iiiii−i−i
χ1611111111-1-1-1-111-1-1-1-1-1-111-1-111−i−i−i−iiiii-11-1-11111-1-1ii−i−iii−i−i−i−iii
χ17222222222222222-2-2-2-22-2-222-2-20000000000002000-20000000000000
χ18222222222222222-2-2-2-22-2-2-2-222000000000000-200020000000000000
χ19222222222222-2-2-222-2-2-22-2000000000000020-2000-202000000000000
χ20222222222222-2-2-222-2-2-22-20000000000000-20200020-2000000000000
χ21222222222222-2-2-2-2-222-2-2200000000000020-2002-2000000000000000
χ22222222222222-2-2-2-2-222-2-22000000000000-20200-22000000000000000
χ2322222222-2-2-2-222-22222-2-2-22222000000000000-2000-20000000000000
χ2422222222-2-2-2-222-22222-2-2-2-2-2-2-2000000000000200020000000000000
χ2522222222-2-2-2-2-2-2222-2-22-2200000000000020-200-22000000000000000
χ2622222222-2-2-2-2-2-2222-2-22-22000000000000-202002-2000000000000000
χ2722222222-2-2-2-2-2-22-2-22222-20000000000000202000-20-2000000000000
χ2822222222-2-2-2-2-2-22-2-22222-20000000000000-20-2000202000000000000
χ2922-2-22-2-2200002-202i−2i2i−2i0002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000001−i−1+i1+i−1−i00000000
χ3022-2-22-2-2200002-202i−2i2i−2i0002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−1+i1−i−1−i1+i00000000
χ3122-2-22-2-2200002-202i−2i2i−2i000−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−1+i1−i−1−i1+i00000000
χ3222-2-22-2-2200002-202i−2i2i−2i000−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000001−i−1+i1+i−1−i00000000
χ3322-2-22-2-2200002-20−2i2i−2i2i0002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−1−i1+i−1+i1−i00000000
χ3422-2-22-2-2200002-20−2i2i−2i2i0002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000001+i−1−i1−i−1+i00000000
χ3522-2-22-2-2200002-20−2i2i−2i2i000−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000001+i−1−i1−i−1+i00000000
χ3622-2-22-2-2200002-20−2i2i−2i2i000−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−1−i1+i−1+i1−i00000000
χ37444-4-44-4-444-4-40000000000000000000000000000000000002-22-20000
χ38444-4-44-4-444-4-4000000000000000000000000000000000000-22-220000
χ39444-4-44-4-4-4-4440000000000000000000000000000000000002i−2i−2i2i0000
χ40444-4-44-4-4-4-444000000000000000000000000000000000000−2i2i2i−2i0000
χ4144-4-44-4-440000-4404i−4i−4i4i0000000000000000000000000000000000000
χ4244-4-44-4-440000-440−4i4i4i−4i0000000000000000000000000000000000000
χ434-44-4-4-44400000040000-40000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ444-44-4-4-44400000040000-4000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ454-44-4-4-444000000-4000040000002-22-2-22-220000000000000000000000
χ464-44-4-4-444000000-400004000000-22-222-22-20000000000000000000000
χ474-4-44-44-444-44-4000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ484-4-44-44-444-44-400000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ494-4-44-44-44-44-44000000000000002-2-22-222-20000000000000000000000
χ504-4-44-44-44-44-4400000000000000-222-22-2-220000000000000000000000
χ514-4-4-4444-44-4-4400000000000000000000000000000000000000002-22-2
χ524-4-4-4444-44-4-440000000000000000000000000000000000000000-22-22
χ534-4-4-4444-4-444-400000000000000000000000000000000000000002i−2i−2i2i
χ544-4-4-4444-4-444-40000000000000000000000000000000000000000−2i2i2i−2i
χ5588-88-8-88-8000000000000000000000000000000000000000000000000
χ568-8888-8-8-8000000000000000000000000000000000000000000000000

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