Finite Group Databasebeta

← Group #178151

Character table — Group #178151

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444444444422224444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-11-1-1-11-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-11-1-1-11-1-1-11111-1-1-1-11111
χ51111111111111111111-1-11-1-11-1111-1-111-1-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111111-1-11-1-11-1-1-11-1-111-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111-1-11-1-1-1111-11-1-1-11-1111-1-1-1-1-1-1-1-11111
χ81111111111111111111-1-11-1-1-11-1-1-11-1-1-11-11-1-111111111-1-1-1-1
χ91111111111-1-1-1-11111-111-1-1-111111-11-1-1-1-11-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-11111-111-1-1-111-1-11-11-1-1-1-1111-1-111-1-111-1-111
χ111111111111-1-1-1-11111-111-1-1-1-1-111-111111-1-1-1-1-1-11111-1-1-1-111
χ121111111111-1-1-1-11111-111-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-1
χ131111111111-1-1-1-11111-1-1-1-1111-11111-1-1-111-1-1-111-1-1-1-111-1-111
χ141111111111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-111-111-1-11111-1-111-1-1
χ151111111111-1-1-1-11111-1-1-1-111-1111-1-1-111-111-1-1-1-111-1-11111-1-1
χ161111111111-1-1-1-11111-1-1-1-111-11-1-1-1-1-111-1111111-1-111-1-1-1-111
χ17222222222-222-2-2-2-22-2200-20002000-200020-200000000000000
χ18222222222-222-2-2-2-22-2200-2000-20002000-20200000000000000
χ19222222222-2-2-222-2-22-2-200200020002000-20-200000000000000
χ20222222222-2-2-222-2-22-2-2002000-2000-200020200000000000000
χ2122222222-222222-2-2-22-222-2-2-2000000-20002000000000000000
χ2222222222-222222-2-2-22-2-2-2-2220000002000-2000000000000000
χ2322222222-22-2-2-2-2-2-2-22222222000000-2000-2000000000000000
χ2422222222-22-2-2-2-2-2-2-222-2-22-2-200000020002000000000000000
χ2522222222-2-222-2-222-2-2-2002002000-200-2200000000000000000
χ2622222222-2-222-2-222-2-2-200200-20002002-200000000000000000
χ2722222222-2-2-2-22222-2-2200-2002000-2002-200000000000000000
χ2822222222-2-2-2-22222-2-2200-200-2000200-2200000000000000000
χ294444-4-4-4-440000000-400000000000000000000022−220000000000
χ304444-4-4-4-440000000-4000000000000000000000−22220000000000
χ314444-4-4-4-4-400000004000000000000000000000002i2−2i200000000
χ324444-4-4-4-4-40000000400000000000000000000000−2i22i200000000
χ3344-4-44-44-400004i−4i0000000000002-2000000002i−2i000000000000
χ3444-4-44-44-400004i−4i000000000000-2200000000−2i2i000000000000
χ3544-4-44-44-40000−4i4i0000000000002-200000000−2i2i000000000000
χ3644-4-44-44-40000−4i4i000000000000-22000000002i−2i000000000000
χ374-44-444-4-4004i−4i0000000000000000000000000000002-22i−2i0000
χ384-44-444-4-4004i−4i000000000000000000000000000000-22−2i2i0000
χ394-44-444-4-400−4i4i0000000000000000000000000000002-2−2i2i0000
χ404-44-444-4-400−4i4i000000000000000000000000000000-222i−2i0000
χ414-44-4-4-4440000004-40000000000000000000000000000000022−22
χ424-44-4-4-4440000004-400000000000000000000000000000000−2222
χ434-44-4-4-444000000-4400000000000000000000000000000022−2200
χ444-44-4-4-444000000-44000000000000000000000000000000−222200
χ454-4-444-4-44040000000-400004i−4i00000000000000000000000000
χ464-4-444-4-44040000000-40000−4i4i00000000000000000000000000
χ474-4-444-4-440-40000000404-400000000000000000000000000000
χ484-4-444-4-440-4000000040-4400000000000000000000000000000
χ4988-8-8-88-88000000000000000000000000000000000000000000
χ508-8-88-888-8000000000000000000000000000000000000000000

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