Finite Group Databasebeta

← Group #72238429

Character table — Group #72238429

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size1111222222444488888888161616161616161616161616161616161616161616163232323232323232323264646464
order1222222222224422222444224444444444444444444424888888884488
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1
χ4111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11-111111-1-1-1-1-1-111
χ6111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-1111111-1-1
χ7111111111111111-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-111-1-1
χ8111111111111111-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-111
χ9111111111111-1-111111-1-1-11-1111-1-111-1-1-1-1-1-111-1-1-1-1-111ii−i−iii−i−ii−ii−i
χ10111111111111-1-111111-1-1-11-1111-1-111-1-1-1-1-1-111-1-1-1-1-111−i−iii−i−iii−ii−ii
χ11111111111111-1-111111-1-1-11-1-1-11-1-111-1-11111-1-11111-1-1-1ii−i−iii−i−i−ii−ii
χ12111111111111-1-111111-1-1-11-1-1-11-1-111-1-11111-1-11111-1-1-1−i−iii−i−iiii−ii−i
χ13111111111111-1-11-1-1-1-1-1-1-11-111111-1-111-1-1-1-1-1-11111-1-11ii−i−i−i−iii−iii−i
χ14111111111111-1-11-1-1-1-1-1-1-11-111111-1-111-1-1-1-1-1-11111-1-11−i−iiiii−i−ii−i−ii
χ15111111111111-1-11-1-1-1-1-1-1-11-1-1-1111-1-111111111-1-1-1-1-11-1ii−i−i−i−iiii−i−ii
χ16111111111111-1-11-1-1-1-1-1-1-11-1-1-1111-1-111111111-1-1-1-1-11-1−i−iiiii−i−i−iii−i
χ172222222222222222222222-2-200-222-2-2-2-20000000000-200000000000000
χ18222222222222222-2-2-2-2222-2-200-2-2-222220000000000-200000000000000
χ19222222222222-2-222222-2-2-2-2200-2-2-2-2-2220000000000200000000000000
χ20222222222222-2-22-2-2-2-2-2-2-2-2200-22222-2-20000000000200000000000000
χ212222222222-2-222-200002-2-22-222-200000022-2-200000020-2000000000000
χ222222222222-2-222-200002-2-22-2-2-2-2000000-2-222000000202000000000000
χ232222222222-2-222-200002-2-2-2200200000000002222-2-2-2-20000000000000
χ242222222222-2-222-200002-2-2-220020000000000-2-2-2-222-220000000000000
χ252222222222-2-2-2-2-20000-2222222-2000000-2-222000000-20-2000000000000
χ262222222222-2-2-2-2-20000-22222-2-2-200000022-2-2000000-202000000000000
χ272222222222-2-2-2-2-20000-222-2-2002000000000022-2-2222-20000000000000
χ282222222222-2-2-2-2-20000-222-2-20020000000000-2-222-2-2220000000000000
χ2944444-44-4-4-400000000004-400000000000000000000000000002i−2i2i−2i0000
χ3044444-44-4-4-400000000004-40000000000000000000000000000−2i2i−2i2i0000
χ3144444-44-4-4-40000000000-4400000000000000000000000000002-2-220000
χ3244444-44-4-4-40000000000-440000000000000000000000000000-222-20000
χ334444-44-44-4-4004400000-4000000000000000000000000002-22-200000000
χ344444-44-44-4-4004400000-400000000000000000000000000-22-2200000000
χ354444-44-44-4-400-4-4000004000000000000000000000000002i−2i−2i2i00000000
χ364444-44-44-4-400-4-400000400000000000000000000000000−2i2i2i−2i00000000
χ374444-4-4-4-4444400-4000000000000004-4000000000000000000000000000
χ384444-4-4-4-4444400-400000000000000-44000000000000000000000000000
χ394444-4-4-4-444-4-400444-4-4000000000000000000000000000000000000000
χ404444-4-4-4-444-4-4004-4-444000000000000000000000000000000000000000
χ4144-4-4040-400004i−4i02-22-2000002-202i−2i00002i−2i002-22i−2i00000000000000000
χ4244-4-4040-400004i−4i02-22-200000-2202i−2i0000−2i2i00-22−2i2i00000000000000000
χ4344-4-4040-400004i−4i0-22-22000002-20−2i2i00002i−2i00-22−2i2i00000000000000000
χ4444-4-4040-400004i−4i0-22-2200000-220−2i2i0000−2i2i002-22i−2i00000000000000000
χ4544-4-4040-40000−4i4i02-22-2000002-20−2i2i0000−2i2i002-2−2i2i00000000000000000
χ4644-4-4040-40000−4i4i02-22-200000-220−2i2i00002i−2i00-222i−2i00000000000000000
χ4744-4-4040-40000−4i4i0-22-22000002-202i−2i0000−2i2i00-222i−2i00000000000000000
χ4844-4-4040-40000−4i4i0-22-2200000-2202i−2i00002i−2i002-2−2i2i00000000000000000
χ4988-8-80-80800000004-4-44000000000000000000000000000000000000000
χ5088-8-80-8080000000-444-4000000000000000000000000000000000000000
χ518-88-880-800000000000000000000000000004i−4i000000000000000000000
χ528-88-880-80000000000000000000000000000−4i4i000000000000000000000
χ538-88-8-80800000000000000000000000000000000004-4000000000000000
χ548-88-8-8080000000000000000000000000000000000-44000000000000000
χ558-8-8800008-80000000000000000000004-40000000000000000000000000
χ568-8-8800008-8000000000000000000000-440000000000000000000000000
χ578-8-880000-888-80000000000000000000000000000000000000000000000
χ588-8-880000-88-880000000000000000000000000000000000000000000000

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