Finite Group Databasebeta

← Group #72338784

Character table — Group #72338784

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1122244888888161616161616161616161616323232323232323264646464646464646464646464646464128128128128
order12222222222222222222444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-11-1-111-1-1-1-111111111-1-1-1-1
χ511111111111111111-1-11-1-11111-1-11111111-1-1111111-1-111-1-1-1-1-1-1
χ611111111111111111-1-11-1-11111-1-11111111-1-1-1-1-1-1-1-111-1-111-1-111
χ711111111111111111-1-11-1-11111-1-1-1-1-1-11-1-1-1-11111-1-111-1-11111-1-1
χ811111111111111111-1-11-1-11111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-11111
χ911111111-1-11-1-111-1-11-1-11-111-111-11111-1-1-11-1ii−i−ii−ii−ii−ii−i1-1i−i
χ1011111111-1-11-1-111-1-11-1-11-111-111-11111-1-1-11-1−i−iii−ii−ii−ii−ii1-1−ii
χ1111111111-1-11-1-111-1-11-1-11-111-111-1-1-1-1-1-1111-1ii−i−i−ii−ii−ii−ii-11i−i
χ1211111111-1-11-1-111-1-11-1-11-111-111-1-1-1-1-1-1111-1−i−iiii−ii−ii−ii−i-11−ii
χ1311111111-1-11-1-111-1-1-11-1-1111-11-111111-1-1-1-11ii−i−ii−i−iii−i−ii-11−ii
χ1411111111-1-11-1-111-1-1-11-1-1111-11-111111-1-1-1-11−i−iii−iii−i−iii−i-11i−i
χ1511111111-1-11-1-111-1-1-11-1-1111-11-11-1-1-1-1-111-11ii−i−i−iii−i−iii−i1-1−ii
χ1611111111-1-11-1-111-1-1-11-1-1111-11-11-1-1-1-1-111-11−i−iiii−i−iii−i−ii1-1i−i
χ172222222222222222200-200-2-2-2-2000000-200000000002i−2i00−2i2i0000
χ182222222222222222200-200-2-2-2-2000000-20000000000−2i2i002i−2i0000
χ1922222222222-2-2-2-22-200-200-2-2-220000002000000002i−2i00−2i2i000000
χ2022222222222-2-2-2-22-200-200-2-2-22000000200000000−2i2i002i−2i000000
χ2122222222222-2-2-2-22-222222222-2220000-200-2-20000000000000000
χ2222222222222-2-2-2-22-2-2-22-2-2222-2-2-20000-200220000000000000000
χ2322222222-2-2222-2-2-2200200-2-222000000-2000000002200-2-2000000
χ2422222222-2-2222-2-2-2200200-2-222000000-200000000-2-20022000000
χ2522222222-2-2222-2-2-222-2-22-222-2-22-20000200-220000000000000000
χ2622222222-2-2222-2-2-22-22-2-2222-2-2-2200002002-20000000000000000
χ2722222222-2-22-2-222-2-200200-2-22-2000000200000000002200-2-20000
χ2822222222-2-22-2-222-2-200200-2-22-200000020000000000-2-200220000
χ294444444-400-40000000040000-400022-2-202-2000000000000000000
χ304444444-400-40000000040000-4000-2-2220-22000000000000000000
χ314444444-400-400000000-40000400022-2-20-22000000000000000000
χ324444444-400-400000000-400004000-2-22202-2000000000000000000
χ3344444-4-4-4004000000040044-4000-40000000000000000000000000
χ3444444-4-4-40040000000-400-44-400040000000000000000000000000
χ3544444-4-4-400400000040040-4400-400000000000000000000000000
χ3644444-4-4-4004000000-400-40-4400400000000000000000000000000
χ3788888-8-8800-8000000000000000000000000000000000000000000
χ38888-8-8000000004-40000000000000004i−4i000000000000000000000
χ39888-8-8000000004-4000000000000000−4i4i000000000000000000000
χ40888-8-800000000-4400000000000004i−4i00000000000000000000000
χ41888-8-800000000-440000000000000−4i4i00000000000000000000000
χ4288-88-800000044000-4000000000000000000002-22-2000000000000
χ4388-88-800000044000-400000000000000000000-22-22000000000000
χ4488-88-8000000-4-40004000000000000000000002i−2i−2i2i000000000000
χ4588-88-8000000-4-4000400000000000000000000−2i2i2i−2i000000000000
χ4688-8-880004400000-40440-4-40000000000000000000000000000000
χ4788-8-880004400000-40-4-40440000000000000000000000000000000
χ4888-8-88000-4-400000404-40-440000000000000000000000000000000
χ4988-8-88000-4-40000040-4404-40000000000000000000000000000000
χ5016-160008-800008-80000000000000000000000000000000000000000
χ5116-160008-80000-880000000000000000000000000000000000000000
χ5216-16000-8808-80000000000000000000000000000000000000000000
χ5316-16000-880-880000000000000000000000000000000000000000000

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