Finite Group Databasebeta

← Group #278598

Character table — Group #278598

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444444488888888888161616161616161616161616161632323232
order12224444442444444488888824888888888448888888888884488
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-111-1-1-1-1-111-1-11111111-1-1-1-1-1-1-11-11-1
χ6111111111111111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1111-1-1-11111-11-11
χ7111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-1-11-11
χ8111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111-11-1
χ9111111111111-1-11-1-11111111-1-1-1-11-1-1111111-1-11-1-11-1-111-1-111-1-1
χ10111111111111-1-11-1-11111111-1-1-1-11-1-11111-1-1111-1-11-1-1-1-111-1-111
χ11111111111111-1-11-1-11111111-1-1-1-11-1-1-1-1-1-111-1-1-111-11111-1-1-1-111
χ12111111111111-1-11-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111-111-111-1-11111-1-1
χ13111111111111-1-11-1-11-1-1-1-1-1-1-1-111-11111-1-111-1-11-1-1-111-1-1111-1-11
χ14111111111111-1-11-1-11-1-1-1-1-1-1-1-111-11111-1-1-1-1111-1-1-11111-1-1-111-1
χ15111111111111-1-11-1-11-1-1-1-1-1-1-1-111-111-1-11111-1-1-1111-1-1-1-111-111-1
χ16111111111111-1-11-1-11-1-1-1-1-1-1-1-111-111-1-111-1-111-1111-1-111-1-11-1-11
χ172222222-2-22-2-222-2-2-2222-2-2222-2-2-2-2220000000000000000000000
χ182222222-2-22-2-222-2-2-22-2-222-2-22-2222-2-20000000000000000000000
χ192222222-2-22-2-2-2-2-222222-2-222-2222-2-2-20000000000000000000000
χ202222222-2-22-2-2-2-2-2222-2-222-2-2-22-2-22220000000000000000000000
χ2122222-2-2222-2-200200-222-2-2-2-2000020022-2-20000-20020000000000
χ2222222-2-2222-2-200200-222-2-2-2-20000200-2-2220000200-20000000000
χ2322222-2-2222-2-200200-2-2-222220000-20022220000-200-20000000000
χ2422222-2-2222-2-200200-2-2-222220000-200-2-2-2-2000020020000000000
χ2522222-2-2-2-222200-200-22222-2-20000-2000000000002i−2i02i−2i00000000
χ2622222-2-2-2-222200-200-22222-2-20000-200000000000−2i2i0−2i2i00000000
χ2722222-2-2-2-222200-200-2-2-2-2-22200002000000000002i−2i0−2i2i00000000
χ2822222-2-2-2-222200-200-2-2-2-2-2220000200000000000−2i2i02i−2i00000000
χ292222-22222-2-2222-222-2000000-2-20000000002-22-200000000000000
χ302222-22222-2-2222-222-2000000-2-2000000000-22-2200000000000000
χ312222-22222-2-22-2-2-2-2-2-2000000220000000002-2-2200000000000000
χ322222-22222-2-22-2-2-2-2-2-200000022000000000-222-200000000000000
χ332222-222-2-2-22-2222-2-2-2000000-2200000000000000000002i−2i2i−2i0000
χ342222-222-2-2-22-2222-2-2-2000000-220000000000000000000−2i2i−2i2i0000
χ352222-222-2-2-22-2-2-2222-20000002-200000000000000000002i−2i−2i2i0000
χ362222-222-2-2-22-2-2-2222-20000002-20000000000000000000−2i2i2i−2i0000
χ374444-4-4-444-44-400-400400000000000000000000000000000000000
χ384444-4-4-4-4-4-4-4400400400000000000000000000000000000000000
χ394-44-4-40000400000000004i−4i0000000002i2−2i222−22000000000000000000
χ404-44-4-40000400000000004i−4i000000000−2i22i2−2222000000000000000000
χ414-44-4-4000040000000000−4i4i0000000002i2−2i2−2222000000000000000000
χ424-44-4-4000040000000000−4i4i000000000−2i22i222−22000000000000000000
χ434-4-4404-4000000004-402i2−2i2002i2−2i2002i2−2i20000000000000000000000000
χ444-4-4404-4000000004-40−2i22i200−2i22i200−2i22i20000000000000000000000000
χ454-4-4404-400000000-4402i2−2i2002i2−2i200−2i22i20000000000000000000000000
χ464-4-4404-400000000-440−2i22i200−2i22i2002i2−2i20000000000000000000000000
χ474-4-440-44000004i−4i00002i2−2i200−2i22i20000022−220000000000000000000000
χ484-4-440-44000004i−4i0000−2i22i2002i2−2i200000−22220000000000000000000000
χ494-4-440-4400000−4i4i00002i2−2i200−2i22i200000−22220000000000000000000000
χ504-4-440-4400000−4i4i0000−2i22i2002i2−2i20000022−220000000000000000000000
χ5188-8-80008-800000000000000000000000000000000000000000000
χ5288-8-8000-8800000000000000000000000000000000000000000000
χ538-88-880000-80000000000000000000000000000000000000000000

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