Finite Group Databasebeta

← Group #98341

Character table — Group #98341

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444224444444224444448888888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1111-1-111-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1111-1-111-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-11111-1-1-1-1-1-1-111111-1-111-1-1-11-1-111ii−i−iii−i−iii−i−iii−i−i
χ1011111111-11111-1-1-1-1-1-1-111111-1-111-1-1-11-1-111−i−iii−i−iii−i−iii−i−iii
χ1111111111-11111-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211111111-11111-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311111111-11111-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-11111-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-11111-1-1-1-1-1-1-1-1-11-1-111-1-1111-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-11111-1-1-1-1-1-1-1-1-11-1-111-1-1111-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-2-22-2-2-2-22222-200-2-200200-200000000000000000000
χ1822222222222-2-22-2-2-2-222-2-2-2002200-200200000000000000000000
χ19222222222-2-222-2-2-2222-200-22200-2-202-2000000000000000000000
χ20222222222-2-222-2-2-2222-200-2-2-200220-22000000000000000000000
χ21222222222-2-2-2-2-222-2-22-200200000000002-22-20000000000000000
χ22222222222-2-2-2-2-222-2-22-20020000000000-22-220000000000000000
χ2322222222-222-2-2-22222-2-222-2002200-200-200000000000000000000
χ2422222222-222-2-2-22222-2-2-2-2-200-2-200200200000000000000000000
χ2522222222-2-2-222222-2-2-2200-22200-2-20-22000000000000000000000
χ2622222222-2-2-222222-2-2-2200-2-2-2002202-2000000000000000000000
χ2722222222-2-2-2-2-22-2-222-2200200000000002-2-220000000000000000
χ2822222222-2-2-2-2-22-2-222-220020000000000-222-20000000000000000
χ2922-22-22-2-202-20002i−2i2i−2i002-20002i−2i0000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ3022-22-22-2-202-20002i−2i2i−2i002-20002i−2i000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ3122-22-22-2-202-20002i−2i2i−2i00-22000−2i2i0000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ3222-22-22-2-202-20002i−2i2i−2i00-22000−2i2i000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ3322-22-22-2-202-2000−2i2i−2i2i002-2000−2i2i0000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ3422-22-22-2-202-2000−2i2i−2i2i002-2000−2i2i000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ3522-22-22-2-202-2000−2i2i−2i2i00-220002i−2i0000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ3622-22-22-2-202-2000−2i2i−2i2i00-220002i−2i000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ37444-44-4-4-44000000000-400000000000000000000002-22-200000000
χ38444-44-4-4-44000000000-40000000000000000000000-22-2200000000
χ39444-44-4-4-4-4000000000400000000000000000000002i−2i−2i2i00000000
χ40444-44-4-4-4-400000000040000000000000000000000−2i2i2i−2i00000000
χ4144-44-44-4-40-440004i−4i−4i4i00000000000000000000000000000000000
χ4244-44-44-4-40-44000−4i4i4i−4i00000000000000000000000000000000000
χ434-444-4-44-40004-4000000000000004i−4i000000000000000000000000
χ444-444-4-44-40004-400000000000000−4i4i000000000000000000000000
χ454-444-4-44-4000-4400000000004i−4i0000000000000000000000000000
χ464-444-4-44-4000-440000000000−4i4i0000000000000000000000000000
χ474-44-4-44-4400000400000-4000000000000000002i−2i2i−2i000000000000
χ484-44-4-44-4400000400000-400000000000000000−2i2i−2i2i000000000000
χ494-44-4-44-4400000-4000004000000000000000002-2-22000000000000
χ504-44-4-44-4400000-400000400000000000000000-222-2000000000000
χ5188-8-8-8-888000000000000000000000000000000000000000000000
χ528-8-888-8-88000000000000000000000000000000000000000000000
χ538-8-8-8888-8000000000000000000000000000000000000000000000

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