Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C127 · Schur multiplier (H2) = C24×C4 |
| direct product | C127×#1436 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C127 | C23 |
| commutator | C22 | C2×C42×C127 |
| Frattini, cosocle | C24 | C23×C127 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C127 ◁ G | |
612 conjugacy classes of subgroups.
7112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#7215, C127×#8347, C2×C127×#1436, … |
| maximal normal subgroup of | C127×#7215, C127×#8347, C2×C127×#1436, … |
| maximal quotient of | C127×#7554, C127×#7556, C127×#7557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 168);