Finite Group Databasebeta

← Group #308128

Character table — Group #308128

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-11-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111-1-1-11111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1111-1-1111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111-111-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111111111-1-1-1-1-1-1-1-11
χ172222222222-22-2-2-222222-20000-22222000000-2-22200000000-2-200000000-2000000000000
χ182222222222-22-2-2-222222-20000-2-2-2-2-2000000-2-2-2-20000000022000000002000000000000
χ192222222222-22-2-2-22-2-2-2-2-20000-2222200000022-2-200000000-2-2000000002000000000000
χ202222222222-22-2-2-22-2-2-2-2-20000-2-2-2-2-20000002222000000002200000000-2000000000000
χ2122222222-2-22-2222-20000-22222-200002222-2-2000022-2-200000000000000000-2000000000
χ2222222222-2-22-2222-20000-22222-20000-2-2-2-2-2-20000-2-222000000000000000002000000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-200002222220000-2-2-2-2000000000000000002000000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-20000-2-2-2-2220000222200000000000000000-2000000000
χ25222-2-2-22-2222-2-22-2-20000222-2-2-2000000002-20000000022-2-2000000000000002-20000000
χ26222-2-2-22-2222-2-22-2-20000222-2-2-2000000002-200000000-2-22200000000000000-220000000
χ27222-2-2-22-2222-2-22-2-200002-2-222-200000000-220000000022-2-200000000000000-220000000
χ28222-2-2-22-2222-2-22-2-200002-2-222-200000000-2200000000-2-222000000000000002-20000000
χ29222-2-2-22-2-2-222-22-222i2i−2i−2i-222-2-2200000000-222i−2i0000000000000000000002i−2i0000000000
χ30222-2-2-22-2-2-222-22-222i2i−2i−2i-2-2-2222000000002-22i−2i000000000000000000000−2i2i0000000000
χ31222-2-2-22-2-2-222-22-22−2i−2i2i2i-222-2-2200000000-22−2i2i000000000000000000000−2i2i0000000000
χ32222-2-2-22-2-2-222-22-22−2i−2i2i2i-2-2-2222000000002-2−2i2i0000000000000000000002i−2i0000000000
χ33222-2-2-22-2-2-2-222-2222i2i−2i−2i20000-20000000000−2i2i00000000000022-2-200000000002i−2i00000
χ34222-2-2-22-2-2-2-222-2222i2i−2i−2i20000-20000000000−2i2i000000000000-2-2220000000000−2i2i00000
χ35222-2-2-22-2-2-2-222-222−2i−2i2i2i20000-200000000002i−2i00000000000022-2-20000000000−2i2i00000
χ36222-2-2-22-2-2-2-222-222−2i−2i2i2i20000-200000000002i−2i000000000000-2-22200000000002i−2i00000
χ3722-22-2-2-222-20-200022-22-20000002i2i−2i−2i22−2−200002i−2i002−22−22−2000000i2i2−i2−i200000000i2−i2000
χ3822-22-2-2-222-20-200022-22-20000002i2i−2i−2i−2−22200002i−2i00−22−22−22000000−i2−i2i2i200000000−i2i2000
χ3922-22-2-2-222-20-200022-22-2000000−2i−2i2i2i22−2−20000−2i2i002−22−22−2000000−i2−i2i2i200000000−i2i2000
χ4022-22-2-2-222-20-200022-22-2000000−2i−2i2i2i−2−2220000−2i2i00−22−22−22000000i2i2−i2−i200000000i2−i2000
χ4122-22-2-2-222-20-20002-22-220000002i2i−2i−2i22−2−20000−2i2i002−2−22−22000000i2i2−i2−i200000000−i2i2000
χ4222-22-2-2-222-20-20002-22-220000002i2i−2i−2i−2−2220000−2i2i00−222−22−2000000−i2−i2i2i200000000i2−i2000
χ4322-22-2-2-222-20-20002-22-22000000−2i−2i2i2i22−2−200002i−2i002−2−22−22000000−i2−i2i2i200000000i2−i2000
χ4422-22-2-2-222-20-20002-22-22000000−2i−2i2i2i−2−22200002i−2i00−222−22−2000000i2i2−i2−i200000000−i2i2000
χ452-2222-2-2-200-20-2220000002i−2i2i−2i02−22−22-22-20000002i−2i0000002−2i2−i2i2−i22−22−20000000000i2−i20
χ462-2222-2-2-200-20-2220000002i−2i2i−2i02−22−2-22-22000000−2i2i0000002−2i2−i2i2−i2−22−220000000000−i2i20
χ472-2222-2-2-200-20-2220000002i−2i2i−2i0−22−222-22-20000002i−2i000000−22−i2i2−i2i2−22−220000000000−i2i20
χ482-2222-2-2-200-20-2220000002i−2i2i−2i0−22−22-22-22000000−2i2i000000−22−i2i2−i2i22−22−20000000000i2−i20
χ492-2222-2-2-200-20-222000000−2i2i−2i2i02−22−22-22-2000000−2i2i0000002−2−i2i2−i2i22−22−20000000000−i2i20
χ502-2222-2-2-200-20-222000000−2i2i−2i2i02−22−2-22-220000002i−2i0000002−2−i2i2−i2i2−22−220000000000i2−i20
χ512-2222-2-2-200-20-222000000−2i2i−2i2i0−22−222-22-2000000−2i2i000000−22i2−i2i2−i2−22−220000000000i2−i20
χ522-2222-2-2-200-20-222000000−2i2i−2i2i0−22−22-22-220000002i−2i000000−22i2−i2i2−i22−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-44-444-4-44-44-40000-400004000000000000000000000000000000000000000000000
χ5544-44-4-4-44-4404000-4000000000000002222−22−2200000000−2222000000000000000000000000000
χ5644-44-4-4-44-4404000-400000000000000−22−2222220000000022−22000000000000000000000000000
χ5744-4-444-4-44-404000-4000000000000000000000000000022−22−222200000000000000000000000
χ5844-4-444-4-44-404000-40000000000000000000000000000−222222−2200000000000000000000000
χ5944-4-444-4-4-440-400044i−4i−4i4i000000000000000000000000000000000000000000000000000
χ6044-4-444-4-4-440-40004−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ614-4444-4-4-400404-4-40000000000022−2222−22000000000000000000−2222000000000000000000000
χ624-4444-4-4-400404-4-400000000000−2222−222200000000000000000022−22000000000000000000000
χ634-44-4-44-440040-4-44000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ644-44-4-44-440040-4-4400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ654-44-4-44-4400-4044-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ664-44-4-44-4400-4044-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ674-4-44-444-40000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ684-4-44-444-40000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ694-4-44-444-4000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ704-4-44-444-4000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ718-8-8-88-888000000000000000000000000000000000000000000000000000000000000000

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