Finite Group Databasebeta

← Group #257920

Character table — Group #257920

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444424444444488888888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1
χ3111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-11-111-1-11-1-111-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-11-1-1-1-11111
χ51111111111111111111111111-1-111-1-11111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1111111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-11111-1-1-1-1
χ91111111111111111-1-1-1-1-1-111-1111111-1-11111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-111-1111111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-111-1-1-111-1-111
χ111111111111111111-1-1-1-1-1-111-111-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-1-111-1-1-1-111
χ121111111111111111-1-1-1-1-1-111-111-1-11111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-111111-1-111
χ141111111111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-1-1111-1-111-1-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-111111-1-1-1-1-1-111
χ172222222222-2-222-2-222-2-222-2-2-2002200220000000000000000-20-20000000000000
χ182222222222-2-222-2-222-2-222-2-2-200-2-200-2-200000000000000002020000000000000
χ192222222222-2-222-2-2-2-222-2-2-2-22002200-2-2000000000000000020-20000000000000
χ202222222222-2-222-2-2-2-222-2-2-2-2200-2-200220000000000000000-2020000000000000
χ2122222222-2-222-2-2222222-2-2-2-2-22200-2-20000000000000000000200000-200000000
χ2222222222-2-222-2-2222222-2-2-2-2-2-2-200220000000000000000000-200000200000000
χ2322222222-2-222-2-222-2-2-2-222-2-222200-2-20000000000000000000-200000200000000
χ2422222222-2-222-2-222-2-2-2-222-2-22-2-200220000000000000000000200000-200000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2222000000000000000000000000000002-202-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-222200000000000000000000000000000-220-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222-2000000000000000000000000000002-20-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222222-200000000000000000000000000000-2202-2000000
χ29222-2-2-22-22-2-2-22-2220000002-202i−2i002i−2i00000022-2-20000000000000000002i−2i0000
χ30222-2-2-22-22-2-2-22-2220000002-202i−2i002i−2i000000-2-222000000000000000000−2i2i0000
χ31222-2-2-22-22-2-2-22-2220000002-20−2i2i00−2i2i00000022-2-2000000000000000000−2i2i0000
χ32222-2-2-22-22-2-2-22-2220000002-20−2i2i00−2i2i000000-2-2220000000000000000002i−2i0000
χ33222-2-2-22-2-22-2-2-2222000000-2202i−2i00−2i2i0022-2-20000000000000002i−2i00000000000
χ34222-2-2-22-2-22-2-2-2222000000-2202i−2i00−2i2i00-2-222000000000000000−2i2i00000000000
χ35222-2-2-22-2-22-2-2-2222000000-220−2i2i002i−2i0022-2-2000000000000000−2i2i00000000000
χ36222-2-2-22-2-22-2-2-2222000000-220−2i2i002i−2i00-2-2220000000000000002i−2i00000000000
χ3722-22-2-2-22-22002-2002i−2i002i−2i000002-2002i−2i2−22−2i2−i2i2−i222−2−2i2i2−i2−i20000000000000000
χ3822-22-2-2-22-22002-2002i−2i002i−2i000002-2002i−2i−22−22−i2i2−i2i2−2−222−i2−i2i2i20000000000000000
χ3922-22-2-2-22-22002-2002i−2i002i−2i00000-2200−2i2i2−22−2i2−i2i2−i2−2−222−i2−i2i2i20000000000000000
χ4022-22-2-2-22-22002-2002i−2i002i−2i00000-2200−2i2i−22−22−i2i2−i2i222−2−2i2i2−i2−i20000000000000000
χ4122-22-2-2-22-22002-200−2i2i00−2i2i000002-200−2i2i2−22−2−i2i2−i2i222−2−2−i2−i2i2i20000000000000000
χ4222-22-2-2-22-22002-200−2i2i00−2i2i000002-200−2i2i−22−22i2−i2i2−i2−2−222i2i2−i2−i20000000000000000
χ4322-22-2-2-22-22002-200−2i2i00−2i2i00000-22002i−2i2−22−2−i2i2−i2i2−2−222i2i2−i2−i20000000000000000
χ4422-22-2-2-22-22002-200−2i2i00−2i2i00000-22002i−2i−22−22i2−i2i2−i222−2−2−i2−i2i2i20000000000000000
χ45444-4-4-44-44-4444-4-4-4000000-4400000000000000000000000000000000000000000
χ46444-4-4-44-4-4444-44-4-40000004-400000000000000000000000000000000000000000
χ4744-44-4-4-444-400-44004i−4i00−4i4i0000000000000000000000000000000000000000000
χ4844-44-4-4-444-400-4400−4i4i004i−4i0000000000000000000000000000000000000000000
χ4944-4-444-4-44400-4-4000000000000000000022−22−22220000000000000000000000000000
χ5044-4-444-4-44400-4-40000000000000000000−222222−220000000000000000000000000000
χ5144-4-444-4-4-4-40044000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ5244-4-444-4-4-4-4004400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ534-44-44-4-4400000000004i−4i0000000000000000000002-22-22i−2i2i−2i0000000000000000
χ544-44-44-4-4400000000004i−4i000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ554-44-44-4-440000000000−4i4i0000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ564-44-44-4-440000000000−4i4i000000000000000000000-22-222i−2i2i−2i0000000000000000
χ574-4-444-44-4004-4004-4000000000000000000000000000000000000000000000002i2−2i2
χ584-4-444-44-4004-4004-400000000000000000000000000000000000000000000000−2i22i2
χ594-4-444-44-400-4400-440000000000000000000000000000000000000000000002i2−2i200
χ604-4-444-44-400-4400-44000000000000000000000000000000000000000000000−2i22i200
χ614-4-4-4-4444004-400-44000000000000000000000000022−22−222200000000000000000000
χ624-4-4-4-4444004-400-440000000000000000000000000−222222−2200000000000000000000
χ634-4-4-4-444400-44004-40000000000000000000000000000022−22−22220000000000000000
χ644-4-4-4-444400-44004-400000000000000000000000000000−222222−220000000000000000
χ658-888-88-8-8000000000000000000000000000000000000000000000000000000000

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