Finite Group DatabasebetaFinite Group Databasebeta| order | 4336 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic271 |
| Sylow | C271 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D271 |
| commutator | C2×C271 | C2×C4 |
| Fitting, prime radical | C23×C271 | C2 |
| socle, cosocle | C22×C271 | C22 |
| hypercenter | C23 | D271 |
| hypocenter | C271 | C22⋊C4 |
| LCS | G ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C22 ◁ C23 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2168 |
Polycyclic presentation:
2^4,271|a^2=d,b^a=bc,e^a=e^2701090 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4336, 18);