Finite Group Databasebeta

← Group #309957

Character table — Group #309957

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11-1-111-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11111111-1-1-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111111-1-1-111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-111-1-1-1-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-11111111-1-111-1
χ17222222222-222-2-22-2-22222-20000-2-2000022000022-2-200000000-200000000000000
χ18222222222-222-2-22-2-22222-20000-2-20000-2-20000-2-22200000000200000000000000
χ19222222222-222-2-22-2-2-2-2-2-2-20000220000220000-2-22200000000-200000000000000
χ20222222222-222-2-22-2-2-2-2-2-2-20000220000-2-2000022-2-200000000200000000000000
χ2122222222-22-2-222-22-20000-2222200222200-2-2-2-200000000000000000-2000000000
χ2222222222-22-2-222-22-20000-2222200-2-2-2-20022-2-2000000000000000002000000000
χ2322222222-22-2-222-22-20000-2-2-2-2-20022-2-200-2-222000000000000000002000000000
χ2422222222-22-2-222-22-20000-2-2-2-2-200-2-22200222200000000000000000-2000000000
χ25222-2-2-2-22-202-20020022-2-2022−2−20000002i−2i002−22i−2i0022−2−2i2i2−i2−i200000000i2−i200000
χ26222-2-2-2-22-202-20020022-2-2022−2−2000000−2i2i002−2−2i2i0022−2−2−i2−i2i2i200000000−i2i200000
χ27222-2-2-2-22-202-20020022-2-20−2−2220000002i−2i00−222i−2i00−2−222−i2−i2i2i200000000−i2i200000
χ28222-2-2-2-22-202-20020022-2-20−2−222000000−2i2i00−22−2i2i00−2−222i2i2−i2−i200000000i2−i200000
χ29222-2-2-2-22-202-200200-2-222022−2−20000002i−2i002−2−2i2i00−2−222−i2−i2i2i200000000i2−i200000
χ30222-2-2-2-22-202-200200-2-222022−2−2000000−2i2i002−22i−2i00−2−222i2i2−i2−i200000000−i2i200000
χ31222-2-2-2-22-202-200200-2-2220−2−2220000002i−2i00−22−2i2i0022−2−2i2i2−i2−i200000000−i2i200000
χ32222-2-2-2-22-202-200200-2-2220−2−222000000−2i2i00−222i−2i0022−2−2−i2−i2i2i200000000i2−i200000
χ332-22-22-22-222-2-2-2-22222i−2i2i−2i-200002i−2i2i−2i00002i−2i000000000000000002-20000000000
χ342-22-22-22-222-2-2-2-22222i−2i2i−2i-200002i−2i−2i2i0000−2i2i00000000000000000-220000000000
χ352-22-22-22-222-2-2-2-2222−2i2i−2i2i-20000−2i2i2i−2i00002i−2i00000000000000000-220000000000
χ362-22-22-22-222-2-2-2-2222−2i2i−2i2i-20000−2i2i−2i2i0000−2i2i000000000000000002-20000000000
χ372-22-22-22-22-2-2-2222-2-22i−2i2i−2i20000−2i2i00000000000000000000000000002i−2i002-2000
χ382-22-22-22-22-2-2-2222-2-22i−2i2i−2i20000−2i2i0000000000000000000000000000−2i2i00-22000
χ392-22-22-22-22-2-2-2222-2-2−2i2i−2i2i200002i−2i00000000000000000000000000002i−2i00-22000
χ402-22-22-22-22-2-2-2222-2-2−2i2i−2i2i200002i−2i0000000000000000000000000000−2i2i002-2000
χ412-22-22-22-2-2222-2-2-22-2000020000002i−2i0000−2i2i0000002-22-2000002i−2i000000000000
χ422-22-22-22-2-2222-2-2-22-2000020000002i−2i0000−2i2i000000-22-2200000−2i2i000000000000
χ432-22-22-22-2-2222-2-2-22-200002000000−2i2i00002i−2i0000002-22-200000−2i2i000000000000
χ442-22-22-22-2-2222-2-2-22-200002000000−2i2i00002i−2i000000-22-22000002i−2i000000000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-4-4440-4400-400000002222−22−220000000000−2222000000000000000000000000000
χ47444-4-4-4-4440-4400-40000000−22−222222000000000022−22000000000000000000000000000
χ4844-444-4-4-40000000000000022−2222−220000000000000022−2200002-22-2000000000000000
χ4944-444-4-4-40000000000000022−2222−2200000000000000−22220000-22-22000000000000000
χ5044-444-4-4-400000000000000−2222−22220000000000000022−220000-22-22000000000000000
χ5144-444-4-4-400000000000000−2222−222200000000000000−222200002-22-2000000000000000
χ5244-4-4-444-404004-40-40000004-4-44000000000000000000000000000000000000000
χ5344-4-4-444-404004-40-4000000-444-4000000000000000000000000000000000000000
χ5444-4-4-444-40-400-44040000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ5544-4-4-444-40-400-4404000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ564-444-44-4-4404-400-400000000000000000000000000022−22−22220000000000000000000
χ574-444-44-4-4404-400-4000000000000000000000000000−222222−220000000000000000000
χ584-444-44-4-4-40-44004004i−4i−4i4i00000000000000000000000000000000000000000000
χ594-444-44-4-4-40-4400400−4i4i4i−4i00000000000000000000000000000000000000000000
χ604-44-44-44-4-4-44444-4-440000-40000000000000000000000000000000000000000000
χ614-4-44-4-4440400-440-4000000000000004i−4i000000000000000000000000000000000
χ624-4-44-4-4440400-440-400000000000000−4i4i000000000000000000000000000000000
χ634-4-44-4-4440-4004-404000000000000000000000000000000000000000000000022−220
χ644-4-44-4-4440-4004-4040000000000000000000000000000000000000000000000−22220
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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