Finite Group Databasebeta

← Group #308102

Character table — Group #308102

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11-1-111-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-111-1-1-111-1-11
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-111-1-1-1-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-11-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-11111-1-1111-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1111111-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-1-11111-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-111-1-11111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-1-1-1-1111-1-1-1-11
χ172222222222-22-2-2-2200002222-2-200002222002200-2-2000000-2-200000000-2000000000000
χ182222222222-22-2-2-2200002222-2-20000-2-2-2-200-2-200-2-200000022000000002000000000000
χ192222222222-22-2-2-220000-2-2-2-2-2-20000222200-2-20022000000-2-2000000002000000000000
χ202222222222-22-2-2-220000-2-2-2-2-2-20000-2-2-2-2002200220000002200000000-2000000000000
χ2122222222-2-22-2222-222220000-2-2222200002200-2-2000000-2-200000000000000000-200000
χ2222222222-2-22-2222-222220000-2-2-2-2-2-20000-2-200-2-20000002200000000000000000200000
χ2322222222-2-22-2222-2-2-2-2-20000-2-222220000-2-20022000000-2-200000000000000000200000
χ2422222222-2-22-2222-2-2-2-2-20000-2-2-2-2-2-200002200220000002200000000000000000-200000
χ25222-2-2-22-2222-2-22-2-222-2-200002-20000000000002-20022-2-20000000000000002-200000000
χ26222-2-2-22-2222-2-22-2-222-2-200002-20000000000002-200-2-222000000000000000-2200000000
χ27222-2-2-22-2222-2-22-2-2-2-22200002-2000000000000-220022-2-2000000000000000-2200000000
χ28222-2-2-22-2222-2-22-2-2-2-22200002-2000000000000-2200-2-2220000000000000002-200000000
χ29222-2-2-22-2-2-222-22-2222-2-22i2i−2i−2i-22000000000000-222i−2i0000000000000000000002i−2i000000
χ30222-2-2-22-2-2-222-22-2222-2-2−2i−2i2i2i-22000000000000-22−2i2i000000000000000000000−2i2i000000
χ31222-2-2-22-2-2-222-22-22-2-2222i2i−2i−2i-220000000000002-22i−2i000000000000000000000−2i2i000000
χ32222-2-2-22-2-2-222-22-22-2-222−2i−2i2i2i-220000000000002-2−2i2i0000000000000000000002i−2i000000
χ33222-2-2-22-2-2-2-222-22200002i2i−2i−2i2-200000000000000−2i2i0000000022-2-2000002i−2i0000000000
χ34222-2-2-22-2-2-2-222-22200002i2i−2i−2i2-200000000000000−2i2i00000000-2-22200000−2i2i0000000000
χ35222-2-2-22-2-2-2-222-2220000−2i−2i2i2i2-2000000000000002i−2i0000000022-2-200000−2i2i0000000000
χ36222-2-2-22-2-2-2-222-2220000−2i−2i2i2i2-2000000000000002i−2i00000000-2-222000002i−2i0000000000
χ3722-2-222-2-22-20-2000200002-22-20022−2−22i2i−2i−2i002i−2i00002−22−22−2000000i2i2−i2−i200000000i2−i2000
χ3822-2-222-2-22-20-2000200002-22-20022−2−2−2i−2i2i2i00−2i2i00002−22−22−2000000−i2−i2i2i200000000−i2i2000
χ3922-2-222-2-22-20-2000200002-22-200−2−2222i2i−2i−2i002i−2i0000−22−22−22000000−i2−i2i2i200000000−i2i2000
χ4022-2-222-2-22-20-2000200002-22-200−2−222−2i−2i2i2i00−2i2i0000−22−22−22000000i2i2−i2−i200000000i2−i2000
χ4122-2-222-2-22-20-200020000-22-220022−2−22i2i−2i−2i00−2i2i0000−22−222−2000000i2i2−i2−i200000000−i2i2000
χ4222-2-222-2-22-20-200020000-22-220022−2−2−2i−2i2i2i002i−2i0000−22−222−2000000−i2−i2i2i200000000i2−i2000
χ4322-2-222-2-22-20-200020000-22-2200−2−2222i2i−2i−2i00−2i2i00002−22−2−22000000−i2−i2i2i200000000i2−i2000
χ4422-2-222-2-22-20-200020000-22-2200−2−222−2i−2i2i2i002i−2i00002−22−2−22000000i2i2−i2−i200000000−i2i2000
χ452-22-22-2-220020-2-2202-22-20000002i−2i2i−2ii2−i2i2−i22i−2i000000000000i2−i2i2−i2i2−i22−22−200000000002−20
χ462-22-22-2-220020-2-2202-22-20000002i−2i2i−2i−i2i2−i2i22i−2i000000000000−i2i2−i2i2−i2i2−22−220000000000−220
χ472-22-22-2-220020-2-2202-22-2000000−2i2i−2i2ii2−i2i2−i2−2i2i000000000000i2−i2i2−i2i2−i2−22−220000000000−220
χ482-22-22-2-220020-2-2202-22-2000000−2i2i−2i2i−i2i2−i2i2−2i2i000000000000−i2i2−i2i2−i2i22−22−200000000002−20
χ492-22-22-2-220020-2-220-22-220000002i−2i2i−2ii2−i2i2−i2−2i2i000000000000i2−i2−i2i2−i2i22−22−20000000000−220
χ502-22-22-2-220020-2-220-22-220000002i−2i2i−2i−i2i2−i2i2−2i2i000000000000−i2i2i2−i2i2−i2−22−2200000000002−20
χ512-22-22-2-220020-2-220-22-22000000−2i2i−2i2ii2−i2i2−i22i−2i000000000000i2−i2−i2i2−i2i2−22−2200000000002−20
χ522-22-22-2-220020-2-220-22-22000000−2i2i−2i2i−i2i2−i2i22i−2i000000000000−i2i2i2−i2i2−i22−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-44-444-4-44-44-400000000-44000000000000000000000000000000000000000000000
χ5544-44-4-4-444-404000-40000000000000000000000000022−22−22220000000000000000000000000
χ5644-44-4-4-444-404000-400000000000000000000000000−222222−220000000000000000000000000
χ5744-44-4-4-44-440-4000400004i−4i−4i4i00000000000000000000000000000000000000000000000
χ5844-44-4-4-44-440-400040000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ5944-4-444-4-4-4404000-400000000002222−22−220000000000000000−222200000000000000000000000
χ6044-4-444-4-4-4404000-40000000000−22−222222000000000000000022−2200000000000000000000000
χ614-444-44-4-400404-4-404-4-44000000000000000000000000000000000000000000000000000
χ624-444-44-4-400404-4-40-444-4000000000000000000000000000000000000000000000000000
χ634-444-44-4-400-40-444000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ644-444-44-4-400-40-44400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ654-44-44-4-4400-4044-40000000000000002i2−2i22i2−2i200000000000000−2i22i2000000000000000000000
χ664-44-44-4-4400-4044-4000000000000000−2i22i2−2i22i2000000000000002i2−2i2000000000000000000000
χ674-4-444-44-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ684-4-444-44-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ694-4-444-44-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ704-4-444-44-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ718-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000

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