Finite Group Databasebeta

← Group #176108

Character table — Group #176108

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444424444422244444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-11-1-1-1-111-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111-1-11-1-1-11-11-1-11-1-111111-1-1-1-11111-1-1-1-1
χ61111111111111111111-1-11-1-1-11-11-1-11-1-1-1-11-1-11111-1-1-1-11111
χ71111111111111111111-1-11-1-1-1-11-1-11-11111-111-1-1-1-1-1-1-1-11111
χ81111111111111111111-1-11-1-1-1-11-1-11-111-1-1-1-1-111111111-1-1-1-1
χ9111111111-1-11-1-11111-111-1-1-1-111111-1-1-111-1-1-111-1-111-1-111-1-1
χ10111111111-1-11-1-11111-111-1-1-1-111111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111-1-11-1-11111-111-1-1-1-1-1-1-11-1111111-1-111-1-1-1-111-1-111
χ12111111111-1-11-1-11111-111-1-1-1-1-1-1-11-1111-1-1111-1-11111-1-111-1-1
χ13111111111-1-11-1-11111-1-1-1-11111-11-1-1-11111-1-1-1-1-11111-1-1-1-111
χ14111111111-1-11-1-11111-1-1-1-11111-11-1-1-111-1-1-11111-1-1-1-11111-1-1
χ15111111111-1-11-1-11111-1-1-1-1111-11-1-111-1-1111-1-1-1-111-1-11111-1-1
χ16111111111-1-11-1-11111-1-1-1-1111-11-1-111-1-1-1-111111-1-111-1-1-1-111
χ1722222222222-2-2-2-22-2-2222-2-2-22000-2000000000000000000000
χ1822222222222-2-2-2-22-2-22-2-2-222-20002000000000000000000000
χ19222222222-2-2-222-22-2-2-222222-2000-2000000000000000000000
χ20222222222-2-2-222-22-2-2-2-2-22-2-220002000000000000000000000
χ2122222222-2222-2-2-2-22-2-200200020-200-20000200000000000000
χ2222222222-2222-2-2-2-22-2-2002000-2020020000-200000000000000
χ2322222222-222-2222-2-22-200-20000200-202-200000000000000000
χ2422222222-222-2222-2-22-200-20000-20020-2200000000000000000
χ2522222222-2-2-2222-2-22-2200-200020-20020000-200000000000000
χ2622222222-2-2-2222-2-22-2200-2000-20200-20000200000000000000
χ2722222222-2-2-2-2-2-22-2-2220020000200-20-2200000000000000000
χ2822222222-2-2-2-2-2-22-2-2220020000-200202-200000000000000000
χ294444-4-4-4-44000000-40004-400000000000000000000000000000
χ304444-4-4-4-44000000-4000-4400000000000000000000000000000
χ314444-4-4-4-4-400000040000004i−4i00000000000000000000000000
χ324444-4-4-4-4-40000004000000−4i4i00000000000000000000000000
χ3344-4-444-4-400004-400000000000000000002i−2i02i−2i000000000000
χ3444-4-444-4-400004-40000000000000000000−2i2i0−2i2i000000000000
χ3544-4-444-4-40000-4400000000000000000002i−2i0−2i2i000000000000
χ3644-4-444-4-40000-440000000000000000000−2i2i02i−2i000000000000
χ374-44-44-44-404i−4i00000000000000000000000000000002-22i−2i0000
χ384-44-44-44-404i−4i0000000000000000000000000000000-22−2i2i0000
χ394-44-44-44-40−4i4i00000000000000000000000000000002-2−2i2i0000
χ404-44-44-44-40−4i4i0000000000000000000000000000000-222i−2i0000
χ414-44-4-44-44000000400-400000000000000000000002i2−2i200000000
χ424-44-4-44-44000000400-40000000000000000000000−2i22i200000000
χ434-44-4-44-44000000-40040000000000000000000022−220000000000
χ444-44-4-44-44000000-400400000000000000000000−22220000000000
χ454-4-444-4-4400040000-4000000000000000000000000000002i2−2i200
χ464-4-444-4-4400040000-400000000000000000000000000000−2i22i200
χ474-4-444-4-44000-400004000000000000000000000000000000022−22
χ484-4-444-4-44000-4000040000000000000000000000000000000−2222
χ4988-8-8-8-888000000000000000000000000000000000000000000
χ508-8-88-888-8000000000000000000000000000000000000000000

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