Finite Group Databasebeta

← Group #290757

Character table — Group #290757

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444444244444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1
χ911111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-11-11-11111-1-1-1-111-1-111-1-1
χ1011111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-11-11-1-1-1-1-11111-1-111-1-111
χ1111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-11-111111-1-1-1-1-1-111-1-111
χ1211111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-11-11-1-1-1-1111111-1-111-1-1
χ1311111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-11-1111-1-1-1-11111-1-1-1-111
χ1411111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-11-11-1-11111-1-1-1-11111-1-1
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-11-111-1-1-1-111-1-11111-1-1
χ1611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-11-1-1-11111-1-111-1-1-1-111
χ17222222222222-2-222222222-2-222-2-2-2-2-2-2000000000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-2-2-222-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000000000000
χ2122222222-2-2-2-22-2000022-2-22-20000002-2002-2020-20000000000000000
χ2222222222-2-2-2-22-2000022-2-22-20000002-200-220-2020000000000000000
χ2322222222-2-2-2-22-20000-2-2222-2000000-22002-20-2020000000000000000
χ2422222222-2-2-2-22-20000-2-2222-2000000-2200-22020-20000000000000000
χ2522222222-2-2-2-2-22000022-2-2-22000000-222-20020-200000000000000000
χ2622222222-2-2-2-2-22000022-2-2-22000000-22-2200-20200000000000000000
χ2722222222-2-2-2-2-220000-2-222-220000002-22-200-20200000000000000000
χ2822222222-2-2-2-2-220000-2-222-220000002-2-220020-200000000000000000
χ29222-2-2-22-22-22-22-22i2i−2i−2i0000-2200002i−2i0000000000000000002-22i−2i0000
χ30222-2-2-22-22-22-22-22i2i−2i−2i0000-2200002i−2i000000000000000000-22−2i2i0000
χ31222-2-2-22-22-22-22-2−2i−2i2i2i0000-220000−2i2i0000000000000000002-2−2i2i0000
χ32222-2-2-22-22-22-22-2−2i−2i2i2i0000-220000−2i2i000000000000000000-222i−2i0000
χ33222-2-2-22-22-22-2-222i2i−2i−2i00002-20000−2i2i00000000000000000000002i−2i2-2
χ34222-2-2-22-22-22-2-222i2i−2i−2i00002-20000−2i2i0000000000000000000000−2i2i-22
χ35222-2-2-22-22-22-2-22−2i−2i2i2i00002-200002i−2i00000000000000000000002i−2i-22
χ36222-2-2-22-22-22-2-22−2i−2i2i2i00002-200002i−2i0000000000000000000000−2i2i2-2
χ37444-4-4-44-4-44-444400000000-4-400000000000000000000000000000000
χ38444-4-4-44-4-44-44-4-4000000004400000000000000000000000000000000
χ3944-444-4-4-444-4-4004-44-400000000000000000000000000000000000000
χ4044-444-4-4-444-4-400-44-4400000000000000000000000000000000000000
χ4144-444-4-4-4-4-444000000000000004i−4i0000000000000000000000000000
χ4244-444-4-4-4-4-44400000000000000−4i4i0000000000000000000000000000
χ4344-4-4-44-444-4-44004i−4i−4i4i00000000000000000000000000000000000000
χ4444-4-4-44-444-4-4400−4i4i4i−4i00000000000000000000000000000000000000
χ4544-4-4-44-44-444-40000000000004i−4i000000000000000000000000000000
χ4644-4-4-44-44-444-4000000000000−4i4i000000000000000000000000000000
χ474-444-4-4-4400000000004i−4i000000000000000000002i−2i2-2000000000000
χ484-444-4-4-4400000000004i−4i00000000000000000000−2i2i-22000000000000
χ494-444-4-4-440000000000−4i4i000000000000000000002i−2i-22000000000000
χ504-444-4-4-440000000000−4i4i00000000000000000000−2i2i2-2000000000000
χ514-4-44-444-40000000000004i−4i00000000000000000000002i−2i2-200000000
χ524-4-44-444-40000000000004i−4i0000000000000000000000−2i2i-2200000000
χ534-4-44-444-4000000000000−4i4i00000000000000000000002i−2i-2200000000
χ544-4-44-444-4000000000000−4i4i0000000000000000000000−2i2i2-200000000
χ558-88-888-8-8000000000000000000000000000000000000000000000000
χ568-8-8-88-888000000000000000000000000000000000000000000000000

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