Finite Group Databasebeta

← Group #251131

Character table — Group #251131

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444888888888888888161616161616161616161616161616161616161632
order12222244444422444224444444888888224444444448888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1111-1-1-1-1-11-111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111111-1-11-1-1-1-1-111-1-1-1-1-1-1-1111
χ4111111111111111111111111-1-1-1-1-1-1-1-11-111-1-1111-1-1-11-1-1111-1-1-1
χ5111111111111111111-1-111-1-111-1-11111-11-1-11111-111-1-1-1-111-1-1-1-1
χ6111111111111111111-1-111-1-111-1-1-1-1-1-1-111-111-1-11-1-1-11-1-1-1-11111
χ7111111111111111111-1-111-1-1-1-1111111-1-11-1-1-1-1-11111111-1-11-1-1-1
χ8111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-11-11111-1111
χ9111111111111-1-1111-111-1-11111111111-11-1-1-1-1-1-1-1-1-111-1-111111-1
χ10111111111111-1-1111-111-1-1111111-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-11
χ11111111111111-1-1111-111-1-111-1-1-1-11111-1-11-111111-1-1-1-111-1-1-111-1
χ12111111111111-1-1111-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1111111-1-11
χ13111111111111-1-1111-1-1-1-1-1-1-111-1-111111111-1-1-1-11-1-1-1-11111-1-1-11
χ14111111111111-1-1111-1-1-1-1-1-1-111-1-1-1-1-1-111-11-1-111-111-1111-1-1111-1
χ15111111111111-1-1111-1-1-1-1-1-1-1-1-11111111-1-111111-1-1-111-1-1-1-11-1-11
χ16111111111111-1-1111-1-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-11111-1-1-111-111-1
χ1722222222-222-200-2-2-202-2002-2222200000-2000000000-2000000000
χ1822222222-222-200-2-2-202-2002-2-2-2-2-20000020000000002000000000
χ1922222222-222-200-2-2-20-2200-2222-2-200000-20000000002000000000
χ2022222222-222-200-2-2-20-2200-22-2-222000002000000000-2000000000
χ21222222-2-22-2-2222-2-22200-2-200000000000000002-200000002-20000
χ22222222-2-22-2-2222-2-22200-2-20000000000000000-220000000-220000
χ23222222-2-22-2-22-2-2-2-22-2002200000000000000002-20000000-220000
χ24222222-2-22-2-22-2-2-2-22-200220000000000000000-2200000002-20000
χ252222-2-22-222-2222-22-2-2002-2000000000000200000-2000-200002000
χ262222-2-22-222-2222-22-2-2002-2000000000000-200000200020000-2000
χ272222-2-22-222-22-2-2-22-2200-22000000000000200000-200020000-2000
χ282222-2-22-222-22-2-2-22-2200-22000000000000-2000002000-200002000
χ292222-2-2-222-222222-2-2-22-2-22-2200000000200-200000000000000000
χ302222-2-2-222-222222-2-2-2-22-222-200000000-200200000000000000000
χ312222-2-2-222-222-2-22-2-222-22-2-2200000000-200200000000000000000
χ322222-2-2-222-222-2-22-2-22-222-22-200000000200-200000000000000000
χ332222-2-2-22-2-22-200-22202200-2-20000000000002-200000002-2000000
χ342222-2-2-22-2-22-200-22202200-2-2000000000000-220000000-22000000
χ352222-2-2-22-2-22-200-2220-2-200220000000000002-20000000-22000000
χ362222-2-2-22-2-22-200-2220-2-20022000000000000-2200000002-2000000
χ37444444-4-4-4-4-4-40044-4000000000000000000000000000000000000
χ384444-4-44-4-44-4-4004-44000000000000000000000000000000000000
χ394-44-40000400-44-4000000000000002i2i−2i−2i0000000002i−2i0000000000
χ404-44-40000400-44-400000000000000−2i−2i2i2i000000000−2i2i0000000000
χ414-44-40000400-4-44000000000000002i2i−2i−2i000000000−2i2i0000000000
χ424-44-40000400-4-4400000000000000−2i−2i2i2i0000000002i−2i0000000000
χ434-4-444-44-40-44000000000000000002i2−2i22i2−2i2000000000000000000000
χ444-4-444-44-40-4400000000000000000−2i22i2−2i22i2000000000000000000000
χ454-4-444-4-4404-400000000000004i−4i000000000000000000000000000
χ464-4-444-4-4404-40000000000000−4i4i000000000000000000000000000
χ474-4-44-44440-4-40000000000000004i−4i0000000000000000000000000
χ484-4-44-44440-4-4000000000000000−4i4i0000000000000000000000000
χ494-4-44-44-4-404400000000000000000000000000000000000000022−220
χ504-4-44-44-4-4044000000000000000000000000000000000000000−22220
χ5188-8-800000000000000000000000022−22−2222000000000000000000000
χ5288-8-8000000000000000000000000−222222−22000000000000000000000
χ538-88-80000-800800000000000000000000000000000000000000000

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