Finite Group Databasebeta

← Group #267656

Character table — Group #267656

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444888888888888888161616161616161616161616161616161616161632
order12222244444444444224444488888888444444448888888888884
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111-1-11
χ4111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1
χ51111111111111111111-1-11-1-111-1-111111-1-1-11-1111-11-111-1-1-1-11-1-1
χ61111111111111111111-1-11-1-111-1-1-1-1-1-1-11-1-1-11-1-11-1-1111-1-111-111
χ71111111111111111111-1-11-1-1-1-1111111-11-1-1-1111-11-11-1-111-1-1-11-1
χ81111111111111111111-1-11-1-1-1-111-1-1-1-11-1-1-11-1-1-1-111-1-1-111111-11
χ911111111111111-1-11-1-111-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1
χ1011111111111111-1-11-1-111-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11
χ1111111111111111-1-11-1-111-111-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1-1
χ1211111111111111-1-11-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1111
χ1311111111111111-1-11-1-1-1-1-1-1-111-1-11111-1111-11-1-11-11-1-1-111-1-11-11
χ1411111111111111-1-11-1-1-1-1-1-1-111-1-1-1-1-1-11-1111-1111-1-11-1-11111-11-1
χ1511111111111111-1-11-1-1-1-1-1-1-1-1-11111111-1111-1-1-1-11-1111-1-1-1-1-111
χ1611111111111111-1-11-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1111-111-111-1-1111-1-1
χ1722222222-222-2-2-200-200220-2-22222000000000000-2-200000000000
χ1822222222-222-2-2-200-200220-2-2-2-2-2-20000000000002200000000000
χ1922222222-222-2-2-200-200-2-202222-2-2000000000000-2200000000000
χ2022222222-222-2-2-200-200-2-2022-2-2220000000000002-200000000000
χ21222222-2-22-2-22-2-2222-2-22-222-200000000002-200000000000000000
χ22222222-2-22-2-22-2-2222-2-2-222-220000000000-2200000000000000000
χ23222222-2-22-2-22-2-2-2-22222-2-22-20000000000-2200000000000000000
χ24222222-2-22-2-22-2-2-2-2222-22-2-2200000000002-200000000000000000
χ25222222-2-2-2-2-2-22200-2002-20-22000000000000000000002i−2i2i−2i00000
χ26222222-2-2-2-2-2-22200-2002-20-2200000000000000000000−2i2i−2i2i00000
χ27222222-2-2-2-2-2-22200-200-2202-2000000000000000000002i−2i−2i2i00000
χ28222222-2-2-2-2-2-22200-200-2202-200000000000000000000−2i2i2i−2i00000
χ292222-2-22-222-222-222-22-200-2000000000002000-200000-2000000020
χ302222-2-22-222-222-222-22-200-200000000000-200020000020000000-20
χ312222-2-22-222-222-2-2-2-2-22002000000000002000-20000020000000-20
χ322222-2-22-222-222-2-2-2-2-2200200000000000-2000200000-2000000020
χ332222-2-2-222-222-2222-2-2200-200000000002000-200000-20000000200
χ342222-2-2-222-222-2222-2-2200-20000000000-200020000020000000-200
χ352222-2-2-222-222-22-2-2-22-200200000000002000-20000020000000-200
χ362222-2-2-222-222-22-2-2-22-20020000000000-2000200000-20000000200
χ374444-4-44-4-44-4-4-44004000000000000000000000000000000000000
χ384444-4-4-44-4-44-44-4004000000000000000000000000000000000000
χ394-44-40000-4004004i−4i0000000000002i2i−2i−2i0000002-20000000000000
χ404-44-40000-4004004i−4i000000000000−2i−2i2i2i000000-220000000000000
χ414-44-40000-400400−4i4i0000000000002i2i−2i−2i000000-220000000000000
χ424-44-40000-400400−4i4i000000000000−2i−2i2i2i0000002-20000000000000
χ434-4-444-4440-4-4000000000000000000000000000000000000022−22000
χ444-4-444-4440-4-40000000000000000000000000000000000000−2222000
χ454-4-444-4-4-4044000000000000000002i2−2i22i2−2i2000000000000000000000
χ464-4-444-4-4-404400000000000000000−2i22i2−2i22i2000000000000000000000
χ474-4-44-444-40-4400000000000004i−4i000000000000000000000000000
χ484-4-44-444-40-440000000000000−4i4i000000000000000000000000000
χ494-4-44-44-4404-40000000000000004i−4i0000000000000000000000000
χ504-4-44-44-4404-4000000000000000−4i4i0000000000000000000000000
χ5188-8-800000000000000000000000022−22−2222000000000000000000000
χ5288-8-8000000000000000000000000−222222−22000000000000000000000
χ538-88-80000800-800000000000000000000000000000000000000000

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