Finite Group Databasebeta

← Group #97753

Character table — Group #97753

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222222222224444444444444448888888822444444444444448888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-111-1-1111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-111111111-1-1-1-1
χ51111111111111111111111-1-1111-1-11111111111-1-1-1-1-11-111111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111111111
χ71111111111111111111111-1-11-1-1-1-1-1-111111111-1111-1-11-1-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-11111-1-1-1-11111
χ911111111-1-1-1-111-1-111-1-1-1-111111-1-111iiii−i−i−i−i1-11-1-1-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-111-1-1-1-111111-1-111−i−i−i−iiiii1-11-1-1-11-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-111-1-111-1-1-1-1111-1-1-1-1-1-1iiii−i−i−i−i11-11-11-11−i−iii−i−iiiii−i−i
χ1211111111-1-1-1-111-1-111-1-1-1-1111-1-1-1-1-1-1−i−i−i−iiiii11-11-11-11ii−i−iii−i−i−i−iii
χ1311111111-1-1-1-111-1-111-1-1-1-1-1-11111111iiii−i−i−i−i-11-111-1-1-1ii−i−i−i−iii−i−iii
χ1411111111-1-1-1-111-1-111-1-1-1-1-1-11111111−i−i−i−iiiii-11-111-1-1-1−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-111-1-111-1-1-1-1-1-11-1-111-1-1iiii−i−i−i−i-1-11-11111−i−iiiii−i−i−i−iii
χ1611111111-1-1-1-111-1-111-1-1-1-1-1-11-1-111-1-1−i−i−i−iiiii-1-11-11111ii−i−i−i−iiiii−i−i
χ172222222222222222-2-2-2-2-2-222-200220000000000-2000-2000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-200-2-2000000000020002000000000000000
χ19222222222222-2-2-2-2222-2-2200-22200-2-2000000000000020-2000000000000
χ20222222222222-2-2-2-2222-2-2200-2-2-200220000000000000-202000000000000
χ21222222222222-2-2-2-2-2-2-222-20020000000000000002-2-20020000000000000
χ22222222222222-2-2-2-2-2-2-222-2002000000000000000-22200-20000000000000
χ2322222222-2-2-2-222-2-2-2-2222222-200-2-20000000000-20002000000000000000
χ2422222222-2-2-2-222-2-2-2-22222-2-2-2002200000000002000-2000000000000000
χ2522222222-2-2-2-2-2-22222-222-200-22200-2-20000000000000-202000000000000
χ2622222222-2-2-2-2-2-22222-222-200-2-2-20022000000000000020-2000000000000
χ2722222222-2-2-2-2-2-222-2-22-2-2200200000000000000022-200-20000000000000
χ2822222222-2-2-2-2-2-222-2-22-2-22002000000000000000-2-220020000000000000
χ29222-22-2-2-222-2-22-2-220000002i−2i0002i−2i0022−2−222−2−20000000000000000i2−i2i2−i2
χ30222-22-2-2-222-2-22-2-220000002i−2i0002i−2i00−2−222−2−2220000000000000000−i2i2−i2i2
χ31222-22-2-2-222-2-22-2-22000000−2i2i000−2i2i0022−2−222−2−20000000000000000−i2i2−i2i2
χ32222-22-2-2-222-2-22-2-22000000−2i2i000−2i2i00−2−222−2−2220000000000000000i2−i2i2−i2
χ33222-22-2-2-2-2-2222-22-20000002i−2i000−2i2i00i2i2−i2−i2−i2−i2i2i20000000000000000−222−2
χ34222-22-2-2-2-2-2222-22-20000002i−2i000−2i2i00−i2−i2i2i2i2i2−i2−i200000000000000002−2−22
χ35222-22-2-2-2-2-2222-22-2000000−2i2i0002i−2i00i2i2−i2−i2−i2−i2i2i200000000000000002−2−22
χ36222-22-2-2-2-2-2222-22-2000000−2i2i0002i−2i00−i2−i2i2i2i2i2−i2−i20000000000000000−222−2
χ37444-44-4-4-444-4-4-444-40000000000000000000000000000000000000000000
χ38444-44-4-4-4-4-444-44-440000000000000000000000000000000000000000000
χ3944-44-44-4-4000000000004i−4i00000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ4044-44-44-4-4000000000004i−4i0000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ4144-44-44-4-400000000000−4i4i00000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ4244-44-44-4-400000000000−4i4i0000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ4344-4-4-4-4440000000000400-40000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ4444-4-4-4-4440000000000400-4000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ4544-4-4-4-4440000000000-40040000000002-2-22-222-200000000000000000000
χ4644-4-4-4-4440000000000-4004000000000-222-22-2-2200000000000000000000
χ474-444-4-44-4000000004-4000000000004i−4i0000000000000000000000000000
χ484-444-4-44-4000000004-400000000000−4i4i0000000000000000000000000000
χ494-444-4-44-400000000-4400000004i−4i00000000000000000000000000000000
χ504-444-4-44-400000000-440000000−4i4i00000000000000000000000000000000
χ514-4-444-4-444-44-40000000000000000000000000000000000000002i−2i2i−2i0000
χ524-4-444-4-444-44-4000000000000000000000000000000000000000−2i2i−2i2i0000
χ534-4-444-4-44-44-440000000000000000000000000000000000000002-2-220000
χ544-4-444-4-44-44-44000000000000000000000000000000000000000-222-20000
χ554-4-4-4444-44-4-44000000000000000000000000000000000002-22-200000000
χ564-4-4-4444-44-4-4400000000000000000000000000000000000-22-2200000000
χ574-4-4-4444-4-444-4000000000000000000000000000000000002i−2i−2i2i00000000
χ584-4-4-4444-4-444-400000000000000000000000000000000000−2i2i2i−2i00000000
χ598-88-8-88-88000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.