Finite Group Databasebeta

← Group #306413

Character table — Group #306413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222444444888888884444444488888888888888884444444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-11-111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-111111111-11-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-1111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-11111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111-1-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-22-22-22-20000-22222-2000022220000-2-22200-2-2000000000000-2000000000000
χ18222222222-22-22-22-20000-22222-20000-2-2-2-20000-2-2-2-200220000000000002000000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-200002222000022-2-200-2-20000000000002000000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-20000-2-2-2-2000022220022000000000000-2000000000000
χ2122222222-22-22-22-222222-20000-222220000-2-2220000-2-2000000000000000-200000000000
χ2222222222-22-22-22-222222-20000-2-2-2-2-20000-2-2-2-2000022000000000000000200000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-22222000022-2-20000-2-2000000000000000200000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-2-2-2-2-200002222000022000000000000000-200000000000
χ25222-2-22-2-2020-20-20222-2-200000022-2-2i2i2−i2−i2002-2000000i2−i20000i2i2−i2−i2i2i2−i2−i200000000i2−i2000
χ26222-2-22-2-2020-20-20222-2-200000022-2-2−i2−i2i2i2002-2000000−i2i20000−i2−i2i2i2−i2−i2i2i200000000−i2i2000
χ27222-2-22-2-2020-20-20222-2-2000000-2-222i2i2−i2−i200-22000000i2−i20000i2i2−i2−i2−i2−i2i2i200000000−i2i2000
χ28222-2-22-2-2020-20-20222-2-2000000-2-222−i2−i2i2i200-22000000−i2i20000−i2−i2i2i2i2i2−i2−i200000000i2−i2000
χ29222-2-22-2-2020-20-202-2-22200000022-2-2i2i2−i2−i200-22000000i2−i20000−i2−i2i2i2i2i2−i2−i200000000−i2i2000
χ30222-2-22-2-2020-20-202-2-22200000022-2-2−i2−i2i2i200-22000000−i2i20000i2i2−i2−i2−i2−i2i2i200000000i2−i2000
χ31222-2-22-2-2020-20-202-2-222000000-2-222i2i2−i2−i2002-2000000i2−i20000−i2−i2i2i2−i2−i2i2i200000000i2−i2000
χ32222-2-22-2-2020-20-202-2-222000000-2-222−i2−i2i2i2002-2000000−i2i20000i2i2−i2−i2i2i2−i2−i200000000−i2i2000
χ3322-22-2-22-2-202020-200000022-2-20i2−i2i2−i22i−2i2i−2i0000002i−2ii2−i200i2i2−i2−i200002−22−200000000002−20
χ3422-22-2-22-2-202020-200000022-2-20i2−i2i2−i2−2i2i−2i2i000000−2i2ii2−i200i2i2−i2−i20000−22−220000000000−220
χ3522-22-2-22-2-202020-200000022-2-20−i2i2−i2i22i−2i2i−2i0000002i−2i−i2i200−i2−i2i2i20000−22−220000000000−220
χ3622-22-2-22-2-202020-200000022-2-20−i2i2−i2i2−2i2i−2i2i000000−2i2i−i2i200−i2−i2i2i200002−22−200000000002−20
χ3722-22-2-22-2-202020-2000000-2-2220i2−i2i2−i22i−2i2i−2i000000−2i2ii2−i200−i2−i2i2i200002−22−20000000000−220
χ3822-22-2-22-2-202020-2000000-2-2220i2−i2i2−i2−2i2i−2i2i0000002i−2ii2−i200−i2−i2i2i20000−22−2200000000002−20
χ3922-22-2-22-2-202020-2000000-2-2220−i2i2−i2i22i−2i2i−2i000000−2i2i−i2i200i2i2−i2−i20000−22−2200000000002−20
χ4022-22-2-22-2-202020-2000000-2-2220−i2i2−i2i2−2i2i−2i2i0000002i−2i−i2i200i2i2−i2−i200002−22−20000000000−220
χ412-2222-2-2-22-2-222-2-222-22-2-200002000000002-200000000002i−2i2i−2i0000000000002i−2i0000000
χ422-2222-2-2-22-2-222-2-222-22-2-200002000000002-20000000000−2i2i−2i2i000000000000−2i2i0000000
χ432-2222-2-2-22-2-222-2-22-22-22-20000200000000-2200000000002i−2i2i−2i000000000000−2i2i0000000
χ442-2222-2-2-22-2-222-2-22-22-22-20000200000000-220000000000−2i2i−2i2i0000000000002i−2i0000000
χ452-2222-2-2-2-222-2-222-20000-22i−2i2i−2i20000000000002i−2i00000000002-22-200000000002i−2i00000
χ462-2222-2-2-2-222-2-222-20000-22i−2i2i−2i20000000000002i−2i0000000000-22-220000000000−2i2i00000
χ472-2222-2-2-2-222-2-222-20000-2−2i2i−2i2i2000000000000−2i2i00000000002-22-20000000000−2i2i00000
χ482-2222-2-2-2-222-2-222-20000-2−2i2i−2i2i2000000000000−2i2i0000000000-22-2200000000002i−2i00000
χ492-2222-2-2-2-2-222-2-2222-22-222i−2i2i−2i-200000000-2200−2i2i000000000000000000002i−2i000000000
χ502-2222-2-2-2-2-222-2-2222-22-22−2i2i−2i2i-200000000-22002i−2i00000000000000000000−2i2i000000000
χ512-2222-2-2-2-2-222-2-222-22-2222i−2i2i−2i-2000000002-200−2i2i00000000000000000000−2i2i000000000
χ522-2222-2-2-2-2-222-2-222-22-222−2i2i−2i2i-2000000002-2002i−2i000000000000000000002i−2i000000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-44-4-40-404040-4000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ55444-4-44-4-40-404040-400000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ5644-44-4-44-440-40-404000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ5744-44-4-44-440-40-40400000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ5844-4-44-4-440000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ5944-4-44-4-440000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ6044-4-44-4-44000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ6144-4-44-4-44000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ624-4444-4-4-444-4-444-4-4000040000-4000000000000000000000000000000000000000000000
χ634-44-4-4-44404040-40-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ644-44-4-4-44404040-40-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ654-44-4-4-4440-40-404044-4-44000000000000000000000000000000000000000000000000000
χ664-44-4-4-4440-40-40404-444-4000000000000000000000000000000000000000000000000000
χ674-4-44-44-444040-40-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ684-4-44-44-444040-40-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ694-4-44-44-44-40-40404000000000000000000000000000000022−22−2222000000000000000000000
χ704-4-44-44-44-40-404040000000000000000000000000000000−222222−22000000000000000000000
χ718-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000

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