Finite Group Databasebeta

← Group #97850

Character table — Group #97850

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444422444444444444444448888888844444444888888888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-11-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ911111111-1-1-1-111-1-111-1-1-1-111-1-111111iiii−i−i−i−i-1-11-11-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-111-1-1-1-111-1-111111−i−i−i−iiiii-1-11-11-11-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-11-1-1iiii−i−i−i−i11-111-1-11−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-111-1-111-1-1-1-111-1-1-1-11-1-1−i−i−i−iiiii11-111-1-11ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-111-1-111-1-1-1-1-1-11111111iiii−i−i−i−i-1-1-11-11-11ii−i−i−i−iii−i−iii
χ1411111111-1-1-1-111-1-111-1-1-1-1-1-11111111−i−i−i−iiiii-1-1-11-11-11−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-111-1-111-1-1-1-1-1-111-1-11-1-1iiii−i−i−i−i111-1-111-1−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-111-1-111-1-1-1-1-1-111-1-11-1-1−i−i−i−iiiii111-1-111-1ii−i−iii−i−i−i−iii
χ17222222222222222-2-2-2-2-22-2222200-200000000000000-2-200000000000000
χ18222222222222222-2-2-2-2-22-2-2-2-2-200-2000000000000002200000000000000
χ19222222222222-2-2-22-2-2-2-2-2200000020000000000002200-2-2000000000000
χ20222222222222-2-2-22-2-2-2-2-220000002000000000000-2-20022000000000000
χ21222222222222-2-2-2-22222-2-2000022-2-2-2000000002-2000000000000000000
χ22222222222222-2-2-2-22222-2-20000-2-2-22200000000-22000000000000000000
χ2322222222-2-2-2-222-22-2-222-2222-2-200-200000000000000-2200000000000000
χ2422222222-2-2-2-222-22-2-222-22-2-22200-2000000000000002-200000000000000
χ2522222222-2-2-2-2-2-22222-2-222000022-2-2-200000000-22000000000000000000
χ2622222222-2-2-2-2-2-22222-2-2220000-2-2-222000000002-2000000000000000000
χ2722222222-2-2-2-2-2-22-2-2-2222-200000020000000000002-200-22000000000000
χ2822222222-2-2-2-2-2-22-2-2-2222-20000002000000000000-22002-2000000000000
χ29222-22-2-2-222-2-22-2200000-202-22-20000022−2−222−2−20000000000002−22−20000
χ30222-22-2-2-222-2-22-2200000-202-22-200000−2−222−2−222000000000000−22−220000
χ31222-22-2-2-222-2-22-2200000-20-22-220000022−2−222−2−2000000000000−22−220000
χ32222-22-2-2-222-2-22-2200000-20-22-2200000−2−222−2−2220000000000002−22−20000
χ33222-22-2-2-2-2-2222-2-200000202-2-2200000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i20000
χ34222-22-2-2-2-2-2222-2-200000202-2-2200000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i20000
χ35222-22-2-2-2-2-2222-2-20000020-222-200000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i20000
χ36222-22-2-2-2-2-2222-2-20000020-222-200000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i20000
χ37444-44-4-4-444-4-4-44-400000400000000000000000000000000000000000000
χ38444-44-4-4-4-4-444-44400000-400000000000000000000000000000000000000
χ3944-44-4-4-4400000000004i−4i000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ4044-44-4-4-4400000000004i−4i00000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ4144-44-4-4-440000000000−4i4i000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ4244-44-4-4-440000000000−4i4i00000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ4344-4-4-444-40000000400000-40000000002-2-22-222-200000000000000000000
χ4444-4-4-444-40000000400000-4000000000-222-22-2-2200000000000000000000
χ4544-4-4-444-40000000-40000040000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ4644-4-4-444-40000000-4000004000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ474-444-4-44-44-44-400000000000000000000000000000000000000000002-22-2
χ484-444-4-44-44-44-40000000000000000000000000000000000000000000-22-22
χ494-444-4-44-4-44-4400000000000000000000000000000000000000000002i−2i−2i2i
χ504-444-4-44-4-44-440000000000000000000000000000000000000000000−2i2i2i−2i
χ514-44-4-44-444-4-44000000000000000000000000000000000002-22-200000000
χ524-44-4-44-444-4-4400000000000000000000000000000000000-22-2200000000
χ534-44-4-44-44-444-4000000000000000000000000000000000002i−2i−2i2i00000000
χ544-44-4-44-44-444-400000000000000000000000000000000000−2i2i2i−2i00000000
χ554-4-4-44-444000000004-4000000000004-40000000000000000000000000000
χ564-4-4-44-444000000004-400000000000-440000000000000000000000000000
χ574-4-4-44-44400000000-44000000004-40000000000000000000000000000000
χ584-4-4-44-44400000000-4400000000-440000000000000000000000000000000
χ598-8-8888-8-8000000000000000000000000000000000000000000000000000

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