Finite Group Databasebeta

← Group #289259

Character table — Group #289259

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222222444444488888888888888888816161616161616161616161632323232
order12222244444444488888888888888888888882224448888884488
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-111111-1-11-1-111-1-111-1-1-1-1
χ31111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ41111111111111111111111111-1-1-1-1-1-1-1-11111-111-111-1-1-1-1-1-111-1-1
χ5111111111111111111111-1-1-1-111111111-1-1-1-1-111-111-1-11111-1-1-1-1
χ6111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-11111-1-111-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ9111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-111-1-1-11-1-1-11-11-1
χ10111111111111111-1-1-1-1-1-111111111-1-111-1-1-1-11-111-11-1-1-11-1-1-11-11
χ11111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-11111-111-111-1
χ12111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-11-1-11-111-11111-1-11
χ13111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-11-1-11-1111-1-1-1-11-11
χ14111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11-1-1111-11-1-11-11-1
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-111-11-1-11-1111-1-11
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1111-111-1
χ1722222222-2-2-2-22-2-222-2-22-200002i2i−2i−2i0000000000000000002i−2i0000
χ1822222222-2-2-2-22-2-222-2-22-20000−2i−2i2i2i000000000000000000−2i2i0000
χ1922222222-2-2-2-22-2-2-2-222-2200002i2i−2i−2i000000000000000000−2i2i0000
χ2022222222-2-2-2-22-2-2-2-222-220000−2i−2i2i2i0000000000000000002i−2i0000
χ21222222-2-22222-2-2-200000022-2-22-22-200000000200-2000000000000
χ22222222-2-22222-2-2-200000022-2-2-22-2200000000-2002000000000000
χ23222222-2-22222-2-2-2000000-2-2222-22-200000000-2002000000000000
χ24222222-2-22222-2-2-2000000-2-222-22-2200000000200-2000000000000
χ25222222-2-2-2-2-2-2-22200000000002i−2i−2i2i000022-2-20000002i−2i00000000
χ26222222-2-2-2-2-2-2-22200000000002i−2i−2i2i0000-2-222000000−2i2i00000000
χ27222222-2-2-2-2-2-2-2220000000000−2i2i2i−2i000022-2-2000000−2i2i00000000
χ28222222-2-2-2-2-2-2-2220000000000−2i2i2i−2i0000-2-2220000002i−2i00000000
χ292222-2-22222-2-2-22-22222-2-200000000000000000220-2-20000000000
χ302222-2-22222-2-2-22-22222-2-200000000000000000-2-20220000000000
χ312222-2-22222-2-2-22-2-2-2-2-222000000000000000002-20-220000000000
χ322222-2-22222-2-2-22-2-2-2-2-22200000000000000000-2202-20000000000
χ332222-2-222-2-222-2-2222-2-2-220000000022-2-2000000000000-22000000
χ342222-2-222-2-222-2-2222-2-2-2200000000-2-2220000000000002-2000000
χ352222-2-222-2-222-2-22-2-2222-2000000002222000000000000-2-2000000
χ362222-2-222-2-222-2-22-2-2222-200000000-2-2-2-200000000000022000000
χ374444-4-4-4-444-4-44-4400000000000000000000000000000000000000
χ384444-4-4-4-4-4-44444-400000000000000000000000000000000000000
χ394-44-400-440000000004-400000000002i2−2i22i2−2i200000000000000000000
χ404-44-400-440000000004-40000000000−2i22i2−2i22i200000000000000000000
χ414-44-400-44000000000-4400000000002i2−2i2−2i22i200000000000000000000
χ424-44-400-44000000000-440000000000−2i22i22i2−2i200000000000000000000
χ434-4-444-4004-44-400000000000000000000022−2222−220000000000000000
χ444-4-444-4004-44-4000000000000000000000−2222−22220000000000000000
χ454-4-444-400-44-4400000000000000000000022−22−22220000000000000000
χ464-4-444-400-44-44000000000000000000000−222222−220000000000000000
χ474-4-44-44004-4-440000000004-4000000000000000000000000000000
χ484-4-44-44004-4-44000000000-44000000000000000000000000000000
χ494-4-44-4400-444-4000000000004-40000000000000000000000000000
χ504-4-44-4400-444-400000000000-440000000000000000000000000000
χ5188-8-80000000000042−42000000000000000000000000000000000000
χ5288-8-800000000000−4242000000000000000000000000000000000000
χ538-88-8008-8000000000000000000000000000000000000000000000

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