Finite Group Databasebeta

← Group #72237576

Character table — Group #72237576

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11222222244888888888888816161616161616161616161632323232323232323232323232323232323232323232
order1222222222222222222244442224444444444444444444444488888888
χ11111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-11-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-11-1-11-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-11-1-11-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-111-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-111-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-22222-2-2-2-2200200-2-200002-200000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-2-200-200220000-2200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-22222200200-2-20000-2200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222-200-2002200002-200000000000000000000
χ21222222222-2-2-222-2-22-22-22-22-20020020000-2-200002-20000000000000000
χ22222222222-2-2-222-2-22-22-22-22-200-200-20000220000-220000000000000000
χ23222222222-2-2-222-2-2-22-22-22-220020020000-2-20000-220000000000000000
χ24222222222-2-2-222-2-2-22-22-22-2200-200-200002200002-20000000000000000
χ25222222222-2-2-2-2-2222-22-2-22-2202002000-2-200002-2000000000000000000
χ26222222222-2-2-2-2-2222-22-2-22-220-200-2000220000-22000000000000000000
χ27222222222-2-2-2-2-222-22-222-22-202002000-2-20000-22000000000000000000
χ28222222222-2-2-2-2-222-22-222-22-20-200-20002200002-2000000000000000000
χ2944444-4-4-4-400000000000040-4000000000000000000000000002i−2i2i−2i0000
χ3044444-4-4-4-400000000000040-400000000000000000000000000−2i2i−2i2i0000
χ3144444-4-4-4-4000000000000-404000000000000000000000000002-2-220000
χ3244444-4-4-4-4000000000000-40400000000000000000000000000-222-20000
χ33444-4-444-4-40000000000040-400000000000000000000000000000002i−2i2i−2i
χ34444-4-444-4-40000000000040-40000000000000000000000000000000−2i2i−2i2i
χ35444-4-444-4-400000000000-40400000000000000000000000000000002-2-22
χ36444-4-444-4-400000000000-4040000000000000000000000000000000-222-2
χ37444-4-4-4-44444-4000000000000400-4000000000000000000000000000000
χ38444-4-4-4-44444-4000000000000-4004000000000000000000000000000000
χ39444-4-4-4-444-4-440000000000000000004-400000000000000000000000000
χ40444-4-4-4-444-4-44000000000000000000-4400000000000000000000000000
χ4144-44-44-44-40000000040-4000000000000000000000000002i−2i2i−2i00000000
χ4244-44-44-44-40000000040-400000000000000000000000000−2i2i−2i2i00000000
χ4344-44-44-44-400000000-404000000000000000000000000002-2-2200000000
χ4444-44-44-44-400000000-40400000000000000000000000000-222-200000000
χ4544-44-4-44-440004-4000000000000000000004-40000000000000000000000
χ4644-44-4-44-440004-400000000000000000000-440000000000000000000000
χ4744-44-4-44-44000-44000000000000400-40000000000000000000000000000
χ4844-44-4-44-44000-44000000000000-40040000000000000000000000000000
χ4944-4-444-4-44000004-400000000000000004-4000000000000000000000000
χ5044-4-444-4-44000004-40000000000000000-44000000000000000000000000
χ5144-4-444-4-4400000-44000000000400-400000000000000000000000000000
χ5244-4-444-4-4400000-44000000000-400400000000000000000000000000000
χ5344-4-44-444-4000000040-4000000000000000000000002i−2i2i−2i000000000000
χ5444-4-44-444-4000000040-400000000000000000000000−2i2i−2i2i000000000000
χ5544-4-44-444-40000000-404000000000000000000000002-2-22000000000000
χ5644-4-44-444-40000000-40400000000000000000000000-222-2000000000000
χ5716-1600000008-800000000000000000000000000000000000000000000000
χ5816-160000000-8800000000000000000000000000000000000000000000000

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