Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C127 · Schur multiplier (H2) = C29 |
| direct product | C4×H(5,𝔽2)×C127 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C127 | C24 |
| commutator | C2 | C24×C4×C127 |
| Frattini, cosocle | C22 | C25×C127 |
| socle | C22×C127 | C25 |
| prime radical | C2×H(5,𝔽2)×C127 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C127 ◁ G | |
1660 conjugacy classes of subgroups.
8636 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#8316, C127×#8318, C127×#17438, … |
| maximal normal subgroup of | C127×#8316, C127×#8318, C127×#17438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 2161);