Finite Group Databasebeta

← Group #272397

Character table — Group #272397

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222222444448888888888888888816161616161616161616161616161616163232
order12222244444444444222224444888888884444488888888888848
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111-1-11-1-111-1-111111-111-1-1111-1-1-1-1-1-1-1-11-1
χ4111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-111-1-11111-11
χ51111111111111111111-1-11111111-1-11111-11-1-11-1-1-1111-1-1-1-111-1-1
χ61111111111111111111-1-111111-1-1-1-1-1-1-1-1-11-1-11-111-1-1-1-1-111-1-111
χ71111111111111111111-1-1-1-11-1-111111111-1-1-1-1-11-1-11-1-11111-1-1-11
χ81111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1111-11111-1-1111-1
χ91111111111111-1-111-1-11111-1111111-1-1-1-11-1-1-1-11-1-1111-1-1-1-1-1-111
χ101111111111111-1-111-1-11111-111-1-11111111-1-1-1-1111-1-1-1-1-11111-1-1
χ111111111111111-1-111-1-111-1-1-1-1-111-1-1-1-1-1-111-1-11-1-1-11-1-11111111-1
χ121111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1111111-1-11-111-11111-1-1-1-1-11
χ131111111111111-1-111-1-1-1-111-11111-1-1-1-1-1-1-1-111-1-1111111111-1-1-1-1
χ141111111111111-1-111-1-1-1-111-111-1-1-1-11111-1-111-1-1-1-1-1-1-111-1-11111
χ151111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-1-111-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1111111-111111-1-1-111-1-111-1-11-1
χ172222222-2-22-2-2222-2-2-2-20000200000000000000000002i−2i00002i−2i00
χ182222222-2-22-2-2222-2-2-2-2000020000000000000000000−2i2i0000−2i2i00
χ192222222-2-22-2-22-2-2-2-2220000-200000000000000000002i−2i0000−2i2i00
χ202222222-2-22-2-22-2-2-2-2220000-20000000000000000000−2i2i00002i−2i00
χ21222222-222-222-200-2-200222-202-200-2-20000-2000020000000000000
χ22222222-222-222-200-2-20022-220-2200220000-20000-20000000000000
χ23222222-222-222-200-2-200-2-22-202-20022000020000-20000000000000
χ24222222-222-222-200-2-200-2-2-220-2200-2-200002000020000000000000
χ252222-2-222-222-2-222-222-20000-200220022-2-200000000-20000000000
χ262222-2-222-222-2-222-222-20000-200-2-200-2-2220000000020000000000
χ272222-2-222-222-2-2-2-2-22-2200002002200-2-22200000000-20000000000
χ282222-2-222-222-2-2-2-2-22-220000200-2-20022-2-20000000020000000000
χ292222-2-22-222-22-2222-2-220022-2-2-2000000000-200200000000000000
χ302222-2-22-222-22-2222-2-2200-2-2-222000000000200-200000000000000
χ312222-2-22-222-22-2-2-22-22-200222-2-2000000000200-200000000000000
χ322222-2-22-222-22-2-2-22-22-200-2-2222000000000-200200000000000000
χ332222-2-2-2-22-2-22200-2200002-20-2200000000002-200000002-2000000
χ342222-2-2-2-22-2-22200-2200002-20-220000000000-220000000-22000000
χ352222-2-2-2-22-2-22200-220000-2202-200000000002-20000000-22000000
χ362222-2-2-2-22-2-22200-220000-2202-20000000000-2200000002-2000000
χ37444444-4-4-4-4-4-4-40044000000000000000000000000000000000000
χ384444-4-4-44-4-44-44004-4000000000000000000000000000000000000
χ3944-4-400-40040004i−4i000000000002i2−2i20022−22000000000000000000000
χ4044-4-400-40040004i−4i00000000000−2i22i200−2222000000000000000000000
χ4144-4-400-4004000−4i4i000000000002i2−2i200−2222000000000000000000000
χ4244-4-400-4004000−4i4i00000000000−2i22i20022−22000000000000000000000
χ434-44-44-40440-4-400000004-400000000000000000000000000000000
χ444-44-44-40440-4-40000000-4400000000000000000000000000000000
χ454-44-44-40-4-40440000000000000000000000000000000000022−220000
χ464-44-44-40-4-404400000000000000000000000000000000000−22220000
χ474-44-4-4404-40-4400000000000000000000000000002i2−2i200000000000
χ484-44-4-4404-40-440000000000000000000000000000−2i22i200000000000
χ494-44-4-440-4404-400000000000000004i−4i00000000000000000000000
χ504-44-4-440-4404-40000000000000000−4i4i00000000000000000000000
χ5188-8-800800-80000000000000000000000000000000000000000000
χ528-8-8800000000000000000000000000004i−4i0000000000000000000
χ538-8-880000000000000000000000000000−4i4i0000000000000000000

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