Finite Group Databasebeta

← Group #175192

Character table — Group #175192

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444224444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-11-1-11-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-11-1-11-1-1-11-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-111111-1-11-1-11-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-1-111111-1-11-1-11-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111-1-1-1-1-1-11-1-1-11-11-1-1111111-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-1-1-1-1-11-1-1-11-11-1-111-1-1-1-11111-1-1-1-11111
χ9111111111-1-1-1-1-1-11111111-1-111-1-1-111-11-11-1-111-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-1-1-11111111-1-111-1-1-111-11-11-1-1-1-111-1-111-1-111-1-111
χ11111111111-1-1-1-1-1-11111111-1-1-1-1-1111-11-1-1-11111-1-111-1-1-1-111-1-111
χ12111111111-1-1-1-1-1-11111111-1-1-1-1-1111-11-1-1-111-1-111-1-11111-1-111-1-1
χ13111111111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ14111111111-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ15111111111-1-1-1-1-1-111111-1-111-1-1-111-11111-1-1-111-1-1-1-11111-1-1-1-111
χ16111111111-1-1-1-1-1-111111-1-111-1-1-111-11111-1-1-1-1-11111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-22000022-2-2-200200-2000000000000000000
χ182222222222222-2-2-2-2-2-220000-2-2-22200-2002000000000000000000
χ19222222222-2-2-2-222-2-2-2-2200002222200-200-2000000000000000000
χ20222222222-2-2-2-222-2-2-2-220000-2-22-2-2002002000000000000000000
χ2122222222-222-2-222-2-222-2222200-200-2000-20000000000000000000
χ2222222222-222-2-222-2-222-2-2-2-2-200-200200020000000000000000000
χ2322222222-222-2-2-2-222-2-2-2000000200020-2002-20000000000000000
χ2422222222-222-2-2-2-222-2-2-20000002000-20200-220000000000000000
χ2522222222-2-2-2222222-2-2-2000000-200020-200-220000000000000000
χ2622222222-2-2-2222222-2-2-2000000-2000-202002-20000000000000000
χ2722222222-2-2-222-2-2-2-222-222-2-200200-200020000000000000000000
χ2822222222-2-2-222-2-2-2-222-2-2-222002002000-20000000000000000000
χ294444-4-4-4-440000000000-400004-4000000000000000000000000000
χ304444-4-4-4-440000000000-40000-44000000000000000000000000000
χ314444-4-4-4-4-40000000000400000004i−4i000000000000000000000000
χ324444-4-4-4-4-4000000000040000000−4i4i000000000000000000000000
χ3344-4-44-44-40004i−4i0000000000000000000000000000000000002i−2i2-2
χ3444-4-44-44-40004i−4i000000000000000000000000000000000000−2i2i-22
χ3544-4-44-44-4000−4i4i0000000000000000000000000000000000002i−2i-22
χ3644-4-44-44-4000−4i4i000000000000000000000000000000000000−2i2i2-2
χ3744-4-4-44-4404i−4i000000000000000000000000002i−2i2-2000000000000
χ3844-4-4-44-4404i−4i00000000000000000000000000−2i2i-22000000000000
χ3944-4-4-44-440−4i4i000000000000000000000000002i−2i-22000000000000
χ4044-4-4-44-440−4i4i00000000000000000000000000−2i2i2-2000000000000
χ414-44-44-4-440000000004-40004i−4i00000000000000000000000000000
χ424-44-44-4-440000000004-4000−4i4i00000000000000000000000000000
χ434-44-44-4-44000000000-4404i−4i0000000000000000000000000000000
χ444-44-44-4-44000000000-440−4i4i0000000000000000000000000000000
χ454-44-4-444-4000004i−4i0000000000000000000000000000002-22i−2i0000
χ464-44-4-444-4000004i−4i000000000000000000000000000000-22−2i2i0000
χ474-44-4-444-400000−4i4i0000000000000000000000000000002-2−2i2i0000
χ484-44-4-444-400000−4i4i000000000000000000000000000000-222i−2i0000
χ494-4-4444-4-400000004-4000000000000000000000000002i2−2i200000000
χ504-4-4444-4-400000004-400000000000000000000000000−2i22i200000000
χ514-4-4444-4-40000000-440000000000000000000000002i2−2i20000000000
χ524-4-4444-4-40000000-44000000000000000000000000−2i22i20000000000
χ538-8-88-8-888000000000000000000000000000000000000000000000

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