Finite Group Databasebeta

← Group #168807

Character table — Group #168807

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444442244444444444888888882444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-11-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-111111111-1-1
χ51111111111111111111111-1-11-1-11111-1-1-1-111111111-111-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111
χ71111111111111111111111-1-11-1-1-1-1-1-1111111111111-1-1-11-11-1-1-1-11111-1-1
χ81111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-111
χ911111111-1-1-1-111-1-11-1-111111-1-1-111-1-111-1-11111-1-1-1-1-11-111-111-1-111-1-11-1
χ1011111111-1-1-1-111-1-11-1-111111-1-1-111-1-111-1-1-1-1-1-11111-11-111-1-1-111-1-111-11
χ1111111111-1-1-1-111-1-11-1-111111-1-1-1-1-111-1-1111111-1-1-1-1-1-11-111-1-111-1-1111-1
χ1211111111-1-1-1-111-1-11-1-111111-1-1-1-1-111-1-111-1-1-1-11111-1-11-11111-1-111-1-1-11
χ1311111111-1-1-1-111-1-11-1-1111-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1111-1-1-1-111-11
χ1411111111-1-1-1-111-1-11-1-1111-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-11-1-11111-1-11-1
χ1511111111-1-1-1-111-1-11-1-1111-1-1-111-1-11111-1-11111-1-1-1-11-111-1-1-1-11111-1-1-11
χ1611111111-1-1-1-111-1-11-1-1111-1-1-111-1-11111-1-1-1-1-1-111111-111-1-111-1-1-1-1111-1
χ172222222222222-222-2-2-22-2-200-20022220000000000000-2-20000000000000
χ182222222222222-222-2-2-22-2-200-200-2-2-2-20000000000000220000000000000
χ19222222222222-22-2-2-222-22-200-2000000222200000000000-20-20000000000
χ20222222222222-22-2-2-222-22-200-2000000-2-2-2-2000000000002020000000000
χ21222222222222-2-2-2-22-2-2-2-22222220000000000000000-2000-200000000000
χ22222222222222-2-2-2-22-2-2-2-22-2-22-2-200000000000000002000200000000000
χ2322222222-2-2-2-22-2-2-2-2222-2-20020022-2-20000000000000-220000000000000
χ2422222222-2-2-2-22-2-2-2-2222-2-200200-2-22200000000000002-20000000000000
χ2522222222-2-2-2-2-2222-2-2-2-22-200200000022-2-200000000000-2020000000000
χ2622222222-2-2-2-2-2222-2-2-2-22-2002000000-2-2220000000000020-20000000000
χ2722222222-2-2-2-2-2-222222-2-2222-2-2-200000000000000002000-200000000000
χ2822222222-2-2-2-2-2-222222-2-22-2-2-2220000000000000000-2000200000000000
χ29222-22-2-2-222-2-2-202-2000200000002i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i20000002−22−2000000
χ30222-22-2-2-222-2-2-202-2000200000002i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2000000−22−22000000
χ31222-22-2-2-222-2-2-202-200020000000−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2000000−22−22000000
χ32222-22-2-2-222-2-2-202-200020000000−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i20000002−22−2000000
χ33222-22-2-2-2-2-222-20-22000200000002i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i20000002−2−22000000
χ34222-22-2-2-2-2-222-20-22000200000002i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2000000−222−2000000
χ35222-22-2-2-2-2-222-20-2200020000000−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2000000−222−2000000
χ36222-22-2-2-2-2-222-20-2200020000000−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i20000002−2−22000000
χ372-2-222-2-222-22-2020002-20-200000000002i−2i2i−2i2−22−22−22−20000000000i2−i2i2−i200
χ382-2-222-2-222-22-2020002-20-200000000002i−2i2i−2i−22−22−22−220000000000−i2i2−i2i200
χ392-2-222-2-222-22-2020002-20-20000000000−2i2i−2i2i2−22−22−22−20000000000−i2i2−i2i200
χ402-2-222-2-222-22-2020002-20-20000000000−2i2i−2i2i−22−22−22−220000000000i2−i2i2−i200
χ412-2-222-2-22-22-2202000-220-200000000002i−2i−2i2i2−22−2−22−220000000000i2−i2−i2i200
χ422-2-222-2-22-22-2202000-220-200000000002i−2i−2i2i−22−222−22−20000000000−i2i2i2−i200
χ432-2-222-2-22-22-2202000-220-20000000000−2i2i2i−2i2−22−2−22−220000000000−i2i2i2−i200
χ442-2-222-2-22-22-2202000-220-20000000000−2i2i2i−2i−22−222−22−20000000000i2−i2−i2i200
χ45444-44-4-4-444-4-440-44000-4000000000000000000000000000000000000000
χ46444-44-4-4-4-4-444404-4000-4000000000000000000000000000000000000000
χ4744-4-4-44-440000000040000-40004i−4i00000000000000000000000000000000
χ4844-4-4-44-440000000040000-4000−4i4i00000000000000000000000000000000
χ4944-4-4-44-4400000000-4000044-400000000000000000000000000000000000
χ5044-4-4-44-4400000000-400004-4400000000000000000000000000000000000
χ514-4-444-4-444-44-40-4000-440400000000000000000000000000000000000000
χ524-4-444-4-44-44-440-40004-40400000000000000000000000000000000000000
χ534-4-4-4444-44-4-44000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ544-4-4-4444-44-4-4400000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ554-4-4-4444-4-444-4000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ564-4-4-4444-4-444-400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ5788-88-8-88-8000000000000000000000000000000000000000000000000000
χ588-888-88-8-8000000000000000000000000000000000000000000000000000
χ598-88-8-8-888000000000000000000000000000000000000000000000000000

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