Finite Group Databasebeta

← Group #72238451

Character table — Group #72238451

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1122244888888161616161616161616161616323232323232323264646464646464646464646464646464128128128128
order12222222222442222224444442244444444444444888888884888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111-1-111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-111-1-1111-1-1-1-1-1-111111111-1-1-1-1
χ511111111111-1-11-1-1-11-111-11-1-1-1111111-11-1-1-1ii−i−iiiii−i−i−i−i1-1i−i
χ611111111111-1-11-1-1-11-111-11-1-1-1111111-11-1-1-1−i−iii−i−i−i−iiiii1-1−ii
χ711111111111-1-11-1-1-11-111-11-1-1-1-1-111-1-1-11-111ii−i−i−i−i−i−iiiii-11i−i
χ811111111111-1-11-1-1-11-111-11-1-1-1-1-111-1-1-11-111−i−iiiiiii−i−i−i−i-11−ii
χ911111111-1-1111-1-1-1-11-11111-1-11111-111-1-11-1-1ii−i−iii−i−iii−i−i-11−ii
χ1011111111-1-1111-1-1-1-11-11111-1-11111-111-1-11-1-1−i−iii−i−iii−i−iii-11i−i
χ1111111111-1-1111-1-1-1-11-11111-1-11-1-11-1-1-1-1-1111ii−i−i−i−iii−i−iii1-1−ii
χ1211111111-1-1111-1-1-1-11-11111-1-11-1-11-1-1-1-1-1111−i−iiiii−i−iii−i−i1-1i−i
χ1311111111-1-11-1-1-11111111-1111-1111-1111-1-111111111-1-1-1-111-1-1-1-1
χ1411111111-1-11-1-1-11111111-1111-1111-1111-1-111-1-1-1-1-1-11111-1-1-1-111
χ1511111111-1-11-1-1-11111111-1111-1-1-11-1-1-11-1-1-1-11111-1-11111-1-111-1-1
χ1611111111-1-11-1-1-11111111-1111-1-1-11-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1111111
χ1722222222002000222-22220-2-2-2000-2000-200000000002i−2i2i−2i000000
χ1822222222002000222-22220-2-2-2000-2000-20000000000−2i2i−2i2i000000
χ192222222200200022-2-2-2-2-20-2-2-200020002000000002i−2i00002i−2i0000
χ202222222200200022-2-2-2-2-20-2-2-20002000200000000−2i2i0000−2i2i0000
χ2122222222002000-2-22-22-2-20-2220002000-2000000002-20000-220000
χ2222222222002000-2-22-22-2-20-2220002000-200000000-2200002-20000
χ2322222222002000-2-2-2-2-2220-222000-2000200000000002-2-22000000
χ2422222222002000-2-2-2-2-2220-222000-200020000000000-222-2000000
χ252222222222222222-22-2-2-22222200-2200-2-2-2000000000000000000
χ2622222222222-2-22-2-2222-2-2-22-2-2-200-22002-22000000000000000000
χ2722222222-2-2222-2-2-2222-2-222-2-2200-2-20022-2000000000000000000
χ2822222222-2-22-2-2-222-22-2-2-2-2222-200-2-200-222000000000000000000
χ294444444-400-4440000-40004400-4000000000000000000000000000
χ304444444-400-4-4-40000-4000-44004000000000000000000000000000
χ314444444-444-400400040000-4000000-400000000000000000000000
χ324444444-4-4-4-400-400040000-4000000400000000000000000000000
χ3344444-4-4-40040000000000004-402200-2-20002-20000000000000000
χ3444444-4-4-40040000000000004-40-2-20022000-220000000000000000
χ3544444-4-4-4004000000000000-4402200-2-2000-220000000000000000
χ3644444-4-4-4004000000000000-440-2-200220002-20000000000000000
χ3788888-8-8800-8000000000000000000000000000000000000000000
χ38888-8-80000000000040-40000000000000000002i−2i2i−2i000000000000
χ39888-8-80000000000040-4000000000000000000−2i2i−2i2i000000000000
χ40888-8-800000000000-4040000000000000000002-2-22000000000000
χ41888-8-800000000000-404000000000000000000-222-2000000000000
χ4288-88-8000000000000004-40000000004-4000000000000000000000
χ4388-88-8000000000000004-4000000000-44000000000000000000000
χ4488-88-800000000000000-44000004-40000000000000000000000000
χ4588-88-800000000000000-4400000-440000000000000000000000000
χ4688-8-8800044044-44-400000-40000000000000000000000000000000
χ4788-8-88000440-4-4-4-440000040000000000000000000000000000000
χ4888-8-88000-4-40444-4400000-40000000000000000000000000000000
χ4988-8-88000-4-40-4-444-40000040000000000000000000000000000000
χ5016-160008-800008-80000000000000000000000000000000000000000
χ5116-160008-80000-880000000000000000000000000000000000000000
χ5216-16000-8808-80000000000000000000000000000000000000000000
χ5316-16000-880-880000000000000000000000000000000000000000000

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