Finite Group Databasebeta

← Group #289244

Character table — Group #289244

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222222444444488888888888888888816161616161616161616161632323232
order12222244444444488884444888888888888882244888888882488
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-111-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111-1-1-1-111-1-1-1-1111111111111-111-111-1-1-1-1-1-1
χ61111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ71111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ81111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1
χ9111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-11-11-111-11-1-1-1-11-11-1
χ10111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-11-111-111-1-1-1-1-11-11
χ11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-11-11-11-1-111111-1-11
χ12111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-11-11111-111-1
χ13111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-11-11-1-11-1-1-1-111-11-11
χ14111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-11-11-1-11-1-1-1111-11-1
χ15111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-1111-1111-1-1-111-1
χ16111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-11-11-11111-1-11-1-11
χ172222222-22-2-2-22-2-222220000-2-200002i2i−2i−2i0000000000002i−2i000000
χ182222222-22-2-2-22-2-222220000-2-20000−2i−2i2i2i000000000000−2i2i000000
χ192222222-22-2-2-22-2-2-2-2-2-200002200002i2i−2i−2i000000000000−2i2i000000
χ202222222-22-2-2-22-2-2-2-2-2-20000220000−2i−2i2i2i0000000000002i−2i000000
χ21222222-22-2222-2-2-2000022-2-20000002-22-200000000200-200000000
χ22222222-22-2222-2-2-2000022-2-2000000-22-2200000000-200200000000
χ23222222-22-2222-2-2-20000-2-2220000002-22-200000000-200200000000
χ24222222-22-2222-2-2-20000-2-222000000-22-2200000000200-200000000
χ25222222-2-2-2-2-2-2-22200000000002i2i−2i−2i2i−2i−2i2i000000000000002-20000
χ26222222-2-2-2-2-2-2-22200000000002i2i−2i−2i−2i2i2i−2i00000000000000-220000
χ27222222-2-2-2-2-2-2-2220000000000−2i−2i2i2i2i−2i−2i2i00000000000000-220000
χ28222222-2-2-2-2-2-2-2220000000000−2i−2i2i2i−2i2i2i−2i000000000000002-20000
χ292222-2-2222-2-22-22-222-2-200002-200000000000022-2-2000000000000
χ302222-2-2222-2-22-22-222-2-200002-2000000000000-2-222000000000000
χ312222-2-2222-2-22-22-2-2-2220000-220000000000002-2-22000000000000
χ322222-2-2222-2-22-22-2-2-2220000-22000000000000-222-2000000000000
χ332222-2-22-2222-2-2-2222-2-20000-220000000022-2-200000-22000000000
χ342222-2-22-2222-2-2-2222-2-20000-2200000000-2-222000002-2000000000
χ352222-2-22-2222-2-2-22-2-22200002-200000000222200000-2-2000000000
χ362222-2-22-2222-2-2-22-2-22200002-200000000-2-2-2-20000022000000000
χ374444-4-4-44-4-4-444-4400000000000000000000000000000000000000
χ384444-4-4-4-4-444-444-400000000000000000000000000000000000000
χ3944-4-400-404000000004i−4i000000000000002i2−2i222−220000000000000000
χ4044-4-400-404000000004i−4i00000000000000−2i22i2−22220000000000000000
χ4144-4-400-40400000000−4i4i000000000000002i2−2i2−22220000000000000000
χ4244-4-400-40400000000−4i4i00000000000000−2i22i222−220000000000000000
χ434-44-44-40404-4-400000000000002i2−2i22i2−2i2000000000000000000000000
χ444-44-44-40404-4-40000000000000−2i22i2−2i22i2000000000000000000000000
χ454-44-44-40-40-444000000000000022−22−2222000000000000000000000000
χ464-44-44-40-40-4440000000000000−222222−22000000000000000000000000
χ474-44-4-44040-44-40000000004i−4i000000000000000000000000000000
χ484-44-4-44040-44-4000000000−4i4i000000000000000000000000000000
χ494-44-4-440-404-4400000004-400000000000000000000000000000000
χ504-44-4-440-404-440000000-4400000000000000000000000000000000
χ5188-8-80080-800000000000000000000000000000000000000000000
χ528-8-880000000000042−42000000000000000000000000000000000000
χ538-8-8800000000000−4242000000000000000000000000000000000000

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