Finite Group Databasebeta

← Group #72238693

Character table — Group #72238693

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111222222444488888888888888888888161616161616161616161616161616163232323232323232323264646464
order1222222222224422222444444444444444222222224444444444444488884444
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1111111-1-1-1-11-11111-1-1-1-111-1-1
χ6111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1111111-1-1-1-11-1-1-1-1-11111-1-111
χ7111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-111-1-1-111111-1-1-1-1-1-111
χ8111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-111-1-1-11-1-1-1-1111111-1-1
χ91111111111-1-111-111111-1111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−iii−i−ii−ii−i
χ101111111111-1-111-111111-1111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iii−i−iii−ii−ii
χ111111111111-1-111-111111-11111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111ii−i−iii−i−i−ii−ii
χ121111111111-1-111-111111-11111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111−i−iii−i−iiii−ii−i
χ131111111111-1-111-1-1-1-1-11-1-1-1-1-11111-1-1-1-1-111-1-111-1-11111-1-111-11ii−i−i−i−iiii−i−ii
χ141111111111-1-111-1-1-1-1-11-1-1-1-1-11111-1-1-1-1-111-1-111-1-11111-1-111-11−i−iiiii−i−i−iii−i
χ151111111111-1-111-1-1-1-1-11-1-1-1-1-1-1-1-1-11111-11111-1-1-1-111-1-111111-1ii−i−i−i−iii−iii−i
χ161111111111-1-111-1-1-1-1-11-1-1-1-1-1-1-1-1-11111-11111-1-1-1-111-1-111111-1−i−iiiii−i−ii−i−ii
χ17222222222222222222222-2-2-2-2000000002220000-2-2-2-20000-2-200000000000000
χ18222222222222222-2-2-2-2222222000000002-2-20000-2-2-2-200002200000000000000
χ19222222222222-2-220000-2-2000000002222-20000222-22-200-2-2000-2000000000000
χ20222222222222-2-220000-2-200000000-2-2-2-2-20000-2-22-22-200220002000000000000
χ21222222222222-2-220000-2-2000022220000-2002200-22-22-2-20000-20000000000000
χ22222222222222-2-220000-2-20000-2-2-2-20000-200-2-200-22-2222000020000000000000
χ232222222222-2-222-222222-2-2-2-2-200000000-2-2-2000022-2-200002200000000000000
χ242222222222-2-222-2-2-2-2-22-2222200000000-222000022-2-20000-2-200000000000000
χ252222222222-2-2-2-2-20000-2200000000222220000-2-2-222-200-2-20002000000000000
χ262222222222-2-2-2-2-20000-2200000000-2-2-2-22000022-222-20022000-2000000000000
χ272222222222-2-2-2-2-20000-22000022220000200-2-2002-2-22-2-2000020000000000000
χ282222222222-2-2-2-2-20000-220000-2-2-2-2000020022002-2-22220000-20000000000000
χ2944444-4-4-44-44400-400000000000000000000000000000000000002-22-200000000
χ3044444-4-4-44-44400-40000000000000000000000000000000000000-22-2200000000
χ3144444-4-4-44-4-4-400400000000000000000000000000000000000002i−2i−2i2i00000000
χ3244444-4-4-44-4-4-40040000000000000000000000000000000000000−2i2i2i−2i00000000
χ334444-444-4-4-400000000004000000000000-400000000000000000000002i−2i2i−2i0000
χ344444-444-4-4-400000000004000000000000-40000000000000000000000−2i2i−2i2i0000
χ354444-444-4-4-40000000000-4000000000000400000000000000000000002-2-220000
χ364444-444-4-4-40000000000-400000000000040000000000000000000000-222-20000
χ374444-4-4-44-440044044-4-4-400000000000000000000000000000000000000000000
χ384444-4-4-44-4400440-4-444-400000000000000000000000000000000000000000000
χ394444-4-4-44-4400-4-4000004044-4-4000000000000000000000000000000000000000
χ404444-4-4-44-4400-4-40000040-4-444000000000000000000000000000000000000000
χ414-44-4000-404004-40004-400000022-2-222-2-2000000000002-22-20000000000000000
χ424-44-4000-404004-40004-4000000-2-222-2-22200000000000-22-220000000000000000
χ434-44-4000-404004-4000-4400000022-2-2-2-222000000000002-2-220000000000000000
χ444-44-4000-404004-4000-44000000-2-22222-2-200000000000-222-20000000000000000
χ454-44-4000-40400-4404-40000000022-2-222-2-200000000000-22-220000000000000000
χ464-44-4000-40400-4404-400000000-2-222-2-222000000000002-22-20000000000000000
χ474-44-4000-40400-440-440000000022-2-2-2-22200000000000-222-20000000000000000
χ484-44-4000-40400-440-4400000000-2-22222-2-2000000000002-2-220000000000000000
χ494-4-44-4000404-40000000002-22-22-22-22-22-20002-22-2000000002-200000000000000
χ504-4-44-4000404-40000000002-22-2-22-22-22-22000-22-22000000002-200000000000000
χ514-4-44-4000404-4000000000-22-222-22-2-22-220002-2-2200000000-2200000000000000
χ524-4-44-4000404-4000000000-22-22-22-222-22-2000-222-200000000-2200000000000000
χ534-4-44-400040-440000000002-22-22-22-22-22-2000-22-2200000000-2200000000000000
χ544-4-44-400040-440000000002-22-2-22-22-22-220002-22-200000000-2200000000000000
χ554-4-44-400040-44000000000-22-222-22-2-22-22000-222-2000000002-200000000000000
χ564-4-44-400040-44000000000-22-22-22-222-22-20002-2-22000000002-200000000000000
χ5788-8-808-800000000000000000000004-4-440000000000000000000000000000000
χ5888-8-808-80000000000000000000000-444-40000000000000000000000000000000
χ5988-8-80-880000000000000000004-4-4400000000000000000000000000000000000
χ6088-8-80-88000000000000000000-444-400000000000000000000000000000000000
χ618-88-800080-80000000000000000000000004-40000000000000000000000000000
χ628-88-800080-8000000000000000000000000-440000000000000000000000000000
χ638-8-888000-80000000000004-4-44000000000000000000000000000000000000000
χ648-8-888000-8000000000000-444-4000000000000000000000000000000000000000

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